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Small and large signal modeling of MM-Wave MHEMT devices

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Title:
Small and large signal modeling of MM-Wave MHEMT devices
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Book
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English
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Clausen, William, 1972-
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University of South Florida
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Subjects / Keywords:
gaas
nonlinear
noise
hemt
transistor
Dissertations, Academic -- Electrical Engineering -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Summary:
ABSTRACT This research effort advances millimeter-wave transistor modeling in a current RF/Microwave circuit simulator (Agilent's Advanced Design System-ADS) for small-signal noise and large signal simulations. The device modeled is a metamorphic High Electron Mobility Transistor (mHEMT) supplied by Raytheon RF components. Because of their structure, these new low noise devices are used in this work to test the abilities to accurately model in the sub 0.5dB noise figure territory and to study model prediction into W-band (75-110 GHz). New modeling issues discussed in this thesis involve the effects of noise modeling in relation to the small-signal model parameters. The noise modeling identifies two methods of extraction and how to determine good noise data. Other modeling topics addressed are the use of an advanced nonlinear model, and the ability to optimize for gain compression in the nonlinear model. Several measurement systems were used in the extraction and validation of this modeling effort. They consist of the ATN NP5 noise system, Maury Automated Tuner System, Agilent's IC-CAP, and Gateway's Special. The concept behind using these systems was to construct a complete modeling reference for a transistor and validate it against noise parameter and nonlinear measured data. Since the modeling work for this thesis is built on previous work, one goal has been to bring past USF field-effect transistor (FET) modeling efforts up to date and refine them for future use. The noise measurements were compared to results from Raytheon to validate the USF ATN noise parameter measurement system. Also the IC-CAP modeling system has been validated in measuring the test devices using the Maury load-pull system. Small-signal and noise modeling were accomplished using techniques standardized from several technical papers and prior USF Ph.D. work relative to the model extraction. The IC-CAP modeling software also provided a straightforward platform for large-signal model extraction that is documented in this thesis. Using optimization in ADS, a final nonlinear was created. Measured DC, S-parameter, noise parameters, harmonic power, TOI, load-pull, and efficiency measurements were shown to compare well with model data simulated in ADS. Temperature scaling was also executed using a linear approximation of model values over measured temperatures in the noise model. The results presented show that the models developed illustrate good fitting of the behavior of the mHEMT device.
Thesis:
Thesis (M.S.E.E.)--University of South Florida, 2003.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
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by William Clausen.
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Title from PDF of title page.
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Document formatted into pages; contains 155 pages.

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University of South Florida
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aleph - 001441503
oclc - 54018084
notis - AJM5943
usfldc doi - E14-SFE0000177
usfldc handle - e14.177
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Mass Transfer of Ionic Species in Direct and Reverse Osmosis Processes by Silvana Melania Stefania Ghiu A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Robert P. Carnahan, Ph.D. Marilyn Barger, Ph.D. Venkat R. Bhethanabotla, Ph.D. Kenneth A. Buckle, Ph.D. Robert W. Flynn, Ph.D. Noreen D. Poor, Ph.D. Date of Approval: October 31, 2003 Keywords: RO membranes, nanofiltration, diffusion, Spiegler-Kedem model, Kimura-Sourirajan model, ion hydration Copyright 2003, Silvana M.S. Ghiu

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DEDICATION To my mother who has constantly urged for ex cellence, to my brother who had many answers to my questions throughout my years in school, and to my father who always has been a restless engineer.

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ACKNOWLEDGEMENTS I would like to express my everlasting gratit ude to Dr. Robert Ca rnahan for providing me the ideal environment to carry on this doctoral program. I am very grateful to Dr. Carnahan for ensuring the financial support and for the technical guidelines throughout the years. Dr. Carnahan has had many words of en couragement and appreciation for me, and that kept me going through the difficult moments. He represents the professor I would like one day to become. Very special thanks to Dr. Marilyn Barger for continuous technical advice, and for promptly answering all my anxious emails, while I was jammed in a theory or a research experiment. I am very thankful to Dr. Barg er for proofreading this dissertation and many other technical papers and for setting very high standards for my work. Many thanks to Bob Smith and Tom Gage for manufacturing several components of my experimental apparatus and to Catherin e High for her timely help whenever it was needed. Last but not least, I am grateful to my friends Cola, Danielly, and Maysson for cheering me up and making this effort more bear able. I thank the Calintaru family for giving me a hand when I needed most.

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iTABLE OF CONTENTS LIST OF TABLES iv LIST OF FIGURES vii LIST OF SYMBOLS xi ABSTRACT xvi CHAPTER 1 INTRODUCTION 1 1.1 Importance of the research problem 1 1.2 Research objectives and approach 2 1.3 Dissertation outline 3 CHAPTER 2 RO MEMBRANE FILTRATION: INTRODUCTION AND RELEVANT PREVIOUS RESEARCH 6 2.1. Background information 6 2.1.1 Hyperfiltration membranes 6 2.1.2 Direct and reverse osmosis processes 9 2.1.3 Reverse osmosis models 11 2.1.3.1 Spiegler-Kedem model 12 2.1.3.2 Kimura-Sourirajan model (Preferential sorptioncapillary flow model) 15 2.1.4 Concentration polarization 17 2.2 Previous research on the transpor t parameters in hyperfiltration membranes 18 2.2.1 Salt and water transport in direct osmosis 18 2.2.2 Salt and water transport in reverse osmosis 21 2.2.2.1 Diffusion and convection in hyperfiltration membranes 22 2.2.2.2 Comparison of RO models 23 2.2.3 Factors controlling the selectivity of salts in hyperfiltration membranes 24 2.2.4 Conclusions on the previous relevant research 25 CHAPTER 3 METHODOLOGY 27 3.1 Chemicals preparation 27 3.2 Instrumentation 28 3.3 Direct osmosis experiments 29 3.3.1 Diffusion cell operation 30 3.3.2 Determination of pure water permeation A' 33 3.4 Reverse osmosis flat sheet membrane experiments 34 3.4.1 RO flat sheet membrane operation 36 3.5 Reverse osmosis spiral wound membrane experiments 37

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ii 3.5.1 Spiral wound membrane operation 40 CHAPTER 4 RESULTS 41 4.1 Salt and water transport in the direct osmosis experiments 42 4.1.1 Salt transport in the direct osmosis experiments 42 4.1.2 Pure water transport in the direct osmosis experiments 49 4.2 Salt and water transport in the RO flat sheet membrane experiments 53 4.2.1 Salt permeability in the Spiegler-Kedem model the absence of concentration polarization 53 4.2.2 Salt permeability in the Spiegler-Kedem modelconcentration polarization 56 4.2.2.1 Cmem at 1 = 1 57 4.2.2.2 Cmem from the film theory combined with Sherwood number correlation 60 4.2.3 Pure water transport in the Spiegler-Kedem model 68 4.2.4 Salt permeability in the Kimura-Sourirajan model 70 4.2.5 Pure water transport in the Kimura-Sourirajan model 73 4.3 Salt and water transport in the RO spiral wound membrane experiments 74 CHAPTER 5 DISCUSSION OF RESULTS 76 5.1 Salt and water transport in the direct osmosis experiments 77 5.1.1 Concentration at the membrane wall in the direct osmosis experiments 78 5.1.2 Salt transport in the direct osmosis experiments 81 5.1.3 Pure water transport in the direct osmosis experiments 84 5.1.4 Salt and water transport in the case of fluxes interaction in direct osmosis experiments 87 5.2 Analysis of the transport parameters in the SK model 88 5.2.1 Salt transport in the seawater membrane AD 89 5.2.2 Salt transport in the brackish water membrane CG 91 5.2.3 Salt transport in the nanofiltration membrane CK 93 5.2.4 Water transport in the SK model 94 5.2.5 Conclusions on the SK model 96 5.3 Comparison of the SK and KS models 97 5.3.1 Comparison of salt transport parameters, PRO and (D/K ) RO 97 5.3.2 Comparison of pure water transport parameters, Lp and A 99 5.3.3 Conclusions on the comp arison of SK and KS models 100 5.4 Comparison of salt permeability in DO and RO experiments 100 5.5 Factors controlling the salt permeability in RO and NF membranes 104 5.5.1 Physical parameters 105 5.5.1.1 Ionic and hydrated radii 105 5.5.1.2 Diffusibility in solution 108 5.5.2 Thermodynamic parameters 112 5.5.2.1 Enthalpy and entropy of hydration 112 5.5.2.2 Relative free energy G 116

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iii 5.5.3 Conclusions on the factors controlling the salt permeability in RO and nanofiltration membranes 121 CHAPTER 6 CONCLUSIONS 125 6.1 Direct osmosis (DO) experiments 125 6.2 Reverse osmosis (RO) experiments 127 6.3 Comparison of DO and RO processes 128 6.4 Factors controlling the salt permeability 132 6.5 Summary 132 CHAPTER 7 RECOMMENDATIONS 134 REFERENCES 139 APPENDICES 144 APPENDIX A: DIAGRAMS OF THE TEST CELLS 145 APPENDIX B: EQUATION OF SALT FLUX IN DIRECT OSMOSIS 149 APPENDIX C: SALT AND WATER TRANSPORT IN DO 152 APPENDIX D: SALT REJECTION IN RO 155 APPENDIX E: FILM THEORY AND SHERWOOD CORRELATION 156 E.1 Film theory 156 E.2 Sherwood correlation 157 APPENDIX F: CONCENTRATION AT THE MEMBRANE WALL FOR SE MEMBRANE AND CORRECTED SALT PERMEABILITIES IN DO 158 APPENDIX G: EXPERIMENTAL ERRORS 161 APPENDIX H: PHYSICAL AND THERMODYNAMIC PROPERTIES OF IONS 164 APPENDIX I: FREE ENERGY PARAMETERS 165 ABOUT THE AUTHOR End Page

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ivLIST OF TABLES Table 2. 1 Comparison of the characteristics of RO and NF membranes (Baker, 1991). 7 Table 3. 1 Instrumentation and its specifications. 28 Table 3. 2 Manufacturer specifications fo r the membranes used in the direct osmosis experiments. 32 Table 3. 3 Salt solutions and their concentrations in the direct osmosis experiments. 33 Table 3. 4 Membranes, salt solution and their concentrations, and the operating pressure for the RO flat sheet membrane experiments. 36 Table 3. 5 Manufacturer specifications for the spiral wound membrane, the salt solutions and their concentrations for the RO spiral wound membrane experiments. 39 Table 4. 1 Pure water permeability. 49 Table 4. 2 Salt transport parameters and th e percentage of the diffusion flux for the SK model in absence of concentration polarization in RO flat sheet membrane experiments. 56 Table 4. 3 Average concentrations at the membrane wall calculated for 1 = 1 for feed concentration of 0.05 molL-1 in RO flat sheet membrane experiments. 57 Table 4. 4 Salt transport parameters and th e percentage of the diffusion flux for the SK model when concentrati on polarization is calculated for 1 = 1 in RO flat sheet membrane experiments. 59 Table 4. 5 Back diffusion coefficient calculated from Sherwood correlation and the concentration at the membrane wall calculated from the film theory in RO flat sheet membrane experiments. 61 Table 4. 6 Salt transport parameters and percentage of the diffusion flux for the SK model in the case of concentration polarization calculated from film theory and Sherwood correlation in RO flat sheet membrane experiments. 63

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vTable 4.7 Pure water permeability and reflection coefficient in the SK model in the absence of concentration polarization in RO flat sheet membrane experiments. 69 Table 4. 8 Pure water permeability and re flection coefficient in the SK model when the concentration at the membrane wall is calculated from film theory and Sherwood correlations in RO flat sheet membrane experiments. 70 Table 4. 9 Salt permeability and back di ffusion coefficient in the KS model in RO flat sheet membrane experiments. 71 Table 4. 10 Pure water parameters of transport in RO flat sheet membrane experiments. 74 Table 4. 11 Salt and water transport parameters in the KS model in the RO spiral wound membrane experiments. 74 Table 5. 1 Pure water permeability and con centrations of the salt solution at the membrane wall at bulk salt solution concentration of 0.05 molL-1 in direct osmosis experiments. 80 Table 5. 2 Differences (as percentages) between the salt permeability in direct osmosis experiments and salt perm eability from SK and KS models in RO flat sheet membranes. 102 Table 5. 3 Comparison of the requirements for the two RO models and the DO model. 103 Table 5. 4 Comparison of the salt parameters in the three cases of SpieglerKedem model. 104 Table 5. 5 The relative free energy for the cations, for Cl-, and for the salts, and the membrane constant. 118 Table C. 1 Comparison of salt permeability for all membranes at 0.05 molL-1 in direct osmosis experiments. 152 Table C. 2 Comparison of salt permeability at different concentration for chlorides for the SE membrane in direct osmosis experiments. 152 Table C. 3 Comparison of salt permeability at different concentration for acetates for the SE membrane in direct osmosis experiments. 152 Table C. 4 Comparison of salt permeability for chlorides and acetates at two concentrations for the SE membrane in direct osmosis experiments. 153

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viTable C. 5 Comparison of pure water flux for all membranes at 0.05 molL-1 in direct osmosis experiments. 153 Table C. 6 Comparison of pure water flux at different concentration for chlorides for the SE membrane in direct osmosis experiments. 153 Table C. 7 Comparison of pure water flux for chlorides and acetates at two concentrations for the SE membrane in direct osmosis experiments. 154 Table D. 1 Average over pressure of salt rejection in RO experiments. 155 Table F. 1 Concentration at the membrane wall for the SE membrane at different bulk concentrations in direct osmosis experiments. 158 Table F. 2 Corrected salt permeability at 0.05 molL-1 in direct osmosis experiments. 158 Table G. 1 Experimental errors for direct osmosis experiments. 161 Table G. 2 Experimental errors for the first case of the SK model in RO flat sheet membrane experiments. 161 Table G. 3 Experimental errors for the second case of the SK model in RO flat sheet membrane experiments. 162 Table G. 4 Experimental errors for the third case of the SK model in RO flat sheet membrane experiments. 162 Table G. 5 Experimental errors for KS model in RO flat sheet membrane experiments. 163 Table G. 6 Total error for the salt and water parameters in all experiments. 163 Table H. 1 Physical parameters of cations. 164 Table H. 2 Hydration number calculated from different methods. 164 Table I. 1 The corrections of ionic radii, the parameter E, and the ionic free energy in the bulk solution. 165 Table I. 2 The corrections of ionic radii and the parameter E at the membrane surface, and the free energy at the membrane surface. 165

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viiLIST OF FIGURES Figure 2. 1 Schematic drawing of anisotropic membranes (Mallevialle et al., 1996). 9 Figure 2. 2 Schematic drawing of water and salt fluxes in direct and reverse osmosis. 10 Figure 2. 3 Fluid flow and concentra tion polarization between two parallel membranes. 17 Figure 3. 1 Experimental set-up for the direct osmosis experiments. 29 Figure 3. 2 Experimental set-up for the RO flat sheet membrane experiments. 35 Figure 3. 3 Experimental set-up for the RO spiral wound membrane experiments. 39 Figure 4. 1 Salt permeability for the different membranes at 0.05 molL-1 in the direct osmosis experiments. 46 Figure 4. 2 Variation of salt permeability with concentration for chlorides in SE membrane in direct osmosis experiments. 47 Figure 4. 3 Variation of salt permeability with concentration for acetates in SE membrane in direct osmosis experiments. 47 Figure 4. 4 Comparison of salt permeability for chlorides and acetates at 0.05 molL-1 in direct osmosis experiments. 48 Figure 4. 5 Comparison of salt permeability for chlorides and acetates at 0.1 molL-1 in direct osmosis experiments. 49 Figure 4. 6 Pure water flux for different membranes at 0.05 molL-1 in the direct osmosis experiments. 50 Figure 4. 7 Variation of pure water flux with concentration for chlorides in SE membrane in direct osmosis experiments. 52 Figure 4. 8 Variation of pure water flux with concentration for acetates in SE membrane in direct osmosis experiments. 52 Figure 4. 9 Comparison of the pure water flux for chlorides and acetates at two concentrations in SE membrane in direct osmosis experiments. 53

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viiiFigure 4. 10 Concentration at the membrane wall normalized to the feed concentration for 1 = 1 in RO flat sheet membrane experiments. 58 Figure 4. 11 Concentration at the membrane wall normalized to the feed concentration from Sherwood correlatio n and thin film theory in RO flat sheet membrane experiments. 62 Figure 4. 12 Comparison of the salt in the SK model at different concentration at the membrane wall for (a) AD membrane; (b) CG membrane; and (c) CK membrane in RO flat sheet membrane experiments. 64 Figure 4. 13 Comparison of the strength of the salt-water coupling in the SK model at different concentration at the membrane wall for (a) AD membrane, (b) CG membrane, (c) CK membrane CK membrane in RO flat sheet membrane experiments. 66 Figure 4. 14 Comparison of the percentage of the diffusive flux of the total flux in the SK model at different concentration at the membrane wall for (a) AD membrane, (b) CG membrane, (c) CK membrane in RO flat sheet membrane experiments. 67 Figure 4. 15 Comparison of the back diffusion coefficient for all membranes in the KS model and from the Sherwood correlation (same for all membranes) in RO flat sheet membrane experiments. 73 Figure 5. 1 Schematic diagram of the pur e water flux as function of the applied pressure across membrane. Modified from Mulder (2003). 79 Figure 5. 2 Salt permeability before and after the correction of the membrane wall for SE, AD, CG and CK membranes in the direct osmosis experiments. 83 Figure 5. 3 Pure water permeability when the skin layer of the membranes faces the low pressure side (A') and the high pressure side (Lp and A). 85 Figure 5. 4 Comparison of the differentia l pressure at the skin layer when the membrane is inverted. 85 Figure 5. 5 Dependence of the relative difference of 1 and 2 on the percentage of the diffusive flux of the total flux for all membranes when concentration polarization is considered. 95 Figure 5. 6 Variation of the difference in the salt permeabilities in the SK and the KS models with the salt-water coupling coefficient. 99 Figure 5. 7 Variation of the salt diffusive flux with the membrane rejection. 100

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ixFigure 5. 8 Variation of salt permeability with ionic radius of the cation for all salts in direct osmosis and reverse osmosis experiments for AD, CG, CK, and SW30 membranes. 106 Figure 5. 9 Variation of salt permeability with hydrated radius of the cation for all salts in direct osmosis and reverse osmosis experiments for AD, CG, CK, and SW30 membranes. 109 Figure 5. 10 Variation of salt permeability with the diffusion coefficient in infinitely dilute solution for all salts in direct osmosis and reverse osmosis experiments for SE, AD, CG, CK and SW30 membranes. 111 Figure 5. 11 Variation of salt permeability with the cation enthalpy of hydration for all salts in direct osmosis a nd reverse osmosis experiments for AD, SE, CG, CK and SW30 membranes. 114 Figure 5. 12 Variation of salt permeability with the cations enthalpy of hydration for all salts in direct osmosis a nd reverse osmosis experiments for SE, AD, CG, CK and SW30 membranes. 115 Figure 5. 13 Variation of the salt permeability with the relative free energy for all salts in direct osmosis and reverse osmosis experiments for the SE, AD, CG, CK and SW30 membranes. 122 Figure 6. 1 The equality of salt permea bility in DO and RO experiments. 126 Figure A. 1 DO test celltop view of the salt solution chamber. 145 Figure A. 2 DO test cell -top view of the DI water chamber. 145 Figure A. 3 DO test cell-assemble view. 146 Figure A. 4 RO flat sheet cell -bottom side. 146 Figure A. 5 RO flat sheet cell -top side. 147 Figure A. 6 RO test cell-assemble view. 147 Figure A. 7 Diagram of a spiral wound membrane configuration. 148 Figure B. 1 Diagram of the salt concentrations across the membrane. 149 Figure E.1 Schematic diagram of the salt fluxes across RO membranes. 156 Figure F. 1 Comparison of salt permeability for chlorides and acetates at 0.05 molL-1 bulk solution concentration after correction in SE membrane in diffusion experiments. 159

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xFigure F. 2 Comparison of salt permeability for chlorides and acetates at 0.1 molL-1 bulk solution concentration after correction in SE membrane in diffusion experiments. 159 Figure F. 3 Variation of salt permeability with bulk solution concentration after correction in SE membrane for chlorides in diffusion experiments. 160 Figure F. 4 Variation of salt permeability with bulk solution concentration after correction in SE membrane for acetates in diffusion experiments. 160

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xiLIST OF SYMBOLS A Pure water permeability when the memb rane skin layer faces the high pressure side A Pure water permeability when the membra ne skin layer faces the low pressure side C Membrane constant in the Free Energy Theory C Difference in the salt concentration across the membrane Cavg Average concentration of salt in the membrane CDI Concentration of salt in the DI chamber in DO experiments (CDI)mem Concentration of salt at the membrane wall in the DI side in DO experiments Cfeed Concentration of salt in the feed solution in RO experiments Cprod Concentration of salt in the product water in RO experiments Cmem Concentration of salt at the membrane wall max memC Concentration of salt at the membrane wall at 1=1 k memC Concentration of salt at the membrane wall calculated from film theory and Sherwood correlation CS Concentration of salt in the salt solution chamber in DO experiments (CS)mem Concentration of salt at the membrane wall in the salt solution side in DO experiments d Thickness of the concentration boundary layer D Diffusion coefficient in membrane dh Hydraulic diameter Dw Diffusion coefficient of salt in infinitely dilute solution (D/K )DO Salt permeability in DO experiments

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xii(D/K )RO Salt permeability in Kimura-Sourirajan model in RO experiments e0 Electron charge Emem Value of parameter E at the membrane – solution interface ES Value of parameter E in the solution Fi,k Generalized forces in Spiegler-Kedem model GS Free energy in the solution Gmem Free energy at the membrane-solution interface G Free energy parameter, G = Gmem GS h Height of the flow channel H Enthalpy of hydration Jconv Salt convective flux Jdiff Salt diffusive flux Ji Generalized fluxes in Spiegler-Kedem model JS Flux of salt in RO experiments (equal to Jtotal) Jtotal Salt total flux, Jtotal = Jdfff + Jconv Jv Flux of product water in RO experiments Jw, DO Pure water flux in DO experiments k Back diffusion coefficient K Partitioning coefficient solution-membrane kRO Back diffusion coefficient in Kimura-Sourirajan model l Width of the flow channel L Length of the flow channel Lik Phenomenological coefficients in the Spiegler-Kedem model Lp Membrane hydraulic resistance

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xiiiMS Salt molecular weight n 2 for 1:1 salts and 3 for 1:2 salts N Number of moles transported in DO experiments nw Hydration number NA Avogadro’s number P Operating pressure PRO (1) Salt permeability in the first case of the Spiegler-Kedem model PRO (2) Salt permeability in the second case of the Spiegler-Kedem model PRO (3) Salt permeability in the third case of the Spiegler-Kedem model R Rejection coefficient Re Reynolds number Rg Gas constant Rh Hydrated radii Ri Ionic radii QP Flow of product water QF Flow of feed water S Membrane surface area S Entropy of hydration Sc Schmidt number T Absolute temperature v Feed flow velocity in RO experiments Vw Water molar volume VDI Volume of water in DI vessel in DO experiments Xmem Molar fraction of salt at the membrane wall

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xivXprod Molar fraction of salt in the product water Zi Ionic charge BW Brackish water membrane DO Direct Osmosis KS Kimura-Sourirajan model NF Nanofiltration membrane RO Reverse Osmosis SK Spiegler-Kedem model SW Seawater membrane Slope of the plot of concentration vs. time for the salt solution chamber i Number of moles of ion “i” in one mole of ionized salt Slope of the plot of concentration vs. time for the DI chamber Membrane thickness mem Value of at the membrane-solution interface S Value of in the solution Difference in osmotic pressure across the membrane S Dielectric constant of the solvent Osmotic pressure coefficient DI Conductivity of the DI solution in DO experiments salt Salt specific conductivity Salt permeability in Spiegler-Kedem model DI Osmotic pressure in the DI chamber in DO experiments p Osmotic pressure of the product water

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xvDO mem Osmotic pressure at the membrane wall in DO experiments Rate of free energy released per uni t volume in Spiegler-Kedem model Reflection coefficient in Spiegler-Kedem model 2 Salt-water coupling coefficient in Spiegler-Kedem model Duration of the DO experiments Cases of the Spiegler-Kedem model

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xviMASS TRANSFER OF IONIC SPECIES IN DIRECT AND REVERSE OSMOSIS PROCESSES Silvana Melania Stefania Ghiu ABSTRACT This dissertation investigates the importan ce of diffusional and convective fluxes for salts in reverse osmosis (RO) and nanofiltrati on (NF) membranes. Moreover, the physical and thermodynamic factors controlling the salt permeability are analyzed. The study utilizes direct osmosis (DO) experiments and RO experi ments, the later using both flat sheet and spiral wound membrane configurations. The salts considered are chlorides and acetates of alkali metals and alkaline earth metals. The equation governing the salt transport in DO experiments is derived and a phenomenon inverse to concentration polarization in RO is observed. The salt permeability in DO is equal to the salt permeability calculated fo r the valid cases of the used RO models. DO is suggested as an alternative method in charact erizing the salt transport in membranes. The method can be more advantageous than RO due to the lower costs and simplicity of the apparatus. The models used to calculate the salt tran sport parameters in RO experiments are Spiegler-Kedem model, which considers both di ffusion and convection of salt, and KimuraSourirajan model, which considers only diffusion of salt. It is found that diffusion is the dominant mechanism of transport in both RO a nd NF membranes. The percentage of the salt diffusional flux of the total flux is highest fo r seawater membranes and it is approximately equal for brackish water and nanofiltration me mbranes. The salt diffusive flux contribute more to the total flux for the 1:2 salts than for 1:1 salts. The two RO models are found equivalent in determining the salt permeab ility for only the seawater membranes. The

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xviiKimura-Sourirajan model overestimates the salt permeability coefficient for salts with rejection coefficient lower than 86%. The permeation rates for studied salts fo llow the lyotropic series regardless the membrane type (RO or NF), the membrane configuration (flat sheet or spiral wound), the process (DO or RO), or the models used for th e calculations. This order of salt permeability is explained by the hydration of the cations, which is quantified by the enthalpy and entropy of hydration. The relative free energy theory can al so be used to predict the salt permeability in a membrane based on preliminary data.

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1 CHAPTER 1 INTRODUCTION 1.1 Importance of the research problem In 1798, Samuel Taylor Coleridge wrote in The Rime of the Ancient Mariner “Water, water every where, Nor any drop to drink”. Th e old lyrics seem to be outdated by the present times, when reverse osmosis (RO) technology offers an efficient method of producing drinking water from seawater. With salty wate r constituting more than 97% of the Earth’s water resources, and in the context of world-wide increasing demands on fresh water supplies, the reverse osmosis solves the equati on “salty watersalt = water” by using a nonpolluting and sustainable method. Reverse osmosis has been r esearched since 1940’s, but it was not until 1959 that the practicality of the RO process was demonstrated In 1959, two students at UCLA, S. Loeb and S. Sourirajan, produced the first synthetic RO membrane from cellulose acetate polymer which was capable of rejecting the salt while p assing the fresh water at reasonable flow rates. This discovery marked the beginning of th e desalination industry using RO membranes. Similar membranes were later adopted in other fields, such as food industry, electronics, and pharmaceuticals. Not all the salt is rejected in the RO pro cesses. In the case of seawater desalination, a membrane rejection coefficient as high as 97%, which means that only 3% of the total salt passes through the membrane, is actually too lo w to produce water at the drinking water standards. For that reason, it is important to understand which transport mechanisms and what salt properties determine even very small amounts of salt to go through the membrane. Identifying the salt transport mechanism will not only provide reliable information for the RO

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2 plant design, but it will benefit the development of membranes with superior selectivity. Moreover, recognizing the salt properties cont rolling the salt rejection makes possible to estimate the rate of salt permeability with a minimum amount of experimental work. 1.2 Research objectives and approach Despite the early research developments c onducted in the RO desalination field, and even though the RO processes are well implemente d in practical applications, the mechanism of salt and water separation in RO membranes is not well understood. There is controversy over the importance of the salt diffusive flux, wh ich is due to a concentration gradient across the membrane, and the salt convective flux, which is caused by the salt-water coupling effect. The objectives of this dissertation are first, to identify what transport mechanism is dominant in hyperfiltration membranes, and second, to confirm the physical and thermodynamic factors controlling the permea tion rate of salts through hyperfiltration membranes. The approach considered in answ ering the first research question is outlined below: Compare the salt permeability coefficient in the direct osmosis (DO) process, for which there is no convective salt flux, with the salt permeability in RO process, for which both diffusional and convective salt fluxes may occur. A new equation for the salt transport in DO needs to be developed; Calculate the percentage of salt diffusional flux of the total flux in RO using the Spiegler-Kedem model, which quantifies both the diffusive and the convective salt fluxes. Identify the consequences of model simplification which often occurs in the literature; Compare the salt permeability obtained from two RO models, the Spiegler – Kedem model, which quantifies both the diffusive and the convective salt

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3 fluxes, and Kimura-Sourirajan model, which assumes that diffusion is the only mechanism of salt transport in hyperfiltration membranes; Perform the above calculations and comparisons for three types of hyperfiltration membranes: seawater me mbrane, brackish water membrane and nanofiltration membranes. Also, the salt transport is studied for three 1:1 salts and three 1:2 salts. It is expected that the importance of the salt diffusional flux depends on the membra ne type and the salt valence. In order to address the second research qu estion, the approach is as follows: For the salts with common anion, the relationship between the salt permeability and physical and thermodyna mic properties of the cations is investigated. The physical properties of the cations are ionic radii and hydrated radii, and the thermodynamic properties are ionic enthalpy and entropy of hydration. The values of the cation ionic and hydrated radii, as well as ionic enthalpy and entropy of hydration are taken from the literature. The salt permeability of both chlorides and acetates is compared to the salt diffusivity in infinitely dilute solu tion, which is calculated based on ions diffusivity coefficients and the ionic charge. The relative free energy parameter is cal culated according to the literature for each chloride salt and the exponential relationship between the salt permeability and the relative free energy parameter is verified. 1.3 Dissertation outline Chapter 2 of this dissertation is divided in two parts. The first part presents general information related to hyperfiltration membranes as well as direct osmosis and reverse osmosis processes. The second part of this chap ter presents a critical review of the previous

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4 research in the area related to this disserta tion. The need for additional research is highlighted. Chapter 3 presents the experimental appara tus, the operating conditions and operating procedure for direct reverse osmosis experiments, along with a description of the instrumentation and the membrane manufacturer specifications. For reverse osmosis experiments, two membrane configurations are used: flat sheet and spiral wound. In Chapter 4 of this dissertation, the results obtained for direct osmosis are presented, followed by the results from the RO flat sheet membrane and the results from the RO spiral wound membranes. The section on the direct osmosis experiments presents first the derivation of the equation used in calculating the salt permeability coefficient, (D/K )DO, along with the values obtained for (D/K )DO in the case of two seawater membranes, one brackish water and one nanofiltration membra ne. The results from the RO flat sheet membrane experiments are interpreted from th e perspective of two models: the SpieglerKedem (SK) model and the Kimura-Sourirajan (KS) model. The KS model is used to determine the salt and water transport paramete rs in the case of RO spiral wound membrane experiments. The transport parameters for the salt and pure water are compared with the transport parameters obtained from the RO flat sheet membrane experiments. Chapter 5 discusses the experimental results and their implications. The first section presents a correction of the equation derived in the previous chapter for the salt transport in direct osmosis experiments. It addresses the concentration at the membrane wall as well as the transport of pure water in direct osmosis assuming that the salt and the water fluxes do not interact within the membrane. The second section of this chapter discusses the salt transport parameters PRO, 1 and 2 as well as the importance of the salt diffusive flux in the SpieglerKedem model. The third section compares the two models, the Spiegl er-Kedem model and

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5 the Kimura-Sourirajan model. The comparison addresses both the salt and the water transport parameters and defines the situations when th e two models can be used interchangeably. The fourth part of this chapter brings together the salt permeability from the direct osmosis experiments and the reverse osmosis experiments. It is shown that the salt permeability is the same in direct osmosis and reverse osmosis, therefore it does not depend on the operating pressure applied. The last part of the Chapter 5 analyzes wh at physical and thermodynamic parameters control the salt permeability in RO and NF membra nes. There is a certain pattern of variation for the salt permeation among the six studied salts regardless the membrane type (RO or NF), the membrane configuration (flat sheet or spiral wound), the type of the experiment (DO or RO), or the model used in calculating the salt permeability (Spiegler-Kedem or KimuraSourirajan). This pattern is explained by an y of the parameters measuring the degree of the hydration for the cations (hydrated radii, enthalpy and entropy of hydration). The relative free energy can be used to predict the permeabilit y of salts in a certain membrane based on known values of the several other salt permeabiliti es in the membrane. Chapter 6 draws the conclusions and the implications of this research and Chapter 7 presents a set of recommendations for continuation of this research.

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6 CHAPTER 2 RO MEMBRANE FILTRATION: INTRODUCTION AND RELEVANT PREVIOUS RESEARCH This Chapter is divided in two main parts. The first part presents general information related to membrane reverse osmosis (RO) filtration. It introduces the hyperfiltration membranes and the direct and reveres osmosis processes, it describes the two RO models used in this dissertation and discusses the im portance of concentration polarization. The second part presents a critical review of research undertaken to date on the topics addressed in this research. The previous studies on salt and water transport in direct osmosis are presented first. The controversy in the existing literature on the distribution of the salt flux (diffusive and convective) is descr ibed next. A comparison of the transport parameters for two RO models, the solutiondiffusion model and the Kedem-Katchalsky model, is addressed. Last, previous work in identifying the factors controlling the salt permeability in hyperfiltration membranes is described briefly. 2.1. Background information Information similar to that presented in this section can be found in numerous publications describing hyperfiltration membranes and pr ocesses. References are made only occasionally and mainly when information is specific to a source. 2.1.1 Hyperfiltration membranes A membrane is defined as a thin film which acts as a separation barrier to the transport of matter. All types of membran es have one common characteristic: limited the passage of some chemical species while allo wing others to pass through. Membranes are

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7 more often defined by what they do rather th an what they are. According to the solute exclusion size, the pressure driven membranes u sed in liquid-liquid separation are divided in microfiltration, ultrafiltration, nanofiltration and reverse osmosis membranes. Hyperfiltration membranes refer to membra nes used in reverse osmosis (RO) and nanofiltration (NF) processes. The two processes are based on the same principles and they are often treated together. Nanofiltration memb ranes are the same as RO membranes, except that the network structure of the membrane polymer is more open in the NF membranes. Reverse osmosis membranes are further divided in sweater and brackish water membranes. Most NF membranes have a net negative charge on the surface which influences the membrane rejection. The RO and NF membranes typically reject species with radii as small as 10-10 m (ionic range), or in terms of molecular weight, they reject low molecular weight solute such as inorganic salts and small organic molecules like glucose and sucrose (Mulder, 2003). A summary of the characteristics of the two typ es of membranes is presented in Table 2.1. Table 2. 1. Comparison of the characteristics of RO and NF membranes (Baker, 1991). Reverse Osmosis (RO) Characteristics Seawater (SW) Brackish Water (BW) Nanofiltration (NF) Typical water source Oceans and Seas Surface Water Groundwater Surface Water Groundwater Source solution concentration (%) 1-5 0.2-0.5 0.05 Rejection NaCl 99.5 97 60 Rejection MgCl2 99.9 99 89 Operating pressure (psi ) 800-100 300-500 100-150 According to membrane morphology, the vast majority of the hyperfiltration membranes used in currently practice are anisotr opic. They consist of a very thin and dense

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8 layer, called the skin layer, and a support la yer, which is thicker and more porous. The thickness of the skin layer represents about 1% of the thickness of the support layer. The support layer functions only as mechanical s upport for the skin and it has a negligible resistance to mass transfer (Mallevialle et al., 1996). The anisotropic membranes are divided in asymmetric and thin film composite membrane (TFC). A schematic drawing of the two anisotropic membrane types is presented in Figure 2.1. The layers in asymmetric membranes are made of the same material. Conversely, for the thin film composite membra nes, the skin and the support layers are made of different materials. The most common configurations of th e hyperfiltration membranes for industrial practices are spiral wound and hollow fine-fiber, while flat sheet membranes are commonly used in laboratory studies. The spiral-wound membranes are manufactured by rolling membrane envelopes that are glued to a cente r tube which collects the product water. The membrane envelopes are made by folding a flat sheet membrane over a permeate carrier mesh, with the skin layer of the membrane faci ng outside of the fold. A diagram of a spiral wound membrane is presented in Figure A.7. Th e hollow fine-fiber membranes consists of a bundle of fine tubes which are folded into an U-shape and the free ends are epoxy-casted in one end of a pressure tube. The skin layer of RO and NF membranes is typically made of organic polymers such as cellulose acetate (CA) and cellulose acetate derivatives such as cellulose triacetate, polyamide (PA) and polyamide derivatives. Th e CA membranes are more hydrophilic than PA membranes and present higher resistance to fouling. However, they are susceptible to hydrolysis, especially at pH outside the range 4 to 6.5, and biological degradation. They compact under high operating pressure. The PA membranes have lower flux permeability

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9 than the CA membranes but they have superior selectivity. They also can be operated at wider pH range and are more stable to biolog ical degradation. However, PA membranes are susceptible to oxidative degradation. Their comp action at high operating pressure is reduced. 2.1.2 Direct and reverse osmosis processes Figure 2.2 presents the solvent (water) and solu te (salt) fluxes in direct osmosis (DO) and reverse osmosis (RO). The membrane is permeable to the solvent and ideally, impermeable to the solute. In DO, due to the differences in the chemical potential across the membrane, the solvent from the low concentration side diffuses to the high concentration side until the equilibrium of chemical potential is reached. Practically, a small amount of the solute is transported through the membrane via diffusion, in DO, and due to diffusion and convection, in RO. The real difference in the osmotic pressure across the membrane in DO is not but where is the reflection coefficient which accounts for the membrane Figure 2. 1. Schematic drawing of anisot ropic membranes (Mallevialle et al., 1996). Thin film composite membrane Skin Layer Asymmetric membrane Asymmetric membrane Support layer Skin layer

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10 permeability to solutes. The reflection coefficien t is discussed in Section 2.1.3.1. When an external pressure, P, larger than the modified osmotic pressure, is applied to the high concentration side, the direction of the solvent flux is reversed. In practical applications, P has to be at least two times higher than It ranges from 150 psi to 350 psi for NF processes and from 200 psi to 1200 psi for RO processes, depending on the solute concentration. Water flux Direct Osmosis Salt flux Water flux Reverse Osmosis Salt flux P > high concentration low concentration high concentration low concentration MembraneMembrane Figure 2. 2. Schematic drawing of water and salt fluxes in direct and reverse osmosis. Direct osmosis has not been studied to a large extent due to the limited number of practical applications of this process. Some studies has shown the application of DO in concentrating liquid food and in food concentr ate for emergency supply of drinking water in lifeboats (Kessler and Moody, 1976; Petrotos et al., 1998; Petrotos et al., 1999; Petrotos and Lazarides, 2001). Direct osmosis does have importance for research in determining the osmotic pressure and the transport coeffici ents through a membrane (Rautenbach and Albrecht, 1989).

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11 Alternatively, reverse osmosis has been st udied intensively for more than 50 years and has a large spectrum of applications. About 50% of the RO systems currently installed produce drinking water from seawater and brackis h water (such as ground water and surface water). Another 40 % produce ultrapure water for electronics, pharmaceutical and power generation industries. The remaining 10% of the RO systems are involved in special applications such as wastewater treatm ent and food processing (Baker, 2000). Since hyperfiltration membranes reject toxic and biol ogic agents, the RO and NF processes are also used by the military. Nanofiltration membranes are used in special applications such as color removal and water softening. 2.1.3 Reverse osmosis models Although the RO processes have been studied for more than 40 years and have been well implemented in practical applications for 20 years, the mechanism of solute separation from the solvent in the membrane is still a matter of controversy. The two models presented in this Chapter are selected based on the cred ibility they have among the researchers as well their domination in practical applications. The two models are conceptually different. The Spiegler-Kedem model is based on irreversib le thermodynamics and introduces the explicit terms and as coefficients to characterize the tr ansport of salt due to diffusion and convection. Alternately, the Kimura-Sourirajan model is a mechanistic membrane model which considers that the solute is transported through the membrane solely by diffusion. It defines the salt permeability coefficient, (D/K starting from Fick’s law of diffusion applied to membranes.

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12 2.1.3.1 Spiegler-Kedem (SK) model The SK model is based on irreversible thermodynamics. Since the membrane structure and the mechanism of transport within the membrane are not known, the membrane is considered a “black box” which separates tw o phases in non-equilibriu m states. The system is divided in small subsystems for which local equilibrium exists. The rate of free energy released per unit volume is given by Equation 2.1 n 1 i i iF J (2.1) where is the free energy dissipated per unit volume, and Ji and Fi are the generalized fluxes and forces, respectively. For sufficiently sl ow processes taking place in membranes, the fluxes are linearly proportional to the conjugate d and non-conjugated for ces, as expressed in Equation 2.2: ) n ,..., 2 1 i ( F L Jk n 1 k ik i (2.2) where Lii are the “straight” coefficients of proportionality for the conjugated forces and Lik are the “cross” coefficients of proportionality for the non-conjugated forces. Substituting Equation 2.2 in 2.1 yields to Equation 2.3 which can be satisfied if Lii 0 and Lii Lkk (Lik)2 (Bitter, 1991): 0 F F Li n 1 i n 1 k k ik (2.3) The SK model leads to Equations 2.4 and 2.5 which describe the fluxes of product water and of salt through the membranes: Jv = Lp( P) (2.4) JS = + (1)Jv Cavg (2.5)

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13 2 CC Cprod mem avg (2.6) where Jv is the product water flux (mL cm-2 s-1), Lp is the membrane hydrodynamic resistance (mL cm-2 s-1 psi-1), P is the operating pressure (psi), is the reflection coefficient, is the difference in the osmotic pressure across the membrane (psi), JS is the total flux of salt permeating the membrane (mol cm-2 s-1), is the salt permeability coefficient (mol cm-2 s-1 psi-1), is the coefficient of coupling between salt and water, and Cavg is the average salt concentrations across the membrane (mol L-1), defined by Equation 2.6 (Mason and Lonsdale, 1990). The coefficient 1 is the Staverman reflection coeffi cient defined by Equation 2.7 and describes how effective the salt is in developing an osmotic pressure across the membrane. It is a indicator of the membrane selectivity and has values between 0 and 1. A reflection coefficient of 1 corresponds to ideal membra nes where there is no solute transport (or rejection coefficient equal unity), and 0 for entirely unselective membranes (Spiegler, 1966). P lim0 v J1 (2.7) The coefficient is zero for perfect coupling (solute convective transport is dominant) and it is unity when there is no coupling solute-solvent (pure diffusive solute transport). The large majority of the research papers considers based on the validity of Onsager reciprocal relationship. However, the equality of and has to be proven experimentally for each separation system

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14 The first term in Equation 2.5 represen ts the flux of salt due to diffusion (Jdiff ) whereas the second term (Jconv (1)JvCavg ) is the flux of salt due to convection. Since the the osmotic pressure is given by nRgT C the term can be expressed as PRO C, where PRO nRgT. The term is the difference in the osmotic coefficient across the membrane, n is the sum of salt valences, Rg is the gas constant, and T is the absolute temperature. The coefficient PRO is introduced in this research for the purposes of an easier comparison of the salt transport coefficients in the Spiegler-Kedem model and Kimura-Sourirajan model. The units for PRO are (cm s-1). Substituting for PRO in Equation 2.5 yields to Equation 2.8: JS = PRO C + (1)JvCavg (2.8) The parameters of transport which need to be determined in the Spiegler–Kedem model are LP, 1, 2 and PRO. Equations 2.4 and 2.8 can be rearranged as Equations 2.9 and 2.10, respectively, which allow the calculations of the transport parameters using a graphical method. For example, LP and 1 are the intercept and the slope, respectively, of the line represented by the Equation 2.9. Similarly, PRO and 2 are the slope and the intercept of the line represent by Equation 2.10. P L P J1 P v (2.9) ) 1 ( P C J C C J J2 RO avg v avg v S (2.10) The Spiegler-Kedem model has the main advantage of quantifying both the diffusional and the convective fluxes of the salt through the membrane. The disadvantage of this model is that in does not provide any in formation on the actual mechanism of separations in hyperfiltration membranes.

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15 2.1.3.2 Kimura-Sourirajan model (Preferential sorption-capillary flow model) The preferential sorption-capillary flow model was introduced in 1970 by Kimura and Sourirajan. It is also referred in the literature and in this dissertation as KimuraSourirajan model. This model assumes that th e solvent and the solute fluxes do not interact with each other and are transported through the membrane by different mechanisms. The membrane skin layer is assumed to be micr oporous and heterogeneous and the mechanism of separation is governed partly by surface phe nomena and partly by fluid transport under pressure through capillary pores. When a pressure is applied to the system, salt and water tend to permeate through the micropores but water is adsorbed into the pores whereas salt is rejected (preferential adsorption of wa ter on the membrane surface due to the physicochemical nature of the surface layer). The water is transported through the capillary pores in a viscous flow whereas the salt is transported due to pore diffusion. The pore size, their shape and number, together with the composition of the surface layer are critical parameters in the separation process. The model uses the film theory to calculate the back diffusion coefficient, k (Appendix E). The expressions for water and salt fluxe s through the membrane are given by Equations 2.11 and 2.12: Jv = A ( P) (2.11) C K D JRO S (2.12) where Jv is the product water flux (mL cm-2 s-1), A is the pure water permeation (mL cm-2 s-1 psi-1), P is the operating pressure (psi), is the difference in the osmotic pressure across the membrane (psi), JS is the flux of salt permeating the membrane (mol cm2 s-1), (D/K RO is the salt permeability coefficient (cm s-1), and C is the difference in salt

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16 concentration across the membrane (mol L-1). The salt permeability coefficient takes into account the diffusivity coefficient of the salt th rough the membrane, D, the partitioning of salt concentration between the bulk solution and th e membrane, K, and the membrane thickness, The model considers (D/K RO as an intrinsic parameter which is not calculated by dividing the diffusivity coefficient to the product of the partitioning coefficient times the membrane thickness. The algorithm proposed by Sourirajan (1970) to calculate the salt permeability is described by the Equations 2.13 through 2.15: 1000 M)R1(C 1S Q JS feed prod v (2.13) mem g v prod memTCnR A J P (2.14) prod prod mem mem prod prod v ROXCXC X X1 J K D (2.15) where Jv is the water flux (mL s-1 cm-2) which cannot be measured when the feed is a salt solution, Qprod is the measured product flow (mL s-1), S is the membrane surface area (cm2),R is the rejection coefficient defined by R 1-Cfeed/Cprod, MS was the salt molecular weight (g/mol), Xmem and Xprod are the salt mole fraction given by Xi = Ci /(Ci + 55.5) at the membrane wall and in the product, respectively. The salt concentration at the membrane wall, Cmem, as well as the mole fraction, Xmem, in Equation 2.15 are obtained from Equation 2.14. One of the advantages of this model is the explicit dependence of pure water permeation and solute permeability on operating conditions such as temperature and pressure. The main

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17 disadvantage of the model is that it assumes diffusion being the only mechanism of salt transport. 2.1.4 Concentration polarization Concentration polarization occurs in an y pressure driven membrane separation process. It describes an increase in the c oncentration at the membrane wall due to the rejection of ionic species transpor ted there by the convective flux, Jfeed. Figure 2.3 shows the solute fluxes in the bulk solution (JvCfeed) and permeating in a direction perpendicular to the membrane (JS), as well as the velocity and concentr ation polarization profiles between two parallel membranes. It is an undesirable phe nomenon which results in the increase of the osmotic pressure at the membrane wall and c onsequently, a reduction in the product flux and the membrane rejection coefficient. In the pol arized layer, the concentration of sparingly soluble salts such as CaCO3 and CaSO4 in a feedwater can increase so much locally that they exceed their solubility limit, precipitate a nd form a scale on the membrane surface. Concentration polarization layer Membrane JS JS JVCfeed Velocity profile Concentration polarization profile Figure 2. 3. Fluid flow and concentration polarization between two parallel membranes.

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18 The concentration gradient at the membrane wall (Figure 2.3) controls the diffusion of the rejected species back into the bulk so lution. The thickness of this boundary layer is established at the equilibrium of three fluxes: the salt convective flux, the salt flux through the membrane, and the salt back diffusive flux. The concentration at the membrane wall is calculated in the literature either by using the resistance layers approach or more often, by combining the film theory with the correlations for the back diffusion coefficient, k (Baker, 2000). Details of the later method are given in Appendix E. 2.2 Previous research on the transport parameters in hyperfiltration membranes This section presents the findings of an extensive search on the previous relevant work performed in the past 40 years. Despite th e progress made in the RO separation field in the past 20 years, the older information is found to be just as valuable as more recent ones. The relevant subjects for this dissertation are th e salt and water transport in direct and reverse osmosis, as well as the factors controlling the salt rejection and permeability in hyperfiltration membranes. 2.2.1 Salt and water transport in direct osmosis The literature of membrane separation is s carce when in the area of salt and water transport in direct osmosis processes. In most of the research papers, transport parameters in direct osmosis are addressed in parallel to a nd compared with the transport parameters in reverse osmosis. This approach is consistent w ith one of the objectives of this dissertation. The research on direct and reverse osmosis conducted by Sherwood et al. (1967) has an historical importance. In 1967, RO was not yet commercialized and the two models later to become classic models, Spiegler-Kedem and Kimura-Sourirajan, were not yet largely used. The authors used the solution-diffusion-imperfection model, which assumes that both salt and

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19 water are transported through the membrane by parallel processes of diffusion and pore flow in RO, and by diffusion in pores and polymer matrix, in DO. The DO experimental apparatus consisted of a diffusion cell with two chambers separated by a cellulose acetate membrane. Individual NaCl and CaCl2 solutions were recirculated through one chamber and DI water was recirculated through the other chamber, bot h at high circulations rate to assure a good mixing. The water and salt permeability were determ ined graphically and compared with the manufacturer specifications for RO. The concentr ation at the membrane wall was considered equal to the concentration in the bulk soluti on. The manufacturer specifications for RO were found 1 to 4 times lower than in DO for water permeability and 18 to 23 times lower than in DO for salt permeability. The differences were a ttributed to the membrane compaction under high operating pressure in reverse osmosis. Lonsdale et al. (1971) has studied the salt and water transport in a DO experiment by using a stirred Plexiglass cell with two cham bers separated by a lab-made symmetrical cellulose acetate membrane. One chamber was filled with a NaCl 5 wt -% salt solution and the other chamber contained DI water. The au thors determined the salt permeability from the steady–state transport and Equation 2.12 (referred in the literature as ti me lag method), using the conductivity readings in the DI water chamber. The pure water permeation was determined based on the water flux measured by collecting the overflow from the NaCl chamber, and using Equation 2.11 with P = 0. The authors considered the salt concentration at the membrane wall equal to the salt concentration in the bulk solution. The transport parameters determined in th e DO experiments were compared with the transport parameters determined from a classic lab-scale RO experiment, when the operating pressure was 1500 psi. The Kimura-Sourirajan m odel was used to calculate the salt and water

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20 permeability in the RO experiments. The salt rejection coefficient was found 98.6%. The thickness of the membrane, measured with a Federal Products Corpor ation Thickness gauge, was of 70 m. A good agreement was found between th e transport parameters in DO and RO. The authors concluded that the salt-water coup ling is not of fundamental importance for the transport of NaCl through the membrane. A different set of DO experiments were conducted by Matsuda and Kamizawa (1984). The authors used a countercurrent type ce ll which assured a constant difference in the concentration across the membrane. The pure water flux was reduced to zero by using NaCl solution on one side of the cell and sucrose solutions (which is highly rejected) on the other side of the cell. The concentration of NaCl was adjusted so that the two solutions had the same osmotic pressure. The salt permeabilit y was calculated using Equation 2.5 from the Spiegler-Kedem model, taking Jv equal zero. The pure water permeability was calculated by applying Equation 2.4 for the systems NaCl-DI water and sucrose-DI water. Ten lab-made asymmetric cellulose acetate membranes were used with different rejection coefficients. The water and salt permeability from DO were comp ared to the salt and water permeability in RO, calculated also from Spiegler-Kedem model. The authors reported very good agreement of the transport parameters in DO and RO for membranes with rejection coefficients higher than 94%. Mori et al. (2000) performed experime nts with NaCl solutions and lab-made symmetric cellulose acetate membranes using a DO experimental setup similar to the one described above for Lonsdale’s research. The diffusivity coefficient, determined using the time lag method, increased with the increase in the salt concentration, and the extrapolated value of diffusivity at zero salt concentration was taken to determine the salt permeability in DO. The salt permeability in DO was calculated as the product of the diffusivity and the

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21 distribution coefficient, determined in an i ndependent adsorption experiment. The values of the salt permeability in DO experiments were in good agreement with the values of the salt permeability in RO experiments calculated from Spiegler-Kedem model. Another comparison of the salt transport pa rameters in DO and RO processes was performed by Chaudry (2002). He used a sy mmetric lab-made RO cellulose acetate membrane and 0.025 to 0.2 mol L-1 feed solutions of NaCl and KCl. In DO experiments, the salt permeability was calculated as the product of the diffusion coefficient with the salt distribution coefficient, defined as the invers e of the salt partitioning coefficient K from the Kimura-Sourirajan model. The diffusion coeffi cient was calculated fro m the time lag method whereas the salt distribution coefficient was ca lculated from the limiting transport numbers of the cations and anion, respectively. In RO experiments, the salt permeability was calculated using the Spiegler-Kedem model. He found that the salt permeability in RO was almost twice as much as the salt permeability in DO. Further experiments with crystal violet Millipore filter paper has proved that this difference can not be attributed to the leaks in the membrane. He concluded that the differences in the salt permeability in DO and RO were a result of the high convective flux of salt (38 %) in the cellulose acetate membrane. 2.2.2 Salt and water transport in reverse osmosis The literature describing theory and practi ce of reverse osmosis is abundant. Each topic addresses its own niche of interest, whet her it regards membrane transport properties, calculations of concentration polarization and back diffusion coefficients, scaling and fouling, design of RO systems or manufacturing of novel membranes. The topic of interest for this research is the importance of diffusional a nd convective fluxes of salt in hyperfiltration membranes. This section is divide d in two parts. The first part presents the previous work on quantification of the salt diffusive and conv ective fluxes. The second part summarizes a

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22 research study which compared the Kedem-Kat chalsky model with the solution-diffusion model. 2.2.2.1 Diffusion and convection in hyperfiltration membranes In a review of the reverse osmosis membra ne and transport made by Soltanieh and Gill (1981), it is concluded that since the diffu sion of salt through the membrane is slow, the contribution of pore flow, and therefore the conv ective flux, is significant. The developments in the membrane manufacturing technology resulted in the production of pore-free membranes (actually, with pores size < 1nm), with improved rejection coefficients. In a more recent book edited by Malleviale et al. (1996) hyperfiltration membranes (reverse osmosis and nanofiltration) are referred to as diffusion controlled membranes. The Spiegler-Kedem model allows one to estimate the importance of the salt diffusive flux by calculating the percentage of the salt diffusive flux of the salt total flux. The calculation of the salt flux distribution is simple once the transport coefficients Lp, PRO, 1 and 2 are determined. A rough estimation of the impor tance of the diffusive flux is given by the salt –water coupling coefficient, 2. Some authors concluded that diffusion is the dominant transport process whenever the cal culated salt-water coupling coefficient, 2, is close to unity, without carrying out the calcula tions to determine the salt flux percentages (Marinas and Selleck, 1992; Urama and Marinas, 1997). Gilron et al. (2001) studied the transport of 1500 ppm and 15,000 ppm NaCl in commercial polypiperazine nanofiltration memb rane. According to the manufacturer, the rejection of NaCl by this membrane is 70%. The feed flux varied approximately between 20 Lm-2h-1 to 100 Lm-2h-1. The Spiegler-Kedem model was used to calculate the relative distribution of the salt flux through the membrane. The authors found that at least half of the salt flux is due to convective coupling, with th e diffusive flux decreasing with the increase in

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23 the feed flux. The relative distribution of NaCl flux in a commercial RO membrane (FT 30 produced by FilmTec) was studied by Bhanus hali et al. (2002), who found a very low contribution of the salt convective flux to the salt total flux. Chaudry (2002) used the Spiegler-Kedem model to calculate the percentage of diffusive and convective fluxes in symmetric lab-made cellulose acetate membranes. He found that 62.9% of the total flux for KCl and 57% for NaCl is attributed to diffusion transport. He calculated that less than 1% of th e total salt flux is due to ion-exchange capacity of the membrane and concluded that the rest of about 38.5% is due to the salt convective flux. The average values of 2 found by Chaudry at 25 oC were 0.931 for NaCl and 0.954 for KCl. There is no indication in this research pape r whether the concentration polarization was considered or not in the application of the Spiegler-Kedem model. 2.2.2.2 Comparison of RO models McCray et al. (1991) had compared the salt and water transport properties in asymmetric cellulose acetate membranes with di fferent acetyl content using two RO models. The first model, named the Kedem-Katchals ky model, is derived from irreversible thermodynamics and provides an identical set of transport equations as the Spiegler-Kedem model described in Section 2.1.3.1. The sec ond model, named the solution-diffusion model, assumes no convective salt flux, and it provides an identical set of transport equation with the Kimura-Sourirajan model, described in Section 2.1.3.2. The authors varied the acetyl content of the cellulose acetate membranes by hydrolyzing commercial reverse osmosis cellulose acetate membranes. They found that both water and salt permeabilities increased, and th e rejection coefficient and the salt-water coupling coefficient decreased with the decrea se in the membrane acetyl content. The calculated water permeability was the same for both models regardless the membrane acetyl

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24 content. The calculated salt permeability was the equal for the two models only for unhydrolyzed membranes, when the salt-water c oupling coefficient was closed to unity. As the membranes underwent hydrolysis, the membra ne rejection coefficient decreased and the salt-water coupling increased. Consequently, th e differences in the salt permeabilities from the two models increased, with a higher salt permeability for the solution –diffusion model than for the Kedem-Katchalsky model. The differe nces were attributed to the increase in the salt convective flux which is not accounted for in the solution-diffusion model. 2.2.3 Factors controlling the selectivity of salts in hyperfiltration membranes Taniguchi and Kimura (2000) have calculated the permeability in a commercial RO spiral wound membrane for different 1:1 and 1:2 chloride and sulfite salts as well as for the boric acid. The authors compared the permeability of the ions with their diffusivity in water. They found that except for the boric acid, the ion permeability increased with the increase in the ion diffusion coefficient in water. Several research papers have studied the dependence of the rejection coefficient for inorganic salts with common anion on the ph ysical and thermodynamic properties of the cations. Johnson (1975) considered the rejection of chloride salts of eighteen heavy metal in lab-made cellulose acetate RO membranes. The author reported that the percentage of the metal removal increases with th e decrease in the cation free energy of hydration and with the increase in the cation entropy at infinite dilu tion. Also, the cation partial molal volumes at infinite dilution were directly correlated to th e metal rejections. The author concluded that thermodynamic solution properties were the contro lling factors for the selective rejection of the heavy metal. Similar results were reported by (Fang and Chian, 1975; Fang and Chian, 1976). They studied the rejection of several alkali a nd alkali-earth halogen salts in cellulose acetate

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25 and aromatic polyamide membrane s. The rejection of ions with the same valence increased with the decrease in the ionic radii and with the increase in the cation entropy of hydration. It was concluded that the enthalpy of hydration of an ion could be used as a single parameter to determine the ionic rejection in a membrane. Matsuura et al. (1975) and Dickson et al. (1975) introduced the relative free energy of a salt as the parameter which controls th e salt permeability in both cellulose acetate and aromatic polyamide RO membranes. The relative free energy of an ion is the difference in the free energy of the ion at the membrane surf ace and in the bulk solution. The sign of the relative free energy determines whether an ion is attracted or repelled by the membrane. The permeability of a salt varies exponentially with the weighted sum of the relative free energy parameter of the salt ions. 2.2.4 Conclusions on the previous relevant research The result reported in the literature on the comparison of salt permeability in RO and DO are controversial. Sherwood et al. (1967) has found larger permeation rate in the DO experiments than in the RO experiments, whereas Chaudry (2002) reported lower salt permeability in DO than in the RO. Finally, L onsdale et al. (1971), Matsuda and Kamizawa, (1984), and Mori et al. (2000) calculated equa l salt permeability coefficients for the two processes. Several methods of calculating the salt permeability in DO are used in the literature, which might be the source of the c ontradictory results. Moreover, most of the research conducted in DO disregards the phenomena of salt dilution occurring at the membrane surface. In 1981, Soltanieh and Gill summarized the fi ndings of the current research at that time and concluded that since the diffusion of salt though the membrane is slow, the contribution of the convective flux is significant. Fifteen years later, Mallevialle et al. (1996)

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26 referred to hyperfiltration membranes (which are RO and nanofiltration membranes), as diffusion controlled membranes. Gilron et al (2001) has found that in a nanofiltration membrane with a rejection coefficient of 70%, at least half of the salt total flux is due to convection. Chaudry (2002) determined that the salt diffusion fluxes in RO membranes contributed by 57% to 63% to the total salt flux. Opposing, Bhanushali et al. (2002) reported that the convective salt flux in RO membranes is insignificant. According to McCray et al. (1991), the solution-diffusion model and the Ke dem-Katchalsky model provided the same salt permeability only for membrane s and salts with a rejection coefficient larger than 94%. These contradictions on the importance of the sa lt diffusive and convective fluxes originate in improper, simplified usage of the theoretical models. The rejection of several inorganic salts in RO processes has been reported to increase with the increase in the cation hydration radii and increase in the cation enthalpy and entropy of hydration. The relative free energy has b een introduced in 1975 as a parameter that controls the solute permeability in hyperfiltration membranes. These theories can be useful in predicting the salt permeability in hyperfiltration membranes and need to be verified for the new types of commercial available membranes.

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27CHAPTER 3 METHODOLOGY This chapter describes the technical procedure utilized in performing the experimental part of this research. The chem ical preparation and the instrumentation are described first followed by the experimental procedures. The types of experiments are: a direct osmosis (DO) study a reverse osmosis study (RO) using a flat sheet membrane a reverse osmosis study (RO) using a spiral wound membrane For each experiment type, a diagram of the equipment set-up is shown with each component briefly described. The details of the te st cells are presented in this chapter and the detailed drawings of the cells are included in A ppendix A. The description of each type of experiment contains a summary table of the membranes used for that stage and their manufacturer specifications, as well as the sa lts solutions used as feedwater, their concentration and the system operating parame ters. The operation of each experimental setup is described in separate s ubsections. The sampling and the measurement protocols, as well as the procedure for the replicate runs are presented for each type of experiment. 3.1 Chemicals Preparation The feedwater for all the experiments is prepared using deionized (DI) water and analytical grade salts from Fisher Scientific. DI water is produced from tap water using a lab scale RO unit. The conductivity of the product is 20 5 S. Only simple binary solutions are considered in this research. The concentra tion of the solutions is calculated from the conductivity measurements using specific conductance for each salt at specific temperature

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28 and concentration. The specific conductance for the salts is taken from the Handbook of Chemistry and Physics (1967). 3.2 Instrumentation The instrumentation used is presented in Table3.1 together with calibration requirements, manufacturer, readings range and accuracy. The sensors presented in Table 3.1 are connected to a computer for data collecti on and analysis using a LabPro interface and a LoggerPro software acquired from Vernier Software & Technology. Table 3. 1 Instrumentation and its specifications. Nr. Instrument Manufacturer Model Calibration Required Range Accuracy 1 Analytical Balance Mettler Toledo Delta Range AE 260 No 0-81g 0.1mg 2 Digital Caliper Fowler ProMax No 0-150mm 0.02 mm 3 Conductivity Probe Vernier Software &Technology Conductivity Probe Yes 0-200 S/cm 020000 S/cm 1% 4 Conductivity Meter &Probe Cole-Parmer Field Cole-Parmer Conductivity Meter/ Yes 0-2 S/cm 0-20 S/cm 0-200 S/cm 0-2000 S/cm 0.2% 0.15% 0.1% 0.15% 0.30% 5 Flowmeter McMillan Model 111 No 20-200 mL/min 1002000 mL/min 3% 6 Pressure Gauge Wika 13x.53 No 0-1000 psig 0.15% 7 Pressure Transmitter Cole-Parmer Economical 0.25% Accuracy Pressure Transmitter No 0-1000 psig 0.25% 8 Stopwatch Cole-Parmer Easy-Grip Stopwatch No 24 h 1.5 s/day 9 Electronic Toploading Balance Ohaus Adventurer No 0-3100g 0.1g

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29 3.3 Direct osmosis experiments The diffusion experiments are conducted under controlled laboratory conditions at the ambient temperature of 23 0.5 oC. The diffusion apparatus consists of a diffusion cell, a peristaltic pump, DI and salt solution ve ssels, magnetic stirrers, tubing and the instrumentation. A diagram of the direct osmo sis experimental set-up is presented in Figure 3.1. Table 3. 1 (Continued) Instrumentation and its specifications. Nr. Instrument Manufacturer Model Calibration Required Range Accuracy 10 Thermistor Vernier Software &Technology Stainless Steel Temperature Probe No -25 OC to 125OC 0.3% 11 Voltage Probe Vernier Software &Technology Voltage Probe No -10 to 10V 0.05% 12 Volumetric Flask Kimble Serialized and Certified Class A with Stopper No 0-10 mL 0.2% 13 Volumetric Flask Kimble Serialized and Certified Class A with Stopper No 1000 mL 0.03% Solution Chamber DI Vessel Magnetic Stirrer DI Chamber Peristaltic Pump Solution Vessel Magnetic Stirrer T C T C PC Figure 3. 1 Experimental set-up for the direct osmosis experiments.

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30 The diffusion cell is machined from stock (acrylic) in the University of South Florida, College of Engineering Shop. It consis ts of two chambers, the salt solution chamber (Figure A.1) and the DI water chamber (Figure A.2). The dimensions of the cell body are 18.9 cm x 14 cm x 5.8 cm. The height of the flow channel is of 0.2 cm in both chambers. The membrane separates the two chambers and has an effective surface area of 88.7 cm2. The skin layer of the membrane faces the solution chamber and the support layer faced the DI chamber. A spacer is placed in the flow channel of each chamber. The spacer is a diamond shaped mesh made of polypropylene with dimensions of 7 cm x 12.6 cm. The circulation of DI water and salt solution is maintained at constant flowrate of 187 mL/min using a two head peristaltic pump (model MasterflexL/S from Cole-Parmer). DI water and salt solution vessels are covered 4.7 liters Nalgene cylindrical jar baths. Holes are drilled in the cover of each solution vessel to allo w the insertion of tubes and instrumentation. Each vessel sits on a magnetic stirrer and one ma gnetic stir bar is introduced in each vessel to maintain complete mixing throughout the r un. The tubing used is flexible TygonLab from Norton. All the piping is 1/4”. A set of conductivity and stainless steel temperature probes is inserted in each of the two solution vessels. The data is recorded by a PC for further analysis using a computer interface and a software, as described in Section 3.2. 3.3.1 Diffusion cell operation DI water is pumped from the DI water vessel to the DI water chamber and back to the DI water vessel whereas the salt solution is pumped from the salt solution vessel to the salt solution chamber and back to the salt solution ve ssel. Initially, 2 liters of salt solution is prepared as described in Section 3.1 and poured into the salt solution vessel and also 2 liters of DI water is poured in the DI water vessel.

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31 Both the DI water vessel and the salt solutio n vessel are weighted in the beginning of each run. The DI water vessel and the salt solution vessel are weighted again at the end of each run to determine the volume of water that diffused through the membrane from the DI vessel to the solution vessel. The weight measur ements for the DI water vessel and the salt solution vessel at the end of the runs is perfo rmed after both chambers of the diffusion cell and the tubing are emptied and the emptied wate r is pored back to the corresponding vessels. The difference in the mass of water lost from the DI vessel and the mass of water gained in the solution vessel is due to evapor ation. Half of the total evaporated water mevap is considered to come from the DI vessel and half from the solution vessel. The total water mass considered to diffuse to the solution vessel is calculated as the sum of two terms: 1) the difference in the weight of the solution vessel between the beginning (mw, t=0) and the end of the run and (mw, t= ) 2) half of the total water evaporated. The water flux Jw, DO is calculated by dividing mass of the total water diffused by the duration of a run (600 minutes) and by the active surface area of the membrane S (88.7 cm2), as shown in Equation 3.1. It represents an average of the pure water flux over the duration of a run. DOevap w,t w,t0 w,1 mmm 2 J S (3.1) The membranes studied in the direct osmosi s experiments are presented in Table 3.2, together with their characteristics and manufacturer specifications. Four flat sheet membranes are considered in this study: a se awater aromatic polyamide membrane (AD), a seawater aromatic polyamide -thin film composite membrane (SE), a brackish water cellulose acetate membrane (CG), and a nanofiltration cellulose acetate membrane (CG), all produced

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32 by GE Osmonics. The membranes are selected based on their differences in the product flux and salt rejection: the cellulose acetate (CA) is a high water production but low rejection membrane whereas the polyamide (PA) is a low water production but high rejection membrane. The membrane types are representatives of the two general categories of RO membranes used in practice today. Each membrane is cut from a one square foot sheet (929 cm2) in order to fit the diffusion cell and stored for 24 hours in fresh DI water at room temperature to keep the membrane saturated. Table 3. 2 Manufacturer specifications for the membranes used in the direct osmosis experiments. Membrane Manufacturer Name and Application Membrane Polymer pH Range Typical Product Flux gfd @ psi (mLm-2min @ atm) Rejection % AD -Seawater PA 4-11 15 @ 800 (425 @ 54) 99.5 CG -Brackish Water CA 2-8 30 @ 420 (849 @ 29) 92 CK -Nanofiltration CA 2-8 28 @220 (792 @ 15) 92 for divalent SE -Seawater TFC 2-11 22 @ 425 (623 @ 29) 98.9 Note: The typical product flux and the rejection are given for 2000 mgL-1 NaCl feed solution at 25oC. The salt solutions and their concentrations fo r the direct osmosis runs are presented in Table 3.3. The solutions are prepared as descri bed in Section 3.1. The conductivity probes are calibrated before each run using two standard solutions provided by Oakton. Conductivity and temperature measurements are automatically taken every minute for duration of 10 hours corresponding to each run. The data is stored in a computer and used for further analysis. Concentrations are evaluated from the conductivity readings. The system is cleaned after each

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33 run by rinsing the diffusion cell and the tubing with DI water until the conductivity of the effluent water is the same as the conductivity of the DI water. Duplicates for the direct osmosis runs for each membrane type are conducted by replacing the membrane with a new piece cut from the same one square foot sheet used in the first run. Duplicate salt solutions are run in the same order as for the first run for each particular membrane. 3.3.2 Determination of pure water permeability coefficient, A' A very similar apparatus with the one descri bed in Section 3.4 is used to determine the pure water permeability A' for the membranes used in the direct osmosis experiments. The only difference is that the RO flat sheet membrane cell is replaced by a replica cell made in the University of South Florida, College of Engineering Shop. The replica cell accommodates membranes with the same dimensions as the membranes used in the direct osmosis experiments (active surface area of 88.7 cm2). After the direct osmosis runs are finished for all the salts for a membrane, the membrane is rinsed with DI water and placed in the replica cell, with the skin layer facing the permeate side of the cell. The membranes are not conditioned for these runs. The feed water Table 3. 3 Salt solutions and their concentr ations in the direct osmosis experiments. Salts Concentration (molL-1) Salts SE AD CG CK LiCl NaCl KCl 0.01, 0.02, 0.05, 0.1, 0.15, 0.2 MgCl2 CaCl2 0.02, 0.05, 0.1 BaCl2 0.05 0.05 0.05 0.05 LiAc NaAc KAc MgAc2 CaAc2 0.05, 0.1 Note: Ac represents the acetate ion CH3COO-.

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34 is DI water. The operating pressures for all four membranes are 300 psi, 250 psi, 200 psi, 150 psi and 100 psi, respectively. The pulse dampen er is set at half the operating pressure. The product sampling and the measurements of th e product flowrate are performed at each operating pressure as described in Section 3.4.1. 3.4 Reverse osmosis flat sheet membrane experiments A conventional lab scale RO apparatus is used to carry out the reverse osmosis experiments. The apparatus consists of a flat sheet membrane cell, a high-pressure pump, a pulsation dampener, a feedwater tank, a refri gerated recirculator, needle valves, and instrumentation. A diagram of the apparatus is presented in Figure 3.2. The flat sheet membrane cell is made of stainless steel and it is manufactured by Osmonics (model Sepa CF). The cell body dimensions are 16.5 cm x 21.3 cm x 5.2 cm. Diagrams of the bottom and top side of the cell are presented in Figure A. 4 and Figure A.5, respectively. The bottom side of the cell is referred as the high pressure of f eed side and the top side is referred as the low pressure or permeate side. The cell is held in a steel holder which with 6 steel bolts to seal the membrane compartments. The holder is made in the University of South Florida, College of Engineering Shop. The active surface area of the membrane is 139 cm2. The feed channel height is 0.2 cm. No feed spacer is used in the flat sheet runs. The bottom side of the cell is fed by a high-pressure diaphragm pump model M-03-E, made by Hydra-cell which provides a flow of 8.3 Lmin-1. Flexible stainless steel tubing is used to connect the pump to the cell. Braided PVC tubes are used for the rest of the piping. All the piping is 1/4” except for the permeate side of the cell for which the piping is 1/8”. A bypass valve installed after the pump is used to maintain the feed flowrate for the cell at 2 Lmin-1. A Blacoh H1020B pulsation dampener is in stalled between the pump and the cell to smooth the flow from the pump. The dampener is initially pressurized at 200 psi using an air

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35 hand pump and then gradually depressurized so that dampener bladder pressure is always maintained half the system operating pressure A Nalgene HDPE 20 liters tank is used to hold the feed solution. A general purpose mixer from Cole-Parmer is used to keep the solution in the feedwater tank completely mixed. The temperature in the feed tank is maintained at 23 0.2oC by using a refrigerated recirculator (Cole-Parmer Polystat model). The temperature in the feed tank is measur ed and recorded using a stainless steel temperature probe described in Table 3.1. Conduc tivity of the feed solution is measured and recorded using a conductivity probe also describe d in Section 3.2. The operating pressure is adjusted at the desired value by using the by pass needle valve and the concentrate needle valve located downstream the cell, on the concentrate side (Figure 3.2). The concentrate flowrate is measured and recorded using a dig ital flowmeter described in Section 3.2. Since the product flowrate represented less than 1% of the concentrate flowrate, the feed flowrate can be approximated as the measured concen trate flowrate. The operating pressure is monitored using a pressure gauge and it is reco rded using a pressure transmitter (Section 3.2). RO Cell Feed Tank T C Refrigerated Recirculator P F P High Pressure Pump Pressure Transmitter Flowmeter Product SamplingTap PC Conductivity Temperature Probe Probe Pulsation Dampener Pump Bypass Figure 3. 2 Experimental set-up for the RO flat sheet membrane experiments.

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36 The concentrate and the product are directed to the feed tank. When samples are taken from the product, they are poured back into the feed tank after conductivity measurements. 3.4.1 RO flat sheet membrane operation The membranes used in these experiments ar e presented in Table 3.4. They are the same membranes used in the direct osmosis st udy except for the SE membrane which is only used for the direct osmosis experiments. The manufacturer specifications are presented in Table 3.2. The membrane pieces are cut from a 1 square foot sheet in order to fit the flat sheet cell and stored for 24 hours in fresh DI water at room temperature to keep the membrane saturated. Then the membrane is placed in the cell with the skin layer facing the high pressure side and conditioned in the cell by feeding 0.05M KCl for 5 hours at 450 psi. The system is further flushed with tap water and finally finished with DI water. After that, the feed solutions of LiCl, NaCl, KCl, MgCl2, CaCl2, and BaCl2 are tested sequentially, at the operating pressures presented in Table 3.4. The feedwaters are prepared as described in the Section 3.1 at a concentration of 0.05 molL-1 for all the runs. The concentrations are calculated form the measured conductivity. For each salt solution and each membrane, the system is first operated at the highest pressu re (400 psi for the AD and CG membranes, and 350 for the CK membrane) and let reach equ ilibrium. After setting the pressure, it takes Table 3. 4 Membranes, salt solution and their concentrations, and the operating pressure for the RO flat sheet membrane experiments. Membrane Name Salts Feed Concentration (molL-1) Operating Pressure (psi) AD 400, 350, 300, 250, 200, 150 CG 400, 350, 300, 250, 200, 150 CK LiCl, NaCl, KCl MgCl2, CaCl2, BaCl2 0.05 350, 300, 250, 200, 150

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37 approximately 60 minutes for the product fl owrate to reach a constant value. The conductivity of the product steadily declined and the equilibrium is reached when it decreases by less than 2% over 30 minutes. Three product samples are consecutively collected at the equilibrium state corresponding to the highest pr essure. The product flow rate is determined volumetrically by recording the time to fill a 10 mL volumetric flask. The conductivity of the product is measured using the auto temperat ure correction probe from Cole-Parmer (Table 3.1) and the product concentration is determined from the product conductivity measurements. Next, the pressure is decreased by 50 psi a nd the system is allowed to re-equilibrate. Three samples of the product are again taken as described earlier. This procedure continued for all the pressures listed on Table 3.4 for each membrane. Tap water and DI water are used to flush the system between runs of different salt solution. After all the salt solution runs are completed with one membrane, the procedure cycle is repeated using DI as feedwater. In this case, the equilibrium is declared when the increase of the product flow is less than 2% over 30 minutes. The duplicates of the RO flat sheet runs for a certain membrane are perform by repeating the sequence of procedures described in this section with a new piece of membrane of the same type. 3.5 Reverse osmosis spiral wound membrane experiments The reverse osmosis experiments carried out with a spiral wound membrane are very similar to those carried out with a flat sheet membrane. The diagram of the experimental setup is shown in Figure 3.3. The membrane element is manufactured by Dow FilmTec (SW302514 model). The main differences from the RO-flat sheet cell are the membrane configuration and the membrane surface area. The membrane characteristics are presented in Table 3.5 and a drawing of the membrane configuration is shown in Apendix A, Figure A.7.

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38 The membrane element dimensions are 6.35 cm (2.5”) diameter and 35.56 cm (14”) length, and the total surface area is 5574 cm2 (6 ft2). The feed channel height is 1.65 mm. The membrane pressure vessel is made of reinforced fiberglass and has a rated maximum operating pressure of 1000 psi. The pressure vessel is produced by Crans Engineering. The high pressure pump, pulsation dampener, refrigerated recirculator and the instrumentation are identical with those used fo r the flat sheet cell (Section 3.4). Due to the large surface area of the membrane, there is no need to bypass any of the pump flow as is done in the RO flat sheet membrane expe riments. The pump capacity is 8.33 Lmin-1 (2.2 galmin-1). The pulsation dampener is precharged at 130 psi which is half of the system pressure. A Nalgene 114 liters HDPE tank is used to hold the feedwater. The product flowrate is sufficiently large to be measured by a digital flowmeter (model 111 from McMillan) which is places in the product line (Figure 3.3). Conductivity and temperature probes are also inserted in the product line. Temperature of the feedwater is maintained constant at 23 0.2oC.

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39 RO Cell Feed Tank T C Refrigerated Recirculator P F P High Pressure Pump Pressure Transmitter Flowmeter PC Conductivity Temperature Probe Probe C T F Pulsation Dampener Figure 3. 3 Experimental set-up for the RO spiral wound membrane experiments. Table 3. 5 Manufacturer specifications for the spiral wound membrane, the salt solutions and their concentrati ons for the RO spiral wound membrane experiments. Membrane Manufacturer Name and Application Membrane Polymer Salts Salts Concentration (molL-1) pH Tolerance Product Flux (gfd@psi) Rejection (%) SW30-2514 Seawater TFC LiCl NaCl KCl MgCl2 CaCl2 BaCl2 0.05 2-11 16.7 @ 800psi 99.4

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40 3.5.1 Spiral wound membrane operation The salt solutions and their concentration ar e identical to those used for the RO flat sheet cell runs. All the RO spiral wound runs are performed at 260 psi. Product sampling is not necessary for the spiral wound runs because all the necessary readings are automatically performed by the probes and recorded by a PC. The membrane is conditioned with a 0.05 molL-1 KCl for 5 hours at 260 psi. The system is further flushed with tap water and fi nally flushed with DI water. After that, the feed solutions of LiCl, NaCl, KCl, MgCl2, CaCl2, and BaCl2 are tested successively at 260 psi. The run for each salt solution is fini shed when the product water conductivity and flowrate are at equilibrium. The equilibrium is based on the same criter ia as that of RO flat sheet membrane experiments (Section 3.4.1). The system evolutio n to the equilibrium state can be visualized on the PC screen by monitoring the product flow rate and the product conductivity. At the end of the runs, the pure water permeability coefficient, A, is determined using DI water. Duplicate runs are performed using the same membrane.

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41CHAPTER 4 RESULTS This chapter presents the results obtained from the three types of experiments described in Chapter 3. First, the results obt ained from the direct os mosis experiments are presented, followed by the results from the RO flat sheet membrane experiments and finally, the results from the RO spiral wound membrane experiments. For each type of the experiments, the results are presented first for the salt transport and next, for the pure water transport. The differences among several type s of membranes (seawater, brackish water and nanofiltration) in the transport of the 1:1 and 1: 2 salts as well as the order of salt permeation rate for the twelve studied salts are emphasized throughout this chapter. The direct osmosis (DO) experiments results section presents the derivation of the equation used in calculating the salt permeability coefficient (D/K )DO and the values obtained for (D/K )DO for four membranes AD (seawater), CG (brackish water), CK (nanofiltration), and SE (seawater) For the seawater membrane SE, the effect of the salt solution concentration is shown together with the differences in the salt permeation for pairs of salts with common cation but different ani ons. The differences in the pure water flux and pure water permeation for the four membranes are presented next. The effect of the salt solution concentration on the pure water flux is highlighted. The results from the RO flat sheet memb rane experiments are presented from the perspective of two models: the Spiegler-Kedem (SK) model and the Kimura-Sourirajan (KS) model. The parameters characterizing th e salt transport in the SK model are PRO, and which represent the salt permeability, the reflec tion coefficient and the salt-water coupling coefficient, respectively. The parameters PRO and are calculated for three cases: 1) the

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42 concentration polarization is neglected; 2) th e concentration polarization is calculated at 1 = 1; and 3) the concentration polarization is calculated by combining the thin film theory with the Sherwood correlation. Multiple comparisons are made for the salt transport parameters obtained in the three cases for each of the three membranes AD, CG, and CK. The values of the salt permeability obtained from the SK model, PRO, are compared with the values of the salt permeab ility obtained from the KS model, (D/K )RO, as well as with the values of the salt permeability fro m the direct osmosis experiments, (D/K )DO. The pure water transport results are also compared from the perspective of the two models. The KS model is also used to determine the salt and water transport parameters in the case of RO spiral wound membrane experiments. The tran sport parameters obtained with the spiral wound membrane are compared with the transport parameters obtained with the RO flat sheet membrane. 4.1 Salt and water transport in the direct osmosis (DO) experiments This Section is divided in two parts. The firs t part (Section 4.1.1) presents the results obtained for the salt permeation coefficient, (D/K )DO, whereas the second part (Section 4.1.2) presents the results obtained for the transport of pure water. 4.1.1 Salt transport in the direct osmosis experiments The equation governing the transport of salts across the membrane assumes that the salt flux and the pure water flux are not coupled within the membrane. The salt is transported through the membrane due to the differential concentration across the membrane. Therefore, the salt transport in direct osmosis is diffusion controlled. Fick's law of diffusion characterizes the diffu sive transport of ionic species in porous materials and it relates the diffusion flux to the differential concentration of the species across

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43 the porous material. Details of the derivation of Equation 4.1 are presented in Appendix B. Equation 4.2 represents the definition of the molar flux. SSDI mem mem DOD JCC K (4.1) SdN J Sdt (4.2) JS represents the number of moles which diffuses through the surface area S in unit time (cmmin-1cm-2), D is the diffusion coefficient in the membrane (cm2s-1), K is the partitioning (solubility) coefficient between me mbrane and solute which is considered the same on both sides of the membrane, is the membrane thickness (cm), (CS)mem is the concentration of the salt solution at the membrane surface (molL-1), and (CDI)mem is the concentration of DI water at the membrane surface (molL-1). The quantity (D/K )DO represents the salt permeability coefficient for diffusion and is considered as an intrinsic parameter. In Equation 4.2, dN is the number of moles of solu te transported in time dt through the surface S. The salt solution concentration at the membrane surface (CS)mem is approximated by the bulk concentration of the salt solution CS. This approximation is based on the fact that the concentration polarization is insignificant in the direct osmosis experiments due to the following: 1) the system run in cross-flow filtration, 2) no pressure is applied on the salt solution side, 3) DI water diffuses across the me mbrane in the opposite direction of the salt (due to the osmotic pressure) impeding the form ation of salt layer on the membrane surface, 4) the use of spacers as turbulence promoters on both sides of the membrane, and 5) the relative short duration of each run which is followed by cleaning with DI water. The concentration of the DI water at the membrane surface (CDI)m is equal to the bulk concentrations of the solution in the DI side, CDI. Therefore Equation 4.1 becomes:

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44 SSDI DOD JCC K (4.3) The experimental results show with a re gression coefficient of 0.98 that salt concentration on both sides of the membrane vary linearly with time. The decrease in the salt solution concentration is represented by Equation 4.4 and the increase of the concentration in the DI water is represented by Equation 4.5: SS tt0CCt (4.4) DIDI tt0CCt (4.5) In these equations, and are the slopes and (Cs) t=0 and (CDI) t=0 the intercepts of the plot of concentration vs. time. The values of , (CS) t=0 and (CDI) t=0 are specific to each salt solution, concentration, and membrane. Their va lues are determined graphically by plotting the concentration versus time from t = 0 (beginning of the run) to t = (end of the run). The salt permeability, (D/K )DO, is calculated using Equation 4.6, which is obtained by integrating Equation 4.1 over the duration, of each run and substituting Equa tions 4.2, 4.4 and 4.5 into 4.3. Details of the calculations are provide d in Appendix B. In this approach, (D/K )DO is considered independent of the solution concentration CS because CS varied by less the 5% from start to finish for each run. DO sDI t0 t0DN1 KS CC0.5() (4.6) The salt permeability coefficient (D/K )DO is calculated using Equation 4.6 for LiCl, NaCl, KCl, MgCl2, CaCl2 and BaCl2 at 0.05 molL-1 for all four membranes. The calculated

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45 coefficients are presented in Table C.1. The sa lt permeates at the lowest rates for the seawater membranes AD (average of 1.5 x10-7 cms-1) and SE (average of 5.9 x 10-7 cms-1). The salt permeates at higher rates for the brackish water membrane CG (average of 54.7 x 10-7 cms-1) and nanofiltration membrane CK (average of 100.1 x 10-7 cms-1). Figure 4.1 illustrates the differences in the salt permeability, (D/K )DO, for the four membranes and for the 1:1 and 1:2 salts. The (D/K )DO is plotted on a logarithmic scale to illustrate the differences in the salt permeability for seawater membranes and nanofiltration membranes. The 1:1 salts permeated at a higher rate than the 1:2 salts for all four membranes. The smallest variation between the average permeab ility of 1:1 salts and the average permeability of 1:2 salts occurs in the seawater membrane SE (22%). The differences between the average permeability of 1:1 salts and the 1:2 salts fo r the AD, CG and CK are 57%, 64% and 56% respectively. Among the 1:1 salts, LiCl has the slowest permeation rate for each of the four membranes while MgCl2 has the slowest permeation rate for each of the four membranes among the 1:2 salts. The order of permeati on in direct osmosis experiments is Mg < Ca < Ba < Li < Na < K in each of the four membranes except for the AD for which the order is Mg < Li < Ca < Ba < Na < K.

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46 SEADCGCK 1xe-171xe-161xe-151xe-141xe-131xe-121xe-11 (D/K)DOMembranes LiCl NaCl KCl MgCl2 CaCl2 BaCl2 Figure 4. 1 Salt permeability for the different membranes at 0.05 molL-1 in the direct osmosis experiments. Figures 4.2 and Figure 4.3 present the vari ation of the salt permeability coefficient with the salt solution concentration Cs for the SE membrane. The values of salt permeability coefficients in these plots are tabulated in Tables C.2 and C.3. The salts having different cations but the common anion Clare referred as chlorides a nd the salts having different cations but the common anion Acare referred as acetates. The salt permeability decreases with the increase in the salt so lution concentration for both chlorides (Figure 4.2) and acetates (Figure 4.3).

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470.000.050.100.150.200.25 3.0 4.5 6.0 7.5 9.0 10.5 (D/K)DO x 10-7 (cm s-1)Solution Concentration Cs (mol L-1) LiCl NaCl KCl MgCl2 CaCl2 Figure 4. 2 Variation of salt permeability with con centration for chlorides in SE membrane in direct osmosis experiments. 0.000.050.100.15 1 2 3 4 5 6 7 8 (D/K)DO x 10-7 (cm s-1)Solution Concentration Cs (mol L-1) LiAc NaAc KAc MgAc2 CaAc2 Figure 4. 3 Variation of salt permeability with concentration for acetates in SE membrane in direct osmosis experiments.

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48 Figure 4. 4 and Figure 4. 5 present the salt permeability for pairs of salts which have a common cation but different anion (such as the pair LiCl and LiAc or the pair MgCl2 and MgAc2) for the SE membrane. The values of sa lt permeability coefficient are tabulated in Table C.4. The acetates permeate slower than th e chlorides at both concentrations (Figure 4.4 at 0.05 molL-1 and Figure 4.5 for 0.1 molL-1) and for all the studied ions. Li+Na+K+Mg+2Ca+2 4 5 6 7 8 9 (D/K)DO x 10-7 (cm s-1)Chloride Salts Chlorides Acetates Figure 4. 4 Comparison of salt permeability for chlorides and acetates at 0.05 molL-1 in direct osmosis experiments.

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49Li+Na+K+Mg+2Ca+2 3 4 5 6 7 8 (D/K)DO x 10-7 (cm s-1)Cations Chlorides Acetates Figure 4. 5 Comparison of salt permeability for chlorides and acetates at 0.1 molL-1 in direct osmosis experiments. 4.1.2 Pure water transport in the direct osmosis experiments Table 4.1 shows the average values of the pure water parameter, A', determined as described in Section 3.3.2 at different operati ng pressures. The two seawater membranes, SE and AD, have close values for the pure water pe rmeability A' (A' is 22% higher for SE than for AD) whereas for the brack ish water membrane, CG, and the nanofiltration membrane, CK, the pure water permeability is considerably higher. Table 4. 1 Pure water permeability. Membrane SE AD CG CK A' x 10-6 (gs-1cm-2psi-1) 0.44 0.34 2.60 3.78 The pure water flux Jw, DO is calculated for each salt and each membrane using Equation 3.1. The pure water flux for the four membranes studied when the salt solution

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50 concentration is 0.05 molL-1 is presented in Figure 4.6 and the data is tabulated in Table C.6. The water flux averaged over all the six salts st udied is the lowest for the SE membrane (6.0 x 10-6 gs-1cm-2) and the largest for the brackish water membrane CG (24.7 x 10-6 gs-1cm-2). SEADCGCK 0 5 10 15 20 25 30 35 Jw, DO x 10-6 (g s-1 cm-2)Membranes LiCl NaCl KCl MgCl2 CaCl2 BaCl2 Figure 4. 6 Pure water flux for different membranes at 0.05 molL-1 in the direct osmosis experiments. The pure water flux is higher for the 1:2 salts than for the 1:1 salts for all the membranes. The difference between the 1:1 an d 1:2 salts is lowest for the SE membrane (28%) and largest for the CK membrane (66%). The pure water flux varies within 10% for the 1:1 salts averaged over the four membranes and within 1% for the 1:2 salts averaged over the four membranes. Details of the calculations are presented in Table C.6. Figure 4.7 and Figure 4.8 present the variation of the pure water flux with solution concentration Cs for the SE membrane. The values of salt permeability coefficient in these figures are tabulated in Tables C.7 and C.8. The pure water flux increased with the increase of the solution concentration for all chlori des (Figure 4.7) and acetates (Figure 4.8).

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51 Figure 4.9 presents the comparison of the pure water flux for pairs of salts which have a common cation but different anion for th e SE membrane. The differences in the pure water flux for 1:1 salts, including chlorides a nd acetates, are less than 7% at 0.05 molL-1 and less than 1% at 0.1 molL-1 (Table C.8). The differences in the pure water flux for the 1:2 salts, including chlorides and acetates, are less than 1% for both concentrations of 0.05 molL-1 and 0.1 molL-1 (Table C.8).

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520.000.050.100.150.20 0 2 4 6 8 10 Jw, DO x 10-6 (g cm2s-1)Solution Concentration Cs (mol L-1) LiCl NaCl KCl MgCl2 CaCl2 Figure 4. 7 Variation of pure water flux with concentration for chlorides in SE membrane in direct osmosis experiments. 0.000.050.100.15 0 2 4 6 8 10 Jw, DO x 10-6 (g cm-2s-1)Solution Concentration Cs (mol L-1) LiAc NaAc KAc MgAc2 CaAc2 Figure 4. 8 Variation of pure water flux with c oncentration for acetates in SE membrane in direct osmosis experiments.

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53 4.2 Salt and water transport in the RO flat sheet membrane experiments Two conceptually different models are used in calculating the salt and water parameters of transport for the RO flat sheet cell experiments. The models are described in detail in Chapter 2, Section 2.1.3. Finally, th e salt permeability coefficients determined for the RO flat sheet membrane experiments are co mpared with the salt permeability coefficients obtained in the direct osmosis experiments. 4.2.1 Salt permeability in the Spiegler-Ked em model the absence of concentration polarization The parameters of salt transport in the Spiegler-Kedem (SK) model are calculated for three cases. First, the concentration at the membrane wall is considered equal to the concentration of the bulk feed solution (i.e. c oncentration polarization is neglected); second, the concentration at the membrane wall is calculated taking 1 = 1; and third, the Li+Na+K+Mg+2Ca+2 0 2 4 6 8 10 12 14 16 Jw, DO x 10-6 (g cm2s-1)Cations Chlorides at 0.05M Acetates at 0.05M Chlorides at 0.1M Acetates at 0.1M Figure 4. 9 Comparison of the pure water flux for chlorides and acetates at two concentrations in SE membrane in direct osmosis experiments.

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54 concentration at the membrane wall is calcu lated by combining the film theory with Sherwood correlation. Although the parameter 1 characterizes the salt transport, it is presented in Section 4.2.3 together with the results for the water transport. In the first case, the salt permeability, PRO, and the salt-water coupling coefficient, are calculated using Equation 2.10 from Chapter 2. The results are presented in Table 4.2, together with the salt diffusive flux, Jdiff, as percentage of the total salt flux, JS. The salt permeability coefficient for the direct osmosis experiments (D/K )DO is also listed in the Table 4.2 for a better comparison with the salt permeability PRO When the concentration polarization is negl ected, the salt permeated at a higher rate in the RO flat sheet membrane experiments th an in the direct osmosis experiments for all three membranes studied. The differences are the smallest for the seawater membrane, AD, and the highest for the nanofiltration membrane, CK. The (D/K )DO is on average, three times less than PRO for the seawater membrane, five times less for the brackish water membrane and nine times less for the nanofiltration membrane Similar to the results from the direct osmosi s experiments, the 1:2 salts have a lower permeability coefficient than the 1:1 salts for all three membranes. The order of the permeation rate for the studied salts in the RO flat sheet membrane is the same as the order of permeation rate shown in the direct osmosis study. According to the PRO, the order of permeability is given by Mg < Ca < Ba < Li < Na < K for all three membranes. As described in Section 4.2.3, Chapter 2, the salt-water coupling coefficient, is zero for no coupling salt-water and one for the pe rfect coupling of the salt-water transport. An estimation of the strength of the salt-water coupling is actually given by 1. In the first case of SK model, the strength of the salt-water coupling is lowest for the seawater membrane AD (0.013 on average), followed by the brackish water membrane CG (0.162 on

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55 average) and by the nanofiltration membrane CK (0.421 on average). For all three membranes, the strength of the coupling salt-water is lower for the 1:2 salts than for 1:1 salts. The differences in the salt-water coupling coeffi cient between 1:2 salts and 1:1 salts are the highest for the nanofiltration membrane CK ( 70 %) and lowest for the seawater membrane AD (0.9 %). The strength of the coupling salt-wat er increases is the same order as the salt permeability coefficient PRO increases, which is Mg < Ca < Ba < Li < Na < K. When concentration polarization is neglected in the SK model, the flux of salt permeating the membrane due to diffusion Jdiff represents, on average, 29% of the total salt flux Jtotal for the AD membrane. For the CG membrane, Jdiff is, on average, 38% from the total salt flux, and for the CK membrane, Jdiff is on average 22% from the total salt flux. The diffusive flux has a higher contribution to the total flux for the 1:2 salts than for the 1:1 salts for the CG and CK membranes. The diffusive flux has a lower contribution for the 1:2 salts than for the 1:1 salts in the case of AD membrane. The values of Jdiff/JS do not show any order for the six salts for any of the three membranes.

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56 4.2.2 Salt permeability in the Spiegler-Ked em model concentration polarization The salt permeability coefficient, the salt-water coupling coefficient and the percentage of the diffusive flux of the total salt flux are calculated using Equation 2.10 when the phenomenon of concentration polarization is c onsidered. The concentration of the feed is replaced by the concentration at the membrane wall, Cmem. The concentration at the membrane wall is determined first at 1 = 1, and next, by combining the film theory with the Sherwood correlation (see Appendix E). Table 4. 2 Salt transport parameters and the percentage of the diffusion flux for the SK model in absence of c oncentration polarization in RO flat sheet membrane experiments. Seawater membrane AD Salt (D/K )DO x 10-7 (cms-1) PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 1.5 4.95 0.984 34 NaCl 2.2 6.63 0.983 27 KCl 2.6 10.9 0.981 43 MgCl2 0.83 1.19 0.993 25 CaCl2 0.91 1.23 0.992 22 BaCl2 1.0 1.42 0.991 24 Brackish water membrane CG (D/K )DO x 10-7 (cms-1) PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 67.1 359 0.773 29 NaCl 77.1 409 0.769 31 KCl 96.9 557 0.756 38 MgCl2 21.9 134 0.913 43 CaCl2 31.6 149 0.908 43 BaCl2 33.4 158 0.906 43 Nanofiltration membrane CK (D/K )DO x 10-7 (cms-1) PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 118 896 0.437 12 NaCl 133 1141 0.429 13 KCl 165 1612 0.416 15 MgCl2 56 520 0.761 34 CaCl2 63 550 0.718 29 BaCl2 65 561 0.710 28

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57 4.2.2.1 Cmem at 1 = 1 Concentration at the membrane wall Cmem when 1 = 1 is calculated at each pressure using Equation 4.7. In this case, the conc entration at the membrane wall is denotedmax memC. The reflection coefficient, 1, reaches its maximum value of 1 for a perfect membrane which does not allow any fraction of the salt to permeate (coe fficient of salt rejection, R =1). This is, of course, an ideal situation. In practice, the coefficient of salt rejection and 1 are always less than 1. Calculating the concentration at the membrane wall from Jv = Lp( P1 ) when 1=1 results in the maximum value of the concentration polarization, max memC. According to Equation 4.7, for a given salt and a given memb rane, at constant feed concentration and constant feed temperature, max memCdepends on the operating pressure The averaged values of max memCover the pressure range are presented in Table 4.3. v P max mem gJ P n2for1:1salts AP Cwhere n3for1:2salts nRT (4.7) Table 4. 3 Average concentrations at the membrane wall for 1 = 1 for feed concentration of 0.05 mol L-1 in RO flat sheet membrane experiments. max memC (molL-1) Salt AD (seawater) CG (brackish water) CK (nanofiltration) LiCl 0.169 0.078 0.073 NaCl 0.142 0.074 0.071 KCl 0.134 0.073 0.064 MgCl2 0.179 0.082 0.097 CaCl2 0.169 0.081 0.094 BaCl2 0.142 0.080 0.088 The normalized values of max memCto the feed concentration Cfeed are presented in Figure 4.10 for the three membranes. The max memCis on average three times higher than the feed

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58 concentration for the AD membrane and on av erage 1.6 times higher for the CG and CK membranes. For all three membranes, the 1:2 salts present a higher membrane concentration than the 1:1 salts. The maximum concentration at the membrane wall increases in the order K < Na < Li and Ba < Ca < Mg for all three membranes. Li+Na+K+Mg+2Ca+2Ba+2 0 1 2 3 4 Cmax mem/CfeedChloride Salts AD CG CK Figure 4. 10 Concentration at the membrane wall normalized to the feed concentration for 1 = 1 in RO flat sheet membrane experiments. Table 4.4 presents the parameters of the salt transport when the concentration at the membrane wall is calculated using 1 = 1. In this case, the transport parameters, PRO and and the percentage of the diffusive flux of the total flux, Jdiff/Jtotal, are modified from the first case of SK model when the concentration polarization is neglected. In the two cases of SK model, the salt permeability PRO varies slightly for the RO membranes AD and CG (by 15% on average) and becomes on average 121% for the nanofiltration membrane CK. As for the first cas e of SK model, the 1:2 salts have again a lower permeation rate than the 1:1 salts for all three membranes. The order of permeation rate

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59 for the studied salts when concentration at the membrane wall is calculated for 1 = 1 remains the same as when the concentration polarization is neglected (Section 4.2.1). When the concentration at the membrane wall is calculated for 1 = 1, the strength of the coupling salt-water 1is reduced for all the salts, howe ver it remains the lowest for the AD membrane (0.001 on average), followed by the CG membrane (0.064 on average) and CK membrane (0.118 on average). For the CG a nd CK membranes, the salt-water coupling coefficient remains higher for the 1:2 salts than for 1:1 salts. The strength of the coupling salt-water increases in the same orde r as the salt permeability coefficient PRO increases, which Table 4. 4 Salt transport parameters and the percentage of the diffusion flux for the SK model when concentration polarization is calculated for 1 = 1 in RO flat sheet membrane experiments. Seawater membrane AD PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 3.96 0.999 91 NaCl 5.92 0.999 89 KCl 9.55 0.999 97 MgCl2 1.24 0.999 89 CaCl2 1.34 0.999 68 BaCl2 1.44 0.999 77 Brackish water membrane CG PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 444 0.893 56 NaCl 499 0.885 57 KCl 616 0.880 63 MgCl2 163 0.995 87 CaCl2 177 0.985 86 BaCl2 190 0.978 82 Nanofiltration membrane CK PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 2878 0.829 65 NaCl 3004 0.803 54 KCl 3258 0.731 54 MgCl2 732 0.991 95 CaCl2 882 0.981 93 BaCl2 919 0.959 85

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60 is Mg
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61 The average over the six salts for k memC is 22% higher than the concentration in the feed for the AD membrane and 37% higher than th e concentration in the feed for the CG and CK membranes. The k memC is 2.6 times lower than S memCfor the AD membrane, 12% lower for the CG membrane and 15% lower for the CK membrane. Figure 4.11 presents k memC normalized to the feed concentration for the three membranes studied. The differences in k memCamong the three membranes are lower than in the case of 1 = 1. Similar tomax memC, the concentration k memC is higher for the 1:2 salts than for the 1:1 salts for all three membranes. However, there is no trend in the variation of k memC among either the 1:1 salts or the 1:2 salts. Table 4. 5 Back diffusion coefficient calcu lated from Sherwood correlation and the concentration at the memb rane wall calculated from the film theory in RO flat sheet membrane experiments. k memC(molL-1) Salt k x 10-3 (ms-1) AD CG CK LiCl 2.16 0.059 0.071 0.069 NaCl 2.40 0.059 0.069 0.069 KCl 2.78 0.061 0.064 0.062 MgCl2 1.93 0.062 0.070 0.071 CaCl2 1.98 0.065 0.069 0.069 BaCl2 2.03 0.059 0.069 0.072

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62Li+Na+K+Mg+2Ca+2Ba+2 0.0 0.5 1.0 1.5 2.0 Ck mem / CfeedChloride Salts AD CG CK Figure 4. 11 Concentration at the membrane wa ll normalized to the feed concentration from Sherwood correlation and thin film theory in RO flat sheet membrane experiments. The transport parameters, PRO and and the percentage of the salt diffusive flux of the salt total flux are presented in Table 4.6 fo r the third case of the SK model. For the AD and CG membranes, the salt permeability PRO has increased on average by 28% in comparison with the salt permeability for the cas e when the concentration polarization was neglected. For the CK membrane, the increas e is on average 144%. These increases are higher compared to the increases of PRO and when the concentration at the membrane wall is calculated at 1 = 1 (Section 5.2.2.1). The order of pe rmeation rate for the studied salts is the same as the order of permeation rate when the concentration polarization is neglected (Section 4.2.1) or when the concentrati on at the membrane wall is calculated at 1 = 1.

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63 Table 4. 6 Salt transport parameters and per centage of the diffusion flux for the SK model in the case of concentration polarization calculated from film theory and Sherwood corre lation in RO flat sheet membrane experiments. Seawater membrane AD PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 5.96 0.989 48 NaCl 7.71 0.988 49 KCl 13.1 0.988 60 MgCl2 1.41 0.995 35 CaCl2 1.49 0.994 33 BaCl2 1.70 0.994 34 Brackish water membrane CG PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 529 0.901 62 NaCl 587 0.894 61 KCl 753 0.891 67 MgCl2 167 0.969 74 CaCl2 184 0.964 72 BaCl2 196 0.961 77 Nanofiltration membrane CK PRO x 10-7 (cms-1) Jdiff /Jtotal (%) LiCl 2796 0.755 54 NaCl 3310 0.733 60 KCl 3965 0.717 52 MgCl2 907 0.951 82 CaCl2 924 0.922 72 BaCl2 976 0.907 71 A comparison of the salt permeability coefficient, PRO, for the three cases of the SK model (absence of concentration polarization, concentration polarization calculated at 1 = 1 and concentration polarization calculated from combination of film theory and Sherwood correlation) is shown in Figure 4.12, each plot corresponding to one membrane. In all three cases of the SK model, the differences in the PRO are lower for the 1:2 salts than for the 1:1 salts for any of the three membranes.

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64 (a) (b) (c) Li+Na+K+Mg+2Ca+2Ba+2 0 3 6 9 12 15 PRO x 10-7 (cm s-1)Chloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0 2 4 6 8 PRO x 10-5 (cm s-1)Chloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0 1 2 3 4 5 PRO x 10-4 (cm s-1)Chloride Salts Cfeed Cmax mem Ck mem Figure 4. 12 Comparison of the salt in the SK model at different concentration at the membrane wa ll for (a) AD membrane; (b) CG membrane; and (c) CK membrane. in RO flat sheet membrane experiments.

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65 The strength of the coupling salt-water 1is also presented in Figure 4.13 for the three cases of the SK model. For the third cas e when concentration polarization is calculated using the Sherwood correlation and the thin film theory, the strength of the coupling saltwater, 1is reduced for all the salts and all the membranes when compared with 1in the absence of concentration polarization. It re mains the lowest for the AD membrane (0.009 on average), followed by the CG membrane (0.070 on average) and CK membrane (0.169 on average). These average values of 1are higher when compared with 1for 1 = 1. For all the membranes, 1is lower for the 1:2 salts than for the 1:1 salts in all three cases of the SK model. The magnitude of 1increase in the same order for the six salts regardless how the concentration at the membrane wall is calcula ted. The order is Mg < Ca < Ba < Li
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66(a) (b) (c) Li+Na+K+Mg+2Ca+2Ba+2 0.000 0.005 0.010 0.015 0.020 0.025 1-Chloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1-Chloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0.0 0.2 0.4 0.6 0.8 1-Chloride Salts Cfeed Cmax mem Ck mem Figure 4. 13 Comparison of the strength of the salt-water coupling in the SK model at different concen tration at the membrane wall for (a) AD membrane, (b) CG membrane (c) CK membrane CK membrane in RO flat sheet membrane experiments.

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67 (a) (b) (c) Li+Na+K+Mg+2Ca+2Ba+2 0.2 0.4 0.6 0.8 1.0 Jdiff / JtotalChloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0.2 0.4 0.6 0.8 1.0 Jdiff / JtotalChloride Salts Cfeed Cmax mem Ck mem Li+Na+K+Mg+2Ca+2Ba+2 0.0 0.2 0.4 0.6 0.8 1.0 Jdiff / JtotalChloride Salts Cfeed Cmax mem Ck mem Figure 4. 14 Comparison of the percentage of the diffusive flux of the total flux in the SK model at different concentration at the membrane wall for (a) AD membrane (b) CG membrane, (c) CK membrane in RO flat sheet membrane experiments.

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68 4.2.3 Pure water transport in the Spiegler-Kedem model As in the case of the transport parameters for the salts, the transport parameters for pure water are analyzed using the two models, Spiegler-K edem (SK) and Kimura-Sourirajan (KS). The results of the pure water transport parameters are presented first for the SK model and next for the KS model. The same three cases of the SK model cons idered in calculating the salt transport are used in calculating the parameters for the water transport. As described before, the three cases are: 1) neglecting the concentration polarizati on; 2) calculating the concentration polarization for 1 = 1; and 3) calculating the concentration pol arization by combining the film theory with the Sherwood correlation. The transport of pure water is characterized in the SK model by the parameter Lp. Although the reflection coefficient, 1, characterizes the salt transport, it appears only in the equation describing the product water flux Jv = Lp( P). Therefore, it is included in the results for the water transport. The Lp and are determined graphically from plotting Equation 2.9 at various operating pressure. v p p1J P LL (2.9) The results are presented in Table 4.7 fo r the first case of the SK model when concentration polarization is neglected. The reflection coefficient has values close to the salt-water coupling coefficient when the concentration polarization is not considered. The differences between and are on average less than 2% for any of the three membranes.

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69 Table 4. 7 Pure water permeability and reflec tion coefficient in the SK model in the absence of concentration polarization in RO flat sheet membrane experiments. AD (seawater) CG (brackish water) CK (nanofiltration) Salt Lp x 10-6 (gs-1cm-2psi-1) 1 Lp x 10-6 (gs-1cm-2psi-1) 1 Lp x 10-6 (gs-1cm-2psi-1) 1 LiCl 1.49 0.956 3.26 0.781 4.16 0.431 NaCl 1.65 0.950 3.21 0.776 4.48 0.414 KCl 1.70 0.943 3.28 0.750 4.37 0.412 MgCl2 1.70 0.993 2.90 0.924 3.73 0.752 CaCl2 1.72 0.991 2.93 0.909 3.71 0.732 BaCl2 1.79 0.989 3.01 0.901 3.87 0.698 The average of hydraulic permeability LP for the seawater membrane AD is 1.68 x 10-6 (gs-1cm-2psi-1), for the brackish water membrane CG is 3.10 x 10-6 (gs-1cm-2psi-1), and for the nanofiltration membrane CK is 4.05 x 10-6 (gs-1cm-2psi-1). Comparing to the pure water permeability for the AD membrane, the pure water permeability for the brackish water membrane CG is 85% larger and 148% for the nanofiltration membrane CK. For the second case of the SK model, is considered to be 1 and Lp is determined experimentally when the feed water is DI water. In this case equation Jv = Lp( P) becomes Jw = Lp P and Lp is equal to the pure water perm eability, A, which is presented later in this Chapter (Table 4.10). Comparison of with from the Table 4.4 shows differences smaller than 4% for all salts in th e seawater membrane as well as for the 1:2 salts for the brackish water and nanofiltration membrane. The values for are up to 12% smaller than for the 1:1 salts in the brackish water membrane and as much as 27% higher than for the 1:1 salts in the nanofiltration membrane. For the third case of the SK model, the calculation of the concentration at the membrane wall uses a combination of the film theory and Sherwood correlation in Equation 4.10 to express The resulting transport coefficients Lp and 1 are presented in Table 4.8.

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70 Table 4. 8 Pure water permeability and reflecti on coefficient in the SK model when the concentration at the membrane wall is calculated from film theory and Sherwood correlati ons in RO flat sheet membrane experiments. AD (seawater) CG (brackish water) CK (nanofiltration) Salt Lp x 10-6 (gs-1cm-2psi-1) 1 Lp x 10-6 (gs-1cm-2psi-1) 1 Lp x 10-6 (gs-1cm-2psi-1) 1 LiCl 1.49 0.965 3.44 0.846 4.34 0.609 NaCl 1.65 0.959 3.36 0.836 4.64 0.516 KCl 1.73 0.950 3.40 0.799 4.46 0.466 MgCl2 1.80 0.999 3.20 0.969 4.17 0.843 CaCl2 1.81 0.999 3.23 0.944 4.07 0.811 BaCl2 1.89 0.999 3.31 0.958 4.03 0.724 The hydraulic permeability LP increases slightly comparing with the first case of the SK model (by 3% on average for the AD, by 7% on average for the CG and by 6% for the CK). The differences between 1 and in the third case of the SK model are very small for the AD and CG membrane (1.3% and 4.3% respectively). For the CK membrane, 1 is on average smaller than by 14% for the 1:2 salts and by 28% for the 1:1 salts. 4.2.4 Salt permeability in the Kimura-Sourirajan model The second model considered in calculati ng the salt transport parameters is the Kimura-Sourirajan (KS) model. In the case of KS model, the salt permeability as well as the back diffusion coefficient, k, depend on the operating pressure and the membrane. The salt permeabilities, (D/K )RO, and the back diffusion coefficients, kRO, are shown for each membrane in Table 4.9.

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71 Table 4. 9 Salt permeability and back diffusion coefficient in the KS model in RO flat sheet membrane experiments. Seawater membrane AD Salt (D/K )RO x 10-7 (cms-1) kRO x 10-4 (cms-1) LiCl 4.40 2.74 NaCl 6.65 3.49 KCl 9.96 3.93 MgCl2 1.37 2.63 CaCl2 1.65 2.92 BaCl2 1.74 2.99 Brackish water membrane CG Salt (D/K )RO x 10-7 (cms-1) kRO x 10-4 (cms-1) LiCl 788 16.1 NaCl 916 20.4 KCl 991 24.1 MgCl2 184 11.8 CaCl2 212 12.9 BaCl2 231 14.3 Nanofiltration membrane CK Salt (D/K )RO x 10-7 (cms-1) kRO x 10-4 (cms-1) LiCl 3701 16.6 NaCl 4887 20.1 KCl 6630 25.5 MgCl2 762 6.6 CaCl2 960 7.0 BaCl2 1068 7.6 The values of the salt permeability (D/K )RO in the KS model are larger than values of the salt permeability, (D/K )DO, obtained in the direct osmosis experiments for all the membranes. The differences are the smallest for the seawater AD membrane, followed by the brackish water membrane CG and the nanofiltrati on membrane CK. Thus, the values of the salt permeability (D/K )DO are on average, three times less than the values of the salt permeability, (D/K )RO, for the seawater membrane AD, nine times less for the brackish water membrane CG and thirty times less for the nanofiltration membrane CK.

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72 Similar to the results obtained in the dir ect osmosis study as well as the results obtained in the RO flat sheet membrane stud y-SK model, the 1:2 salts present a lower permeability coefficient than the 1:1 salts for all three membranes. The order of permeation rate for the studied salts remained the same as the order of permeation rate calculated in the direct osmosis study and in the RO study-SK model. According to the (D/K )RO coefficient, the order of permeation is Mg < Ca < Ba < Li < Na < K for all three membranes. The values of the back diffusion coefficient, kRO, for the three membranes are presented in Figure 4.15 together with the values of the back diffusion coefficient, k, calculated from the Sherwood correlation. The seawater membrane AD presents on average over all salts the lowest kRO (3.1 cms-1), followed by the nanofiltration membrane CK (13.9 cms-1) and the brackish water membrane CG (16.6 cms-1). The back diffusion coefficient is lower for the 1:2 salts than for the 1:1 salts fo r all three membranes. The differences between the 1:2 salts and the 1:1 salts are 16% on av erage for the AD membrane, 36% on average for the CG membrane and 66% on average for th e CK membrane. The order the coefficient increases is Li < Na < K and Mg < Ca < Ba in all the cases.

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73Li+Na+K+Mg+2Ca+2Ba+2 0 5 10 15 20 25 30 k x 10-4 (cms-1)Chloride Salts KS model-AD KS model-CG KS model-CK Sherwood Nr. Figure 4. 15 Comparison of the back diffusion coefficient for all membranes in the KS model and from the Sherwood correlation (same fo r all membranes) in RO flat sheet membrane experiments. 4.2.5 Pure water transport in the Kimura-Sourirajan model The pure water transport is characterized in the Kimura-Sourirajan (KS) model by the parameter, A, called the pure water permeability which is a characteristic of the membrane. It is determined experimentally by running de materialized water as feedwater. Table 4.10 presents the average of A over the pressure range for the three membranes. The pure water permeability Lp is also presented for comparison. The seawater membrane AD presented the smallest pure water permeability among the three membranes. The pure water permeab ility is 65% larger for the brackish water membrane CG and by 148% larger for the nanofiltration membrane CK. The differences between A and Lp (1) are of 4% for the AD membrane, 8% for the CG membrane and 7% for the CK membrane. The differences between A and Lp (3) are of 1% for the AD and CK membrane and of 13% for the CG membrane.

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74 Table 4. 10 Pure water parameters of transport in RO flat sheet membrane experiments. Membrane A x 10-6 (gs-1cm-2psi-1) Lp (1) x 10-6 (gs-1cm-2psi-1) Lp (3) x 10-6 (gs-1cm-2psi-1) AD 1.75 1.68 1.73 CG 2.88 3.10 3.32 CK 4.34 4.05 4.29 Notes: (1) Denotes the averaged values obtain in th e first case of the SK model (absence of concentration polarization). (3) Denotes the averaged values obtain in th e third case of the SK model (when the concentration polarizati on is calculated from film theory and Sherwood correlation). 4.3 Salt and water transport in the RO spiral wound membrane experiments The results from the RO spiral wound membra nes are determined using only the KimuraSourirajan model. The parameters of salt and water transport in the KS model are presented in Table 4.11 for the seawater membrane element SW30 used in the RO-spiral wound membrane experiments. The concentration at the membrane wall calculated from at 1 = 1 is also shown in Table 4.11. Table 4. 11 Salt and water transport parameters in the KS model in the RO spiral wound membrane experiments. Salt (D/K )RO x 10-6 (cms-1) kRO x 10-4 (cms-1) max memC (molL-1) A x 10-6 (gs-1cm-2psi-1) LiCl 1.91 9.65 0.084 NaCl 2.00 10.7 0.080 KCl 2.26 11.5 0.078 MgCl2 1.28 6.50 0.101 CaCl2 1.34 6.63 0.102 BaCl2 1.44 6.79 0.100 2.41 In the case of the RO spiral wound membra ne experiments, the salts permeate the membrane in the same order as in the case of the direct osmosis experiments and the RO flat sheet membrane experiments. The order the salt permeability increases is given by Mg
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75 SW30 is four times larger than the salt permea bility for the seawater membrane AD used in the flat sheet experiments. The back diffusion coefficient kRO is lower for the 1:2 salts than for the 1:1 salts for the spiral wound membrane element SW30 by 37% on average. The order the coefficient increases is given by and Mg
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76CHAPTER 5 DISCUSSION OF RESULTS This chapter analyses the results presen ted in Chapter 4. Comparisons to the analogous findings presented in the literature are made throughout the chapter. The discussion is divided in five sections. The firs t section presents a correction of the equation derived in the previous chapter for the salt tr ansport in direct osmosis experiments. It discusses the concentration at the membrane wa ll as well as the transport of pure water in direct osmosis assuming that the salt and the water fluxes do not interact within the membrane. The second section of this chapter discu sses the salt transport parameters: the salt permeability, PRO, the reflection coefficient, 1, and the salt-water coupling coefficient, 2. This section also discusses the importance of the salt diffusive flux in the Spiegler-Kedem model. The differences in the salt transport parameters are analyzed for three cases of the model. In the first case, the increase in the c oncentration at the membrane wall is neglected whereas for the second and the third cases, th e effects of concentration polarization are considered. The concentration at the membra ne wall is calculated in the second case by taking 1=1 and in the third case, by combining the film theory with the Sherwood correlation. It is shown that the concentrati on polarization cannot be neglected (case one) and that the diffusion is the dominant mechanism of salt transport in both RO and NF membranes (case two and three). The third section compares the two most common models used in calculating the salt permeability in RO and NF membranes: th e Spiegler-Kedem model and the KimuraSourirajan model. The comparison regards both the salt and the water transport parameters

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77 and defines the situations when the two models can be used interchangeably. The fourth part of this chapter brings together the salt perm eability from the direct osmosis experiments and the reverse osmosis experiments, both from Spie gler-Kedem and Kimura-Sourirajan model. It is shown that for the salt permeability is the sa me in direct osmosis and reverse osmosis, therefore it dose not depend on the operating pressure applied. The last part of the chapter analyzes what physical and thermodynamic parameters control the salt permeability in RO and NF membra nes. There is a certain pattern of variation for the salt permeation among the six studied sa lt regardless the membrane type (RO or NF), the membrane configuration (flat sheet or spiral wound), the type of the experiment (DO or RO), or the model used in calculating the salt permeability (Spiegler-Kedem or KimuraSourirajan). This pattern is explained by any of the parameters correlated to the degree of the hydration for the cations (hydrated radii, enthalpy and entropy of hydration). The relative free energy can be used to predict the permeabilit y of salts in a certain membrane based on known values of the several other sa lt permeabilities in the membrane. 5.1 Salt and water transport in the direct osmosis experiments The objectives of this sections are 1) to determine the concentration at the membrane wall in the case of direct osmosis, 2) to derive the set of equations for water and salt fluxes in direct osmosis; and 3) to calculate the corr ected salt water permeability coefficient, (D/K )DO. The salt permeability coefficient in the direct osmosis experiments, (D/K )DO, is calculated using Equation 4.6 and considering that the concentration at the membrane wall is equal to the concentration of the salt solution in the bulk. The validity of this assumption has to be reconsidered in the context of having the salt flux and the pure water flux moving in opposite directions through the membrane. The opposing directions of the salt and water fluxes is observed experimentally from the meas ured increase in the salt concentration in the

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78 DI water (due to the transport of salt) and th e increase in the salt solution volume in the salt solution vessel (due to the transport of pure water). 5.1.1 Concentration at the membrane wa ll in the direct osmosis experiments Assuming that the two fluxes do not inter act with each other within the membrane (Rautenbach and Albrecht, 1989), the equation de scribing the transport of pure water in the direct osmosis experiments can be derived fro m Equation 2.11. A graphical representation of the Equation 2.11 is presented in Figure 5.1. Jv = A( P) (2.11) It can be observed that when the differe nce in the applied pressure across the membrane P is lower than the difference in the osmotic pressure across the membrane the direction of the pure water flux is revers ed. In the direct osmosis experiments, the differential pressure P is zero since there is no external pressure applied on the membrane. Therefore, Equation 2.11 becomes Equation 5.1. In direct osmosis experiments, the pure water permeates the membrane by flowing first through the support layer of the membrane and then through the skin layer. The pure water permeability is different from the pure water permeability, A, when the water flows first through the skin layer and next through th e support layer, due to membrane asymmetry. The pure water permeability in the direct osmosis experiments is denoted A'. Jw, DO = A (5.1)

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79 Since A' cannot be determined in a dir ect osmosis experiment, it is determined experimentally in a reverse os mosis experiment at a range of transmembrane pressures form 100 psi to 300 psi (Chapter 3, Section 3.3.2). In direct osmosis experiments, the pressure across the membrane is less than 54 psi, theref ore lower than the pressure at which A' is determined. However, the variation of A' with pressure is less than 6% for the seawater membranes and less than 11% for both the br ackish water and nanof iltration membranes. Hence, the use of A' determined in RO e xperiments for the DO experiments is adequate. Disregarding the negative sign in Equation 5.1 which only reflects the change in direction of the pure water flux in direct osmo sis, and considering the pure water permeability A' instead of A, Equation 5.1 becomes Equation 5.2. Combining Equation 5.2 with the expression of the osmotic pressure = nRgTC, results in Equation 5.3 which allow the calculation of the concentration at the membrane wall in the direct osmosis experiments DO memC. P Jv0 Jw, DO tan -1 A Jv = A ( P) Figure 5. 1 Schematic diagram of the pure wate r flux as function of the applied pressure across membrane. Modified from Mulder (2003).

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80 DO memDIw,DOJA'A' (5.2) DO w,DO memDI gCCJ A'nRT (5.3) For a given membrane and salt solution, th e concentration at the membrane wall, DO memC, obtained from Equation 5.3 varies duri ng a DO run due to variations of the concentration CDI. The pure water flux, Jw, DO, is considered constant during a run (once the steady state in reached) and the rest of the te rms in Equation 5.3 are constant for a given membrane and salt solution. Since CDI increases linearly with time for the duration of a run (Equation 4.5), and the term Jw,DO/ A' nRgT is a constant it results thatDO memC increases linearly with time for the duration of a run. The slope of the line for the plot DO memC= f (t) is the same as the slope for the plot CDI = f(t). The intercept is given by (Jw,DO/ A' nRgT) + (CDI)t=0 Table 5.1 presents DO memCaveraged over the duration of a run for all four membranes when bulk salt solution concentration is 0.05 molL-1. The DO memCaveraged over the duration of a run at different bulk salt solution c oncentrations is presented in Table F.1. Table 5. 1 Pure water permeability and concen trations of the salt solution at the membrane wall for bulk salt solution concentration of 0.05 molL-1 in direct osmosis experiments. DO memC (molL-1) Salts SE AD CG CK LiCl 0.015 0.024 0.010 0.003 NaCl 0.017 0.030 0.010 0.002 KCl 0.016 0.031 0.010 0.003 MgCl2 0.022 0.032 0.011 0.005 CaCl2 0.022 0.032 0.011 0.005 BaCl2 0.022 0.029 0.011 0.005

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81 As shown in Table 5.1 and Table F.1, the concentration at the membrane wall is lower than the bulk salt solution concentration. Similar observations are made by Rautenbach and Albrecht (1989). The “dilution” phenomena at the membrane surface due to the counter water flux in the direct osmosis experiments is the opposite of the concentration polarization phenomena existing in the reverse osmosis experiments. 5.1.2 Salt transport in the direct osmosis experiments Equation 4.4 describing the linear variation of the bulk salt solution concentration in time during a run is corrected for the concentration at the membrane wall DO memC and becomes Equations 5.4. Consequently, Equation 4.6 beco mes Equation 5.5 which is used to calculate the new salt permeability coefficients (D/K )DO. Figure 5.2 presents the salt permeability coefficients (D/K )DO before and after correction. DODO memmem tt0CCt (5.4) g w,DO DOAnRT DN KSJ (5.5) Figure 5.3 shows a significant increase of the salt permeability coefficient when the concentration from the bulk solution is replaced by the concentration at the membrane wall DO memC. The increase of the salt permeability is lo west for the seawater membranes SE and AD (by 2.4 times in average over the six salts) and it is highest for the nanofiltration membrane CK (by 12.2 times in average over th e six salts). The increase corresponds to the decrease in the salt solution c oncentration from the bulk value CS to DO memC, which is lowest for the seawater membranes SE and AD and high est for the nanofiltration CK (Table 5.1).

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82 The order the salts permeate through the me mbranes remains the same as before the correction, which is MgCl2 < CaCl2 < BaCl2
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83 LiClNaClKClMgCl2CaCl2BaCl2 5 10 15 20 25 30 35 LiClNaClKClMgCl2CaCl2BaCl2 0 2 4 6 8 LiClNaClKClMgCl2CaCl2BaCl2 0 2 4 6 8 10 12 Salts Salts Salt permeability x 10-7 (cm s-1) Salt permeability x 10-5 (cm s-1)Salts Before correction After correction SE membrane CG membraneLiClNaClKClMgCl2CaCl2BaCl2 00 10 20 30 40 50 Salts Salt permeability x 10-4 (cm s-1) CK membraneSalt permeability x 10-7 (cm s-1) AD membrane Figure 5. 2 Salt permeability before and after th e correction of the membrane wall for SE, AD, CG and CK membranes in the direct osmosis experiments.

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84 (Lonsdale et al., 1965; Heyde et al., 1974; Gl ueckauf, 1976) and for aromatic polyamide membranes (Frommer et al., 1973; Strathmann and Michaels, 1977). Assuming that K is independent of the concentration in Chaudry’s research, and since is a constant, it results that (D/K )DO increases with bulk concentration, wh ich disagrees with Heyde’s results and the results of this research. This contradi ction can come from the assumption that K is independent of the bulk solution concentration or from the differences in evaluating the salt permeability coefficient. 5.1.3 Pure water transport in the direct osmosis experiments As presented in Table 4.1, the order the pu re water permeability A' increases is given by A'SE< A'AD< A'CG< A'CK. To date, there are no results found in the literature about the differences in the pure water permeability when the membrane is inverted. Assuming that by inverting the membrane the order of pure water permeability remains the same among the four membranes, the order A' increases for the four membranes is consistent with the order found in the literature, which is Aseawater
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85 smaller than the pure water permeation when the skin layer faces the high pressure side (A). An illustration of the differences in the pressu re across the skin layer for A and A' is presented in Figure 5.4, assuming that 8% of the total membrane resistance to the flow is due to the support layer. Pskin= P1 P2 = P1Skin layer Support layer Pskin= P1 8 % P1P2 = 92 % P1Skin layer Support layer P1 P18% P1 P2 = 0 P2 = 0 P1 AA' Figure 5. 4 Comparison of the differential pressure at the skin layer when the membrane is inverted. ADSECGCK 0 1 2 3 4 5 Pure water flux x 10-6 (g s-1cm-2psi-1)Membrane A' Lp A Figure 5. 3 Pure water permeability when the sk in layer of the membranes faces the low pressure side (A’) and high pressure side (Lp and A).

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86 According to the Table 4.2, the flux of pure water, Jw,DO, in the nanofiltration membrane, CK, is higher than in the seawater membranes but lower than in the brackish water membrane, CG. A larger pure water flux in a brackish water membrane than in a less “tight” membrane, such as the nanofiltration me mbrane, might seem surprising. According to the Equation 5.2, there are two factors controlling the flux of the pure water in direct osmosis: the pure water permeability, A', and the differential osmotic pressure, The order of A' among the four membranes is given by A'AD< A'SE< A'CG< A'CK, whereas the order of is CK< CG< SE< AD. Since the pure water flux is determined by the product A' (Equation 5.2), no ranking of the pure wate r flux can be established among the four membranes. For all four membranes, the pure water flux is higher for the 1:2 salts than for the 1:1 salts. This can be explained by Equation 5.2 and considering that 1) the concentration at the membrane wall DO memCis higher for the 1:2 salts than for 1:1 salts (Table 5.1); and 2) the concentration in the DI water side CDI is negligible comparing to DO memC (is less than 6%). Equation 5.2 also explains the increase in the pure water flux with the increase in the salt concentration in the bulk solution (Figures 4.7 and 4.8). As presented in Table F.1, the increase in the bulk solution concentration determ ines an increase in the concentration at the membrane wall which results in higher pure water flux. Moreover, Equation 5.2 explains that fo r a given membrane and for a given bulk solution concentration, the pure water flux is th e same for all 1:1 salts (Figure 4.9). The pure water flux is also the same for all 1:2 salts in a given membrane at constant bulk solution concentration. As shown in Table F.1, at a given bulk solution concentration, the concentration at the membrane wall depends onl y on the valence of the cation and anion in the salt (ie 1:1 or 1:2). Since A' is constant for a membrane and CDI is negligible comparing to

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87DO memC, it results that at constant bulk solution concentration, the pure water flux depends only on the salt valence configuration. This result ve rifies the assumption that the water and salt fluxes do not interact with each other within the membrane in direct osmosis (Section 5.1.1). 5.1.4 Salt and water transport in the case of fluxes interaction in direct osmosis experiments If the salt and water fluxes interact within the membrane, Equation 5.2 describing the transport of pure water and Equation 5.5 describi ng the transport of salt in the direct osmosis experiments have to be corrected with terms counting for the fluxes interaction. By analogy with the equations in the Spiegler-Kedem mode l (Chapter 2, Section 2.1.3.1), a possible way of correcting Equations 5.2 and 5.5 is given in Equations 5.7 and 5.8. 1w,DOpJL (5.7)2savgw,DOJC(1)J (5.8) Assuming that the concentration at the membrane wall DO memCis known, the parameters Lp, 1, and can be determined by performi ng DO runs at several pressures lower than so that the water and salt flux have opposite directions. The coefficients and can be determined graphically from Equation 5.8 whereas Lp and 1 can be determined graphically from Jw, DO = Lp( P1 ). The key point here is to know DO memC. The possibility of applying the film theory to determine DO memCneeds to be explored further and is beyond the purpose of this research.

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88 5.2 Analysis of the transport parameters in the SK model Several authors using the SK model in calculating the salt transport parameters assume that the concentration at the membrane wall is equal to the feed concentration in the bulk solution (Diawara, et al. 2003; Pontie et al. 2003; Schaep et al. 1998; Van Gauwbergen and Baeyens 1998). Moreover, a resulting salt-water coupling coefficient 2 close to 1 makes some authors conclude that the coupling salt-wate r is insignificant and the transport of salt is diffusion dominant (Marinas and Selleck, 1992; Urama and Marinas, 1997). Only a few authors have taken the next step to actually cal culate the percentage of the diffusive flux of the total flux, Jdiff/Jtotal (Gilron et al. 2001; Chaudry 2002). The phenomenon of concentration polarizati on cannot be neglected a priori in any filtration processes using membranes, unless either measurements or calculations prove otherwise. In this research, concentration polari zation is neglected in the first case of the SK model in order to analyze the implications in determining the salt and water transport parameters. As presented in the previous chapter, Figures 4.15 and 4.16, significant differences in the salt transport parameters result when con centration at the membrane wall is replaced by the concentration polarization in the SK model. The objectives of this section are: 1) to analyze the changes in the salt permeability, PRO, the reflection coefficient 1, the salt-water coupling coefficient, 2, as well as Jdiff/Jtotal when the concentration polarization is considered; 2) to compare the two methods of calculating the concentration polarization for the three membranes; 3) to compare the changes in water transport, LP, as well as 1 and 2 when concentration polarization is considered; and, 4) to determine the most appropriate way of calculating the concentration at the membrane wall in the SK model.

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89 First, the discussion addresses the transport of salt though the three membranes used in the RO flat sheet cell experiments. This part of the discussion is divided for each membrane type for an easier analysis. Next, th e discussion addresses the transport of water in the same three membranes. 5.2.1 Salt transport in the seawater membrane AD In the first case of the SK model when the concentration polarization is ignored, the results lead to contradictory conclusions for the AD membrane. As shown in Table 4.2, 2 has a minimum value of 0.981 which would co rrespond to uncoupled fluxes for salt and water ( 2 1). However, the percentage of the diffusi ve flux of the total flux is lower than 43% (Table 4.2). It results that the salts are mainly transported through the seawater membrane in a convective flux, therefore the water and salt fluxes are strongly coupled. These contradictory results come from disreg arding the concentration polarization at the membrane wall. The second case of the SK model considers the concentration at the membrane wall when 1=1. Calculating the concentration at the membrane wall from Jv = Lp( P1 ) when 1=1 results in the maximum value of the concentration polarization, max memC. Since the seawater membrane has high rejec tion (R is higher than 0.995), max memCrepresents a good approximation of the real concentration at the membrane wall. max memCis on average over six salts, 3.1 times higher than the concentration in the bulk solution. max memCincreases in the order MgCl2
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90 salt-water coupling coefficient 2 increases to 0.999 and becomes equal for all six salts. The equality of the salt-water coupling coefficients for all the salts is expected for high selective membranes (Mulder, 2003). The diffusive flux Jdiff becomes dominant in the total flux for all salts. This is in agreement with the literature which refers RO and nanofiltration membranes as being diffusion-controlled proce sses (Mallevialle et al., 1996). In the third case of the SK model, the con centration at the membrane wall, calculated from the film theory and Sherwood correlation is significantly lower than max memC(Figures 4.7 and 4.8). It is on average over the six salts 1.4 times higher than the concentration in the bulk. Moreover, there is no specific order of deve loping concentration polarization among the six salts it this case. The salt permeability, PRO, is 19% higher than PRO calculated at the bulk solution concentration. The sa lt-water coupling coefficient 2 increases slightly and remains higher for the 1:2 salts than for the 1:1 salts. The salt convective flux is dominant (except for KCl) which, similar to the first case of the SK model, is an erroneous result. The differences in the concentration polarization obtained when 1=1 and from combination of the film theory with the Sherwood correlation can come from multiple sources. First, the application of the film theo ry in its original form is criticized in the literature because 1) it assumes the membrane as being a non-porous smooth wall and 2) it assumes that a uniform concentration polariza tion layer is developed (Sutzkovere et al., 2000). Second, the Sherwood correlation might not be suitable because 1) there are differences in equipment geometry (Sablani et al., 2001); 2) the mass transfer coefficient, k, might not be strictly equal to D/ (Bhattacharya and Hwang, 1997); and 3) the changes in the viscosity and diffusivity due to concentration polarization are ignored (Gekas and Hallstorm, 1987).

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91 5.2.2 Salt transport in the brackish water membrane CG When the concentration polarization is ignored for the CG membrane, 2 has a minimum of 0.756 which corresponds to a percenta ge of the diffusive flux of the total flux of 38%. The value of 2 shows a higher salt-water coupling effect than in the case of AD membrane and correspondingly, a convective flux do minant in the salt transport. The values of 2 and Jdiff/Jtotal do not lead to contradictory results as in the case of AD membrane (for which at 2 =0.992, the Jdiff/Jtotal is only 22%). However, it results that when the concentration polarization is ignored, the convection is the dominant term of the salt flux in the brackish water membrane. This result is in disagreement with the literature (Mallevialle et al., 1996). In the second case of the SK model, the valu es of the concentration at the membrane wall calculated for 1=1, max memC, are on average 1.6 times higher than the concentration in the bulk solution. The salt transport parameter is equa l (within the experimental error) to the salt parameter when the concentration polariza tion is ignored and the salt-water coupling coefficient 2 increases on average by 12%. The order 2 increases among the six salts remains the same as when the concentrati on polarization was ignored. An existing order among 2 of the six salts is in agreement with fi ndings from literature which suggest that in less selective membranes, an approx imate relationship exists between 2 and the solute size (Mulder, 2003). In this research, it is obser ved that the higher the hydrated radii of the cations, the higher the 2. The hydrated radii of the cations are discussed later in Section 5.5.1.1. The diffusive flux Jdiff becomes dominant in the total flux of salt for all salts (72% in average), although not as such high percentage as for the AD membrane (85%). The percentage of Jdiff/Jtotal for the 1:2 salts are higher than the percentage of Jdiff/Jtotal for the 1:1 salts. This can be explain by the stronger watersalt coupling for the 1:1 salts than for the 1:2

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92 salts. The dominancy of the diffusion flux is in agreement with the results from the literature (Mallevialle et al., 1996). In the third case of the SK model, the co ncentration polarization calculated from the film theory and Sherwood correlation,k memC, is on average over all salts 1.4 times higher than the concentration in the bulk. Unlike for th e seawater membrane, for the brackish water membrane k memCis very close to max memC. The values of the salt transport parameters, PRO and 2, as well as Jdiff/Jtotal are very close to their corresponding values when concentration at the membrane wall is max memC. The order 2 increases among the six salts is the same as for max memCand the diffusive flux Jdiff is dominant (68% on average over all salts), with higher percentages for the 1:2 salts than for the 1:1 salts. Unlike for the seawater membrane, for the brackish water membrane the differences between the set of PRO, 2 and Jdiff/Jtotal are very small in the last two cases of the SK model (i.e. when the concentration polarization is calculated at =1 and from film theory combined with Sherwood correlations). Moreover, both cases lead to the right conclusion that the diffusive flux is dominant in the brackish water membrane. This suggests that using the film theory combined with the Sherwood co rrelation is appropriate for the brackish water membrane, CG. Some possible explanations to the fact that the film theory combined with the Sherwood correlation is appropriate for the CG membrane but not for the AD membrane are 1) the CG membrane is made of cellulose acetate and has a smoother surface than the AD membrane made of polyamide (Elimelech et al ., 1997) and 2) the variation of the viscosity and diffusivity due to concentration polarizati on are lower for the CG membrane than for the AD membrane sincemax memCis 3 times higher than the bulk concentration for AD but only 1.6 times higher for CG.

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93 5.2.3 Salt transport in the nanofiltration membrane CK When the concentration polarization is ignored for the CK membrane, 2 has a minimum of 0.416 which corresponds to a percenta ge of the diffusive flux of the total flux of 15%. This shows the highest salt-water coupling effect among the three membranes studied. Correspondingly, the convective flux is dominant in the salt transport (more than 71%). This result is in disagreement with the literature (Mallevialle et al., 1996). The concentration at the membrane wall when 1 = 1, max memC, is on average over six salts the same as max memCfor the brackish water membrane (1.6 times the bulk concentration). The salt transport parameter PRO and 2 increase significantly comparing to their values when concentration polarization is ignored (on average by 109% for PRO and by 59% for 2). The order 2 increases among the six salts is the same as for the brackish water membrane. The diffusive flux Jdiff is dominant and it is higher for the 1:2 salts than for the 1:1 salts. Jdiff/Jtotal is almost the same as for the brackish water membrane (74% in average). The values of concentration at the membra ne wall calculated from the film theory and Sherwood correlation are on average the same as for the CG membrane (1.4 times the bulk concentration). In this case, the values of the salt transport parameters, PRO and are equal (within the experimental error –Table G.6) with the corresponding values when 1 =1. The diffusive flux Jdiff becomes almost as the same percentage as for the CG membrane (65% on average), with higher percentages for the 1:2 salts than for the 1:1 salts. Just as in the case of the brackish water me mbrane, the results from the last two cases of the SK model are very similar for the nanofiltr ation as well. This shows that calculating the concentration at the membrane wall by combining the film theory and the Sherwood correlation is adequate for the nanofiltration membrane. Moreover, when the concentration

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94 polarization is considered, the diffusive salt flux represents almost the same percentage of the total salt flux for the brackish water membra ne, CG, and for the nanofiltration membrane, CK. For both CG and CK, 2 and Jdiff/Jtotal are lower for the 1:1 salts and 1:2 salts. This shows the similarity in the transport mechanism for the two membranes. This is in agreement with the literature which refers nanofiltration memb ranes as “loose” RO membranes with high rejection for the 1:2 salts and low rejection for the 1:1 salts (Mallevialle et al., 1996). 5.2.4 Water transport in the SK model The three cases of the SK model presen ted above for the discussion of the salt transport parameters are considered in analyzing the hydraulic permeability Lp. Also the discussion includes the investigation on the va lidity of the Onsager reciprocal relation 1 = 2. The hydraulic permeabilities, Lp, are equal within the experimental error (Table G.6) for all three cases of the SK model. The order Lp increases for the three membranes is Lp(seawater) < Lp(brackish water) < Lp(nanofiltration). This order is in agreement with the membranes manufacturer data for the typical produc t flux at the same operating pressure P (Table 3.2). The Onsager reciprocal relation 1 = 2 is verified in all three cases of the SK model and for all three membranes, except for the 1: 1 salts for the nanofiltration membrane when 1 is 27% lower than 2.The large majority of the authors using the SK model assume that the Onsager reciprocal relation is verified and deal with only one parameter = 1 = 2 in the SK model equations. However, according to Mason et al. (1972), the coefficients 1 and 2 are equal only if proven to be so experimentally. According to Mason and Lonsdale (1990), 1 represents the effectiveness of a salt to develop an osmotic pressure across the membrane whereas 2 describes the effectiveness of

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95 the membrane to separate salt and water in th e volume flow of the product. Assuming that for a membrane the salt is transported entirely due to diffusion, 2 =1 because there is no convective flux for the salt. The reflection coefficient, 1, can be lower than 1 because the membrane is not rejecting the salt 100%, since there is a salt diffusive flux. The higher the membrane rejection, the closer 1 is to 1. Therefore 1 = 2 only in ideal membranes with a salt rejection of 100% and 1< 2 for any non-ideal membranes. The differences in the two coefficients 1 and 2 are smaller for membranes with hi gher diffusion fluxes. This is illustrated in Figure 5. 5 using data from Tables 4.3, 4.5 and 4.7. As shown in Sections 5.2.1 through 5.2.3, when the concentration polarization is considered, all three membranes are diffusion domi nant in regards to the salt transport. This explains that 1 = 2 (within the experimental error-Table G.6) for all membranes and all salts except for 1:1 salts in nanofiltration membrane. The percentage of Jdiff/Jtotal is lowest for the 1:1 salts in the nanofiltration memb rane (55%) which explains that 1 is lower than 2 5060708090100 0 10 20 30 40 (-1)/2 (%)Jdiff/Jtotal(%) Figure 5. 5 Dependence of the relative difference of 1 and 2 on the percentage of the diffusive flux of the total flux for all membranes when concentration polarization is considered.

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96 5.2.5 Conclusions on the SK model Neglecting the concentration polarization in the SK model leads to the erroneous result that convection is the main mechanism of transport in all three membranes. This case is disregarded from any further discussion in this Chapter. Two cases of calculating the concentration at the membrane wall are considered: 1) when 1=1 and 2) combining the film theory with the Sherwood correlation. Both methods lead to close results for the salt transport para meters for the brackish water membrane as well as for the nanofiltration membrane. It results that the diffusion is the dominant flux in the transport of salt across the membranes (68% to 72% for the CG membrane and 65% to 74% for the CK membrane). The sa lt –water coupling coefficient has a certain trend of increasing among the six salts which can be explained by th e hydrated radii of the salts. The contribution of the diffusive flux to the total flux is on aver age lower for the 1:1 salts than for the 1:2 salts which is a consequence of the differences in the salt-water coupling coefficient for the 1:1 salts and 1:2 salts. Only the first case of calculating the con centration at the membrane wall (i.e. when 1=1) is acceptable for the seawater membrane. In this case, the diffusion flux is dominant at a higher percentage than for the brackish water and nanofiltrati on membrane (85% on average over all salts). The salt –water coupling coefficient is equal for the six salts which can be explained by the high rejec tion of this membrane (R>99.5%). The hydraulic permeability, LP, is equal within the experimental error for the two cases of calculating the concentration at the me mbrane wall. The Onsager reciprocity relation 1 = 2 is valid only for high Jdiff/Jtotal, i.e for all membranes and all salts in this research except for the 1:1 salts in NF membrane.

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97 5.3 Comparison of the SK and KS models The differences of the results from the transport models, Spiegler-Kedem and Kimura-Sourirajan, are analyzed in this Sec tion. The discussion refers first to the salt transport and next to the water transport. The obj ective is to prove that the two models lead to identical salt and water permeability coefficients for the membranes with high percentage of the salt diffusive flux. 5.3.1 Comparison of salt transport parameters, PRO and (D/K ) RO As mentioned before, the first case of the Spiegler-Kedem model neglects the concentration polarization and leads to errone ous results for all three membranes. For the seawater membrane, the third case of the SK model also leads to erroneous results. The discussion below considers only the valid cases of the SK model, which are 1) for the seawater membrane, the second case of the SK model when the concentration polarization is calculated for 1 = 1 and 2) for the brackish wate r membrane and the nanofiltration membrane, both the second and the third case of the SK model. The salt transport parameter PRO and (D/K RO are equal (within the experimental error-Table G.6) for the seawater membrane, AD, for all studied salts. For the brackish water membrane, CG, and the nanofiltration membrane CK, the discussion has to be divided between 1:1 salts and 1:2 salts. Thus, for th e 1:1 salts, the salt transport parameter PRO is 24% to 46% lower than the salt permeability (D/K RO whereas for the nanofiltration membrane CK, PRO is 22 % to 51% lower than the salt permeability (D/K RO For the 1:2 salts, the differences between PRO and (D/K RO are within the experimental error (Table G.6) for both CG and CK. These results can be explained by looking back to the assumptions made in calculating (D/K RO in the Kimura-Sourirajan model.

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98 The KS model assumes that there is no convective flux of the salt (or no coupling salt-water) and the transport is due to the di fferences in salt concentrations across the membrane. Salt permeability (D/K RO can be related to PRO in Equation 5.9 which results by equaling Equations 2.8 and 2.12: 2vavg RO RO(1)JC D P KC (5.9) The two salt transport parameters will be equal when the salt-water coupling coefficient, 2, is one. This situation is equivalent to the absence of any convective salt flux. The closer 2 is to one, the lower the difference between (D/K RO and PRO. As presented in Table 4.3 and 4.5, the lowest value of 2 is 0.989 for the AD membranes which validates the equality of the two parameters PRO and (D/K RO for this membrane for all salts. For the CG and CK membranes, PRO and (D/K RO are equal for the 1:2 salts when has minimum values of 0.961 and 0.907, respectively. The largest difference (46%) between PRO and (D/K RO is achieved for NaCl in CG membrane when 2 is 0.885 (Table 4.5). Similar, the largest difference of 51% between PRO and (D/K RO is achieved for KCl in CK membrane when 2 is 0.731 (Table 4.5). Figure 5. 5 presents the differences between PRO and (D/K RO as function of 2 It is observed from Figure 5. 5 that large differences between PRO and (D/K RO correspond to large values of 2, which in turn, correspond to low percentages of th e salt diffusive flux. It results that the two parameters PRO and (D/K RO are equal for high 2 when the diffusive flux dominates. Similar results are presented by McCray et al. (1991) for cellulose acetate membranes. The authors found that the differences between PRO and (D/K RO increase as 2 decreases. For

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99 comparison, the variation of [PRO (D/K RO]/PRO with 2 according to McCray et al. (1991) is also plotted in Figure 5. 6. 5.3.2 Comparison of pure water transport parameters, Lp and A The hydraulic conductivity of the membranes, LP, is calculated in two cases of the SK model. First, considering the concentr ation at the membrane wall equal to the concentration in the bulk solution, and second, calculating the concentration polarization from combining the film theory with the Sher wood correlation. These results are compared with the pure water permeability A for the KS model for all three membranes (Table 4.6). The hydraulic conductivity, Lp, is equal in both cases of the SK model and equal with the pure water permeability, A, calculated from the KS model. This shows that Lp and A are identical parameters which are intrin sic characteristics of the membranes. 0.50.60.70.80.91.0 0 10 20 30 40 50 60 70 80 90 100 This research[PRO-(D/K)RO]/PRO (%)2 McCray et al. Figure 5. 6 Variation of the difference in the salt pe rmeabilities in the SK and the KS models with the salt-water coupling coefficient.

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100 5.3.3 Conclusions on the compar ison of SK and KS models The two RO models, Spiegler-Kedem and Ki mura-Sourirajan, lead to equal salt and water transport parameters for diffusion-contro lled membranes for which the diffusive flux is at least 67%. For diffusion-controlled membranes for which the diffusive flux is lower than 67% (such as brackish water membrane and na nofiltration membrane for the 1:1 salts), the salt permeability in the KS model is larger th an in the SK. Since low percentage of the diffusive salt flux is directly correlated to low membrane rejection (Figure 5.7, coefficient of correlation of 0.73), it is concluded that KS mode l is inappropriate to be used for salts with low rejection in a membrane. 5060708090100 50 60 70 80 90 100 Jdiff/Jtotal (%)Rejection (%) Figure 5. 7 Variation of the salt diffu sive flux with membrane rejection. 5.4 Comparison of salt permeability in DO and RO experiments The salt permeability obtained in Section 5.1.2 from the direct osmosis experiments is compared to the salt permeability from: 1) RO flat sheet membrane experiments-SK model (valid cases only Section 5.3.1) and 2) RO flat sheet membrane experiments-KS model. The

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101 objective of this section is to demonstrate that the salt permeabilities in the direct osmosis and reverse osmosis experiments are equa l for high rejection membranes. The differences in the salt permeabilities are reported as percentages of the salt permeability in direct osmosis in Table 5.2. The differences are within the experimental error (Table G.6) in all cases except for the salt perm eability in the KS model for the 1:1 salts in the brackish water and nanofiltration membranes. The case of 1:1 salts in the KS model for the brackish water and nanofiltration membranes is discussed in Section 5.3 where it is concluded that the KS model is not appropria te to be used for these salts with these membranes.

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102 The equality of the salt permeabilities in dir ect osmosis (zero external pressure) and reverse osmosis (external pressure up to 400 psi) shows that the rate the salt is transported through the membrane does not depend on the exte rnal pressure applied. It also shows the validity of the three models used. It leaves th e possibility to choose what type of experiment and what model is the most appropriate to use in different circumstances. For example, the SK model is the most laborious model, requiri ng data from at least three different operation pressures as well as the pre-determination of the concentration at the membrane wall. The Table 5. 2 Differences (as percentages) between the salt permeability in direct osmosis experiments and salt permeability from SK and KS models in RO flat sheet membranes. Seawater membrane AD Salts PRO (2) (D/K )RO LiCl 13 2 NaCl 8 18 KCl 25 28 MgCl2 10 1 CaCl2 7 13 BaCl2 21 0 Brackish water membrane CG Salts PRO (2) PRO (3) (D/K )RO LiCl 16 29 53 NaCl 18 30 55 KCl 16 31 48 MgCl2 20 22 29 CaCl2 17 20 30 BaCl2 16 19 31 Nanofiltration membrane CK Salts PRO (2) PRO (3) (D/K )RO LiCl 23 21 40 NaCl 13 2 32 KCl 27 4 38 MgCl2 14 31 18 CaCl2 19 23 26 BaCl2 19 23 30 Notes: PRO (2) denotes the salt permeability for the second case of the SK model (when the concentration at the membrane wall is calculated for 1=1). PRO (3) denotes the salt permeability for the third case of the SK model (when the concentration at the membrane wall is from combination of the film theory and Sherwood correlation).

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103 benefit of this model is the quantification of the diffusion and convection fluxes for the salt. The use the KS model requires data at only one operating pressure but also needs a value for pure water permeation that has to be determined by preliminary independent pure water runs. The direct osmosis experiments can be done usin g lower cost apparatus and with low energy requirements. However, the con centration at the membrane has to be determined also. A summary of the RO and DO models characteristi cs is presented in Table 5. 3 and 5.4. Table 5. 3 Comparison of the requirements for the two RO models and the DO model. Requirements RO: Spiegler-Kedem RO: Kimura-Sourirajan DO Operating pressure At least 3 1 N/A Preliminary water runs No Yes Yes Other parameters required Concentration polarization No No Energy/Apparatus cost s High High Low Usage for 1:1 and 1:2 salts Appropriate for all salts Inappropriate for salts with low rejection (below 84%) Appropriate for all salts Error of the method High Medium Low Information provided 1.Diffusive and convective salt flux 2. Salt-water coupling coefficient 1. Mechanism of transport 2. Salt and water parameters of transport Salt and water parameters of transport Apparatus procurement Easy Easy Custom-made cell Temperature Control Easy Easy Constant ambient temperature (1oC)

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104 5.5 Factors controlling the salt permeability in RO and NF membranes It is shown throughout Chapter 4 that ther e is a pattern of permeability rate among the six salts, regardless of the experiment, m odel, the membrane material, and membrane configuration used. The order the salt permeability increases is given by Mg2+ < Ca2+ < Ba2+ < Li+ < Na+ < K+ which is in agreement with the results from the literature (Sourirajan, 1970; Yazdani, 1991). The order is also the same as the lyotropic series. The objective of this section is to dete rmine what physical and thermodynamic factors determine the order of the salt permeab ility in the studied membranes. The situations considered for analysis are: Direct osmosis (DO) experiment s-SE, AD, CG, and CK membrane Reverse osmosis (RO)-flat sheet membrane experiments-AD, CG, CK membranes a. Spiegler-Kedem model, second case (i.e. for 1=1) b. Kimura-Sourirajan model Reverse osmosis (RO)-spiral w ound membrane experiments-SW30 membrane Table 5. 4 Comparison of the salt parameters in the three cases of the Spiegler-Kedem model. Case 1 Case 2 Case 3 Characteristics Absence of concentration polarization Concentration polarization for 1 = 1 Concentration polarization from film theory and Sherwood correlation PRO Adequate for SW and 1:2 salt in BW Adequate for all membranes Adequate for BW and NF Jdiff/Jtotal Inadequate for all membranes Adequate for all membranes Adequate for BW and NF Notes: SW, BW and NF represents seawater, brackish water and nanofiltration membranes, respectively.

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105 Since the salt permeability has different notati ons in each of these experiments and each model implied for the calculations, in this s ection is named generically “ salt permeability”. 5.5.1 Physical parameters The dependency of the salt permeability in the membrane on several physical parameters of the ions in water is analyzed in this section. The physical parameters considered are the cation ionic radii, the cation hydrated radii and the diffusion coefficient of the salt in infinite dilute solution. 5.5.1.1 Ionic and hydrated radii Although the selectivity of hyperfiltratio n membranes is acknowledged not to be based on a sieving mechanism, the most intuitiv e parameter to be considered in analyzing what factors control the salt permeability is the size of the ions. The studied salts are strong electrolytes in an aqueous solvent and at the concentration of 0.05 molL-1 they dissociate and exist in the form of independent cations a nd anions (Cussler, 1997). Any movement of the cation (Li+, Na+, K+, Mg+2, Ca+2, and Ba+2) through the membrane implyes an associate movement of the anion Clin order to maintain electr oneutrality. Since all the salts considered in this research have a common anio n, it is important to consider the physical properties of the cations in examining th e differences in the salt permeabilities. Figure 5.8 shows the variation of the salt pe rmeability with the ionic radii for direct osmosis (DO) and reveres osmosis (RO) experiments for SE, AD, CG, CK, and SW30 membranes. The plots suggest a rather controve rsial result: for salts with common anion, the larger the ionic size of the cation, the faster it permeates the membrane. For example, the ionic radii of Li+ and K+ are 0.60 and 1.33 , respectively, and the permeability of NaCl and KCl in the SW30 membrane are 1.91 x10-6 cm s-1 and 2.26 x10-6 cm s-1, respectively.

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106 0608101214 0 2 4 6 8 10 12 14 0608101214 0 2 4 6 8 10 0608101214 0 2 4 6 8 10 12 14 0608101214 10 15 20 25 30 35 Ri ()Salt permeability x 10-7 (cm s-1) Salt permeability x 10-4 (cm s-1)Ri () Ri () Direct Osmosis Reverse Osmosis-SK Reverse Osmosis-KS AD membrane1:2 salts 1:1 salts CK membrane1:1 salts 1:2 salts 0608101214 05 10 15 20 25 30 Salt permeability x 10-6 (cm s-1) SW30 membrane1:1 salts 1:2 salts Ri ()Salt permeability x 10-5 (cm s-1) CG membrane1:1 salts 1:2 salts Ri ()Salt permeability x 10-6 (cm s-1) SE membrane1:1 salts 1:2 salts Figure 5. 8 Variation of salt permeability with cation ionic radius of the cation for all salts in direct osmosis and reverse osmosis experiments for AD, CG, CK, and SW30 membranes.

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107 Moreover, there are three pairs of salts with cations of almost the same ionic size (LiCl and MgCl2; NaCl and CaCl2; KCl and BaCl2) which have significant different rate of permeation through membranes. For example, the ionic radii of K+ and Ba+2 are 1.33 and 1.35 , respectively, and the permeability of KCl and BaCl2 in the SE membrane are 29.3 x10-7 cm s-1 and 9.02 x10-7 cm s-1, respectively. Therefore the differences in the ionic radius of the cations can not explain the order the salts move in the studied membranes. The inconsistencies between the order of the ionic radii and the order of the salt permeability is explained if the ionic radius of a cation is replaced by its hydrated radius. The phenomenon taking place when an ion is introduced in a polar solvent is known as solvation or hydration if the solvent is aqueous. Due to dipolar nature of the water molecules, the dissociated ions form new aggregates consisti ng of a shell of water molecules known as water of hydration surrounding the ion. The kinetic entity is no longer the bare ion but the ion accompanied by the hydration sphere. However, the water molecules in the hydrate sphere are dynamically exchanged with farther water mo lecules due to energy fluctuations (ErdeyGruz, 1974). The smaller the ionic radius of an ion and the larger the charge, the stronger the interaction with the water molecules because the electric force at the periphery of the ions is larger. Consequently, the hydrated radius is larger. The hydrated radii Rh is related to ionic radii Ri by Equation 5.10: 33 w hi AV w44 RRn 33N (5.10)

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108 where Rh is the hydrated radii ( ), nw is the number of water molecules surrounding the ion, known as hydration number, Ri is the ionic radii ( ), Vw is the molar volume of water ( 3), and NA is Avogadro’s number. There is a considerable discrepancy of the values of the hydration number, nw, reported in the literature for individual ions. The discrepancies are the result of different methods of measurement of nw, different assumptions made for the hydration of the chlorine ion, or whether the primary or secondary she ll of water molecules is considered. However, the order of hydration remains the same among the studied ions regardless the source considered for the nw values (Table H.2). Li+ and Mg+2 are the most hydrated of the monovalent and divalent cation se ries, respectively (Table H.2). The order the hydrated radii increases among the six cations is the reverse order the ionic radii increases. For example, the ionic radii increase from Li+ to K+ whereas the hydrated radii decrease from Li+ to K+. This leads to the conclu sion that the larger the hydrated radii of the cation, the slower the cation transport across membrane. Figure 5. 9 illustrates the variation of salt permeability with the hydrated radii. Regardless the membrane type (seawater, brackish water or nanofiltration), the type of the experiment (direct osmosis or reverse osmosis), and the membrane configur ation (flat sheet or spiral wound), the salt permeabilities are inversely proportional to the hydrated radii of the cations. 5.5.1.2 Diffusibility in solution It is shown in the previous sections that the mechanism of transport in dense films such as hyperfiltration membranes is diffusion dominant. In Figure 5.10, the salt permeability is plotted against the overall diffusion coefficien t of the salt in infinitely dilute solution, Dw, which is calculated based on the diffusion coeffi cient for ions in infinitely dilute solution using Equation 5.11(Cussler, 1997). The Dw, ij is the calculated overall diffusion coefficient

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109 323436384042 0 2 4 6 8 10 12 14 323436384042 0 2 4 6 8 10 323436384042 0 2 4 6 8 10 12 14 323436384042 10 15 20 25 30 35 Rh ()Salt permeability x 10-7 (cm s-1) Salt permeability x 10-4 (cm s-1)Rh () Rh () Direct Osmosis Reverse Osmosis-SK Reverse Osmosis-KS AD membrane CK membrane35 40 05 10 15 20 25 30 Salt permeability x 10-6 (cm s-1) SW30 membraneRh ()Salt permeability x 10-5 (cm s-1) CG membraneRh ()Salt permeability x 10-6 (cm s-1) SE membrane Figure 5. 9 Variation of salt permeability with hy drated radius of the cation for all salts in direct osmosis a nd reverse osmosis experiments for AD, CG, CK, and SW30 membranes.

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110 is plotted against the overall diffusion coefficien t of the salt in infinitely dilute solution, Dw, which is calculated based on the diffusion coeffi cient for ions in infinitely dilute solution using Equation 5.11(Cussler, 1997). The Dw, ij is the calculated overall diffusion coefficient of the “ij” salt in infinitely dilute solutions, |zi| represents the absolute value of the charge for ion “i”, and Dw, i represents the tabulated diffusion coe fficient for the ion “i” in infinitely dilute solution. It must be emphasized that the diffusion coefficient D from (D/K characterizes the salt diffusion within the me mbrane phase and it is different than salt diffusion coefficient, Dw, in infinitely dilute solutions. ij w,ij j i w,jw,izz D z z DD (5.11) Figure 5.10 shows a linear relationship (ave rage of regression coefficients of 0.93 8%) between the salt permeability and Dw for both 1:1 and 1:2 salts. The diffusion coefficient in water explains the order of permeation among salts with identical valences configuration (i.e. 1:1 salts or 1:2 salts) but does not explain the significant shift up of the 1:1 salts starting at Dw=1.38 x 10–5 (cm2s-1). The shift up for the 1:1 salts can be explained by the partition coefficient, K, between the membrane and the sa lt solution. According to Heyde et al. (1974), the membrane/solution partitioning coefficient, de fined as 1/K, increases with the decrease in the salt charge. The authors found 1/K equal to 45 and 43 for Na+ and K+, respectively, and 1.1 and 6.2 for Mg2+ and Ca2+, respectively. The values of 1/K for the monovalent cations are one order of magnitude higher than for the divale nt cations and this explains the difference in the salt permeability for salts with similar diffusion coefficients in water.

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1111214161820 0 2 4 6 8 10 12 14 1214161820 0 2 4 6 8 10 1214161820 0 2 4 6 8 10 12 14 1214161820 10 15 20 25 30 35 Dw x 10-5 (cm2s-1) Dw x 10-5 (cm2s-1) Salt permeability x 10-7 (cm s-1) Salt permeability x 10-4 (cm s-1)Dw x 10-5 (cm2s-1) Direct Osmosis Reverse Osmosis-SK Reverse Osmosis-KS AD membrane1:2 salts 1:1 salts CK membrane1:2 salts 1:1 salts 1214161820 05 10 15 20 25 30 Salt permeability x 10-6 (cm s-1) SW30 membrane1:2 salts 1:1 salts Dw x 10-5 (cm2s-1)Salt permeability x 10-5 (cm s-1) CG membrane1:2 salts 1:1 salts Dw x 10-5 (cm2s-1)Salt permeability x 10-6 (cm s-1) SE membrane1:2 salts 1:1 salts Figure 5. 10 Variation of salt permeability with the diffusion coefficient in infinitely dilute solution for all salts for SE, AD, CG, CK and SW30 membranes.

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112 Among the salts of the same valence configur ation (i.e. either 1:1 or 1:2 salts), a highly diffusive salt in solution phase is also highly diffusive in the membrane phase. This suggests that the partition coefficient does not play a significant role in determining the order of salt permeability among the salts with the sa me valence configuration. The importance of this finding is that Dw (which is found in the literature) can be used as a rough parameter based on which an unknown salt permeability can be estimated from plots similar to those in Figure 5.10. For example, if the salt permeability is experimentally de termined for LiCl and NaCl for a certain membrane, the salt permeability for KCl, RbCl and CsCl in that membrane can be roughly estimated from the gra ph using the published values of Dw for K+, Rb+ and Cs+. In the DO experiments for the SE membra ne (Section 5.1.2), the salt permeabilities for acetate salts are smaller than the salt perm eabilities for the chloride salts (considering pairs with the same cation). The differences can be explained by the fact that the values of Dw for the acetate salts are lower than for the chloride salts. The values of Dw for acetate salts are presented in Table H.1. 5.5.2 Thermodynamic parameters The dependency of the salt permeability in the membrane on several thermodynamic parameters of the ions in water is analyzed in this section. The physical parameters considered are the ionic enthalpy and entropy of hydration as well as the relative Gibbs (free) energy. 5.5.2.1 Enthalpy and entropy of hydration The process of ion hydration is complement ed by changes in th e energy of the ionsolvent system. The enthalpy of hydration, H, is a measurement of the interactions between

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113 the ions and the solvent molecules. It is equa l to the energy released when a mole of a particular ion dissolves in a large amount of water and forms an infinitely dilute solution. The H has negative values since it measure the energy released to the exterior (water). Similar to the hydrated radii, the enth alpy of hydration is higher (more negative) for smaller cations with large ionic charge, with the largest value corresponding to Mg2+ and the smallest corresponding to K+. Unlike for the hydration number, the enthalpy of hydration for a salt is not an equivocal parameter character izing the degree of hydration. The various methods to measure of a salt result in variations w ithin few percentages (Erdey-Gruz, 1974). Figure 5.11 shows the variation of the salt permeability with the cation enthalpy of hydration, Hcation. For salts with a common anion, the permeability varies inversely to the enthalpy of hydration of the cation. Cations presenting a large H determine a slow transport of the salts through the membrane. Similar to Rh, enthalpy of hydration of the cation can be used as an indicator of the order the salts with common anion permeate the membranes. Similar results were found by Yazdani (1991) who investigated the transport of salts with a common anion through RO cellulose acetate and thin film composite membranes. Another way of looking at hydration is from the solvent perspective, i.e. the modifications occurring in the water structure. In the process of hydration, the water molecules transfer from the bulk solvent to the h ydration shell, and a considerable ordering in the water structure around each ion takes place. Large monovalent ions such as K+ are referred as structure-breaking ions whereas small and/or multicharged ions such as Li+, Na+, and Mg2+ are referred as structure making ions (Chang, 2000). The thermodynamic quantity associated with the degree of orderi ng is the entropy of hydration, S. The S is negative when there is loss of freedom for the water mol ecules. Figure 5.12 presents the variation of

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1140500100015002000 0 2 4 6 8 10 12 14 0500100015002000 0 2 4 6 8 10 0500100015002000 0 2 4 6 8 10 12 14 0500100015002000 10 20 25 30 35 -Hcation (kJ mol-1) -Hcation (kJ mol-1) -Hcation (kJ mol-1) -Hcation (kJ mol-1) Salt permeability x 10-7 (cm s-1) Salt permeability x 10-4 (cm s-1)-Hcation (kJ mol-1) Direct Osmosis Reverse Osmosis-SK Reverse Osmosis-KS AD membrane CK membrane0500100015002000 05 10 15 20 25 30 Salt permeability x 10-6 (cm s-1) SW30 membraneSalt permeability x 10-5 (cm s-1) CG membraneSalt permeability x 10-6 (cm s-1) SE membrane Figure 5. 11 Variation of salt permeability with the cation enthalpy of hydration for all salt in direct osmosis and reverse osmosis experiments for AD, SE, CG, CK and SW30 membranes.

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115050100150200250300 0 2 4 6 8 10 12 14 050100150200250300 0 2 4 6 8 10 050100150200250300 0 2 4 6 8 10 12 14 -Scation (kJ mol-1) -Scation (kJ mol-1) -Scation (kJ mol-1) Salt permeability x 10-7 (cm s-1) Salt permeability x 10-4 (cm s-1)-Scation (kJ mol-1) Direct Osmosis Reverse Osmosis-SK Reverse Osmosis-KS AD membrane CK membrane050100150200250300 05 10 15 20 25 30 Salt permeability x 10-6 (cm s-1) SW30 membraneSalt permeability x 10-5 (cm s-1) CG membrane050100150200250300 100 150 200 250 300 350 -Scation (kJ mol-1) Salt permeability x 10-6 (cm s-1) SE membrane Figure 5. 12 Variation of salt permeability with th e cations entropy of hydration for all salt in direct osmosis and reverse osmosis experiments for SE, AD, CG, CK and SW30 membranes.

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116 the salt permeability with the cation en tropy of hydration. Similar to Hcation, Scation can be used to predict the pattern of permeation for salts with a common anion. 5.5.2.2 Relative free energy G The thermodynamic parameter that depends on both the enthalpy and entropy of hydration is the Gibbs (free) energy defined as G = H-T S, with T being the absolute temperature. The relative Gibbs energy, G = ( Gmem) Gs) relates the Gibbs energy of the hydrated ion in the bulk solution, GS, to that at the solvent-membrane interface, Gmem. The relative Gibbs energy depends not only on the ionic species and the solvent but also on the membrane porosity (Matsuura et al., 1975). The dependence of the salt permeability on th e relative free energy is presented only for 1) direct osmosis, the SE membrane, 2) reverse osmosis, Spiegler-Kedem model for 1=1 for the AD, CG, and CK membranes, and 3) re verse osmosis, Kimura –Sourirajan model and SW30 membrane element. The values of – G for Li+, Na+, K+, Mg2+, Ca2+, and Ba2+ in chloride solutions of 0.05 molL-1 for SE, AD, CG, CK, and SW30 membranes are calculated following the procedure described in the literature (Mats uura et al., 1975) using Equations 5.12 through 5.14. i iimems memsEE G RR (5.12) 2 i0 sAZe 1 1 EN 2 (5.13)

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117 i i igG RTP saltCe (5.14) where Gi is the relative free energy (kcalmol-1) of the ion “i”, Ri is the ionic radius ( ), S and mem are the corrections to the ionic radius in the bulk solution and at the membrane surface, respectively, ES and Emem are the values of E defined in Equation 5.13 for bulk solution and at the membrane interface, respectively, NA is Avogadro’s number, Zi is the ionic charge, e0 is the electron charge, s is the dielectric constant of the solvent, Psalt is the salt permeability (cms-1), C is a constant depending on the membrane porosity, i is the number of moles of the ion “i” in one mole of ionized solute, Rg is the gas constant, and T is the absolute temperature (K) ES and S are calculated in the literature from the slope and the intercept of the plot of (– GS)i vs. Ri (Friedman, 1973). The data is presented in Table I.1. For a given membrane, the set of parameters Emem and mem is unique for ions with the same sign and magnitude of the charge (i.e. there is one set for monovalent cations, one set for divale nt cations, one set for monovalent anions, etc.). In order to determ ine the set corresponding to monovalent cations, for example, experimental values of the salt permeability for a minimum of three salts with monovalent cations and with a common anion are necessary. In this dissertation, the set of Emem and mem for monovalent cations is determined by applying Equations 5.12 and 5.14 for LiCl, NaCl, and KCl whereas the set of Emem and mem for the divalent cations are determined applying the same equations for MgCl2, CaCl2, and BaCl2. The values of the relative free energy are calculated from Equation 5.12 using Emem and mem. The membrane constant and the G for Clare determined by applying Equation 5. 14 to any pair of 1:1 and 1:2 salts. The parameters obtained are presented in Table 5.4.

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118 Table 5. 5 The relative free energy for the cations, for Cl-, and for the salts and the membrane constant. Seawater membrane SE Salts G/RgT for cations G/RgT for ClG/RgT C LiCl -6.89 -13.86 NaCl -6.54 -13.52 KCl -6.00 -12.97 MgCl2 -0.31 -14.26 CaCl2 -0.24 -14.19 BaCl2 -0.20 -6.8 -14.15 1.26 Seawater membrane AD Salts G/RgT for cations G/RgT for ClG/RgT C LiCl -5.36 -11.11 NaCl -4.96 -10.71 KCl -4.48 -10.23 MgCl2 -0.77 -12.27 CaCl2 -0.69 -12.20 BaCl2 -0.62 -5.75 -12.13 2.66 x 10-2 Brackish water membrane CG Salts G/RgT for cations G/RgT for ClG/RgT C LiCl -2.82 -7.30 NaCl -2.71 -7.18 KCl -2.50 -6.97 MgCl2 -0.69 -9.64 CaCl2 -0.61 -9.55 BaCl2 -0.54 -3.13 -9.48 1.72 x 10-2 Nanofiltration membrane CK Salts G/RgT for cations G/RgT for ClG/RgT C LiCl -1.11 -5.58 NaCl -1.07 -5.54 KCl -0.99 -5.46 MgCl2 1.07 -7.87 CaCl2 1.26 -7.69 BaCl2 1.30 -4.47 -7.65 7.69 x 10-3 Seawater membrane element SW30 Salts G/RgT for cations G/RgT for ClG/RgT C LiCl -1.82 -2.91 NaCl -1.77 -2.87 KCl -1.65 -2.74 MgCl2 -1.12 -3.31 CaCl2 -1.07 -3.27 BaCl2 -1.00 -1.10 -3.20 3.50 x 10-5

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119 According to Matsuura et al., (1975), a negative Gi means that an ion requires energy to advance from the bulk phase to the me mbrane surface and, therefore, is repelled by the membrane surface. On the other hand, an ion with a positive Gi is attracted to the surface. Furthermore, the authors correlated the sign of the relative free energy of an ion to the sign of the charge on the membrane surface. The cations have G < 0 for membranes with a positive surface charge and G > 0 for membranes with a negative surface charge. As presented in Table 5.4, all cations studi ed in this dissertation are repelled by the membranes except for the divalent cations in the nanofiltration membrane. Similar, the anion Clis also repelled by the membrane surface for all five membranes. The SW30 membrane element has a negative surface charge, accordi ng to the manufacturer. No information about the surface charge could be obtained from the membrane’s manufacturer for the SE, AD, CG, and CK membranes. The surface charge of a membrane is commonly measured in the literature using the zeta potential. Using this method, all the cellulose membrane and polyamide/thin film composite membranes are re ported in the literature to have a negative surface charge at pH higher than 5 (Baker et al., 1991; Childress and Elimelech, 1996; Childress and Deshmukh, 1998; Deshmukh and Childress, 2001; Vrijenhoek et al., 2001). Assuming that the surfaces of the five membrane s are negatively charged, the repulsion of the anion by the membrane surface is correlated with the surface charge for the five membranes. The identity of the signs in the relative fr ee energy for cations and anions is in disagreement with Matsuura’s findings. The disa greement can be explained as follows: If the membrane repels the anion due to charge simila rity, it should attract the cation. However, the two opposing charged ions, cation and anion, ar e tied together electrostatically in their movements in order to maintain the solution electroneutrality. The cations move back and forth from the bulk solution to the membrane vicinity and whether they prefer one location to

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120 another, depends on whether the interaction be tween the cations and the membrane sites is stronger or weaker than the interaction between the cation and the anion of its ion pair. The negative G for the cations in Table 5. 4 reflects a stronger interaction of the cation-anion pair than cation-membrane surface. The positive G (divalent cations in the nanofiltration membrane) reflects a weaker interaction ca tion-anion than cation-membrane surface. Moreover, the membrane surface charge can be reduced by 1) the effect of concentration polarization (in RO) and 2) the adsorption of di valent cations in the membrane surface sites (Deshmukh and Childress, 2001; Vrijenhoek et al ., 2001). A reduced negative charge on the membrane surface will favor the dominancy of th e cation-anion interaction and therefore, the repulsion of the cation by the membrane. As shown in Table 5. 4, the values of (G/RgT) increases in the order Mg2+
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121 The relative free energy emerges as a para meter that can be used in predicting the salt permeability in RO and NF membranes. Fi gure 5. 13 presents the variation of the salt permeability with the relative free energy for the salt, (G/RgT). The very good linearity confirms Equation 5.13 for the studied membranes. If the values of salt permeability for 2 more other salts with a common cation and two different monovalent anions are known for a membrane, the plots from Figure 5.12 can be used to predict the salt permeability of any 1:1 and 1:2 salts for that particular membrane. For example, if the salt permeability for NaF and NaI are known for the seawater membrane AD (in addition to the salt permeabilities for the six salts needed to draw the plot), the set of Emem and mem for the monovalent anions can be determined, from which the relative free energy for any monovalent anion can be calcula ted. Since the relative free energy of any monovalent and divalent cation can be determ ined based of the corresponding sets of Emem and mem, the plot from Figure 5.13 for the AD membrane can be used to determine the salt permeability for any combination of 1:1 and 1:2 salts (ie fluorides, chlorides, bromides and iodides of any alkali and alkaline earth metals). 5.5.3 Conclusions on the factors controlling the salt permeability in RO and nanofiltration membranes The salt permeability for the six st udied salts ranks in the order MgCl2
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122-13 -12 -11 -10 -17 -16 -15 -14 -13 -12 -9-8-7-6-5-4 -95 -90 -85 -80 -75 -70 -10-9-8-7-6 -110 -105 -100 -95 -90 -15 -14 -13 -12 -120 -115 -110 -105 -100 -95 -90 iG/RgT)iLn(Salt permeability) Ln(Salt permeability) Ln(Salt permeability) Ln(Salt permeability)iG/RgT)i AD membrane CK membrane-34-32-30-28-26 -140 -135 -130 -125 -120 -115 SW30 membraneiG/RgT)i CG membraneiG/RgT)iiG/RgT)iLn(Salt permeability) SE membrane Figure 5. 13 Variation of the salt permeability with the relative free energy for all salts in direct osmosis and re verse osmosis experiments for the SE, AD, CG, CK and SW30 membranes.

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123 Mg2+), (Na+ and Ca2+), and (K+ and Ba2+) have close value of the ionic radii, however, the salt permeabilities are significantly slower for the divalent cations than for the monovalent cations. There is a strong interaction of the solute ions with water molecules (ion-dipole interaction), and one should cons ider the effective radii of th e ions, which take into account the water molecules bounded around the charged ions in a 3-dimensional space. The degree of hydration is a function of both size and ch arge, being higher for small ions with large charge. There are several ways of describing th e degree of hydration. The hydrated radii explain the order of salt permeation, however, it is a parameter not uniquely defined, in that its values vary with the method of measuremen t. The enthalpy of hydration as well as the entropy of hydration represent more precise quantifications of the degree of hydration and can be used in a qualitative evaluation of th e permeation rate for a salt in RO and NF membranes by performing comparative studies. Unlike the entropy and enthalpy of hydra tion, the relative free energy takes in consideration not only the interaction ion-solven t in the bulk solution but the interactions at the membrane surface. It is a function of ionic species as well as on the membrane material. The relative free energy permits the calcula tion of salt permeability based on several preliminary data. The free energy, as well as th e enthalpy and entropy of hydration have the limitations of not providing any insight into the actual mechanism of salt transport in the membrane. The salt permeability increases with the incr ease of the salt diffusion coefficient in infinitely dilute solutions. The diffusion coeffici ent of a salt in infinite dilute solution can be used as an indicator of the order the salt permeat es through the membrane for either 1:1 or 1:2 salts. However, the salt diffusion coefficient in wa ter fails to describe the differences between

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124 the 1:1 and 1:2 salts. These differences are attr ibuted to the differences of the partitioning coefficient for the 1:1 and 1:2 salts.

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125CHAPTER 6 CONCLUSIONS In this Chapter, the experimental results of this dissertation are summarized. The importance and the implications of these re sults with respect to the theoretical and engineering aspects are emphasized. The Chapter c oncludes the findings of the direct osmosis experiments, followed by the reverse osmosis experiments and by a pa rallel between the two processes. Last, this Chapter concludes on the factors controlling the salt permeability. 6.1 Direct osmosis (DO) experiments The results from the direct osmosis experiments show that the concentration at the membrane wall is lower than the concentrati on in the bulk solution. The effect of salt depletion at the membrane wall is more pr onounced for nanofiltration membranes for which the concentration at the membrane wall is found ab out ten times less than the concentration in the bulk solution. Disregarding the effect of dilution for the salt solution at the membrane surface results in lower salt permeabilities than the salt permeabilities when the dilution is considered. In this research, concentration at the membrane wall is calculated based on the measured pure water flux and the pure wate r permeability of the membrane, which is determined from a reverse osmosis experiment A new equation is desired to calculate the concentration at the membrane wall without the need of pure water permeability, which requires an extra RO experiment. This research shows that the pure water flux in DO depends only on the valence of the salt (such as 1:1, 1:2 etc), which implies that the pure water flux and the salt flux do not interact with each other inside the membrane. Demonstrating that the

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126 salt and water fluxes are uncoupled in direct os mosis can be used as an initial premise in developing a new theoretical method for the calculation of the salt permeability in DO. Figure 6.1 presents the cases for which the salt permeability measured in DO experiments is equal to the salt permeabilit y in RO experiments. The SW, BW and NF represent the seawater, brackish water and na nofiltration membrane, respectively, and (1:2) represents the 1:2 salts. The coefficient (D/K )DO represent the salt permeability in direct osmosis experiments, PRO (1) is the salt permeability in the RO Spiegler-Kedem model when the concentration polarization is neglected, PRO (2) is the salt permeability in the RO SpieglerKedem model when the concentration polarization is calculated for the reflection coefficient equal unity, PRO (3) is the salt permeability in the RO Spiegler-Kedem model when the concentration polarization is calculated by combining the film theory with the Sherwood correlation, and (D/K )RO is the salt permeability in RO Kimura-Sourirajan model. The implications of this equality are presente d in Section 6.3, Comparison of DO and RO processes. RO )3( RO )2( RO )1( RO DOK D PPP K D BW, NF SW, BW(1:2), NF(1:2) SW, BW, NF SW, BW(1:2) SW, BW(1:2) BW, NF Figure 6. 1 The equality of salt perm eability in DO and RO experiments.

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127 6. 2 Reverse osmosis (RO) experiments a) Spiegler-Kedem model The first case of the Spiegler-Kedem mode ls neglects the concentration polarization and leads to erroneous result that the convecti on is the dominant transport mechanism of salt through the hyperfiltration membranes. The second case of the Spiegler -Kedem model (reflection coefficient ) is adequate to calculate both the salt permeability and the percentage of the diffusive salt flux of the total salt flux for all three membrane types, seawater, brackish water and nanofiltration me mbranes. However, this case requires an additional experiment with pure water in order to determine the hydraulic permeability of the membrane. The third case of the SK model is appropriate to calculate both the salt permeability and the percentage of the diffusi ve salt flux of the total salt flux only for brackish water and nanofiltration membranes. Th e third case requires information about the test cell geometry as well as the Reynolds num ber. As summarized in Figure 6.1, the salt permeabilities for the three cases of the Spiegl er-Kedem model are equal for all salts in seawater membrane and 1:2 salts in brackish wa ter membrane (R>94%). This implies that for situations when the rejection coefficient is higher than 94%, the first case of the SpieglerKedem model should be used in calculating the salt permeability since it requires fewest number of parameters. The results from Spiegler-Kedem model demonstrate that the mechanism of salt transport in RO processes is diffusion dominan t for both reverse osmosis and nanofiltration membranes. However, convective flux can contribute as much as 32% to the total flux for seawater membranes and as much as 46% in the case of brackish water and nanofiltration membranes. The diffusive flux is more importa nt for the 1:2 salts than for 1:1 salts in brackish water and nanofiltration membrane. The importance of the diffusion mechanism has

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128 practical applications to the membrane manufact uring. The diffusive properties of the salts should be considered in developing the polym ers and processes for membranes in order to achieve a desired salt selectivity. The two salt parameters, the reflection coefficient, 1 and the salt-water coupling coefficient, 2, in the Spiegler-Kedem model are assu med equal in the literature. The results of this dissertation show that the two parame ters are equal only for membranes/salts with a diffusive salt flux of at least 65% of the total salt flux (Figure 5.5), which in turn corresponds to a rejection coefficient higher than 86% (Fi gure 5.7). This implies that the number of unknown parameters in the Spiegler-Kedem model cannot be reduced to three (LP, and PRO), as presented in the literature, unless the re jection is higher than the threshold value of 86% found in this work. b) Kimura Sourirajan model The two RO models, Spiegler-Kedem and Kimura-Sourirajan, are used interchangeably in the literature to charact erize the salt transport in hyperfiltration membranes. It is shown in this dissertation th at the two RO models are equivalent only for membranes/salts with a rejection coefficient of at least 86% (all salts in seawater membrane, and only 1:2 salts in brackish water and nanof iltration membranes). The use of the KimuraSourirajan model for rejection coefficients lo wer than 86% results in overestimating the salt permeability coefficient and consequently, to over-designing a membrane separation system. 6.3 Comparison of DO and RO processes The equality of the salt permeability for DO and RO experiments validates the equation derived in Section 5.1.2 for the salt permeability in the DO processes. It also allows one to choose the most convenient experime ntal set-up and, independently, the most convenient model (for RO) to determine the salt permeability. The decision for choosing the

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129 best option depend on many factors, such as the membrane type, the rejection coefficient, the parameters needed for analysis, the sequence of performing the experiments for a number of salts, the time schedule, the availability of ope rators, the possibilities of temperature control, and the available budget. The implications of these decision factors are briefly discussed below: Membrane type/Rejection coefficient and parameters needed for analysis If the salt permeability needs to be determin ed, the valid experiments and models one can choose from are presented in Figure 6.1. The DO experiments are appropriate for all hyperfiltration membranes, whereas the Kimura -Sourirajan model is appropriate only for membranes/salts with rejection higher than 86% The first case of the Spiegler-Kedem model can be used to calculate the salt permeability fo r situations when rejection is higher than 94%. The second and the third cases of the Spiegler-K edem model can be used to calculate the salt permeability for all hyperfiltration membranes, regardless the rejection coefficient. In choosing the most appropriate RO model, one should consider that The Spiegler –Kedem model requires the run for each salt to be carri ed out at several operating pressures, whereas the Kimura-Sourirajan model needs only one op erating pressure per salt. However, the Kimura-Sourirajan model requires additional runs with DI water to determine the pure water permeability. If the pure water permeability is needed and DI water is available, both RO models can be used since the equations defining DI water transport are identical. However, the situations when only the pure water permeability is needed are not often; in most of the practical cases, the pure water permeability needs to be obtained whenever the salt permeability is sought. The advantage of using either the first or the third case of the

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130 Spiegler-Kedem model is that the salt and water permeability can be obtained simultaneous with no additional DI water run which will be re quired if the Kimura Sourirajan is used to calculate both the salt and water permeability. If the percentage of the diffusive salt flux of the total salt flux has to be calculated, the only analysis available for the seawater membranes is the second case of the Spiegler-Kedem model. For brackish water and nanofiltration membranes, both the second and the third cases of the Spiegler-Kedem model can be used. Sequence of salts It is observed that unlike in RO, concentr ation polarization does not develop in DO. Moreover, the salt concentration at the me mbrane wall in DO is lower than the salt concentration in the bulk solution. This phe nomenon suggests that DO experiments would be preferred to RO experiments when the salt pe rmeability for a sequence of several salts is required. In RO processes, the membrane is su sceptible to scaling, fouling and compaction, and the salt permeability of a particular salt is influenced by the history of the membrane exposure, and therefore may require using a new sheet of membrane for each experiment. Time schedule The duration of the experimental work requi red to determine the parameters of the Spiegler-Kedem model is at least 9-10 hours per desired salt. Additionally, at least one run of 3 to 4 hours must be conducted for the pure water permeability if the second case of the model is considered. The Kimura-Sourirajan model requires only one operating pressure, which shortens the experimental time for one sa lt to 3 hours, plus 3-4 hours for a pure water experiment. The length of the DO runs in this research were of 10 hours, however the time can be shortened to only few hours if conductivit y probes with high accuracy in the range of DI water conductivity are used. The high accur acy conductivity sensors can detect the small increases in the DI water conductivity occurri ng in the first hours of the DO experiments.

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131 Operators availability The most involvement of the experiment ope rator is needed for the Spiegler-Kedem model because each run has to be performed at several operating pressures. The SpieglerKedem model also requires the intervention of th e operator because the system needs to be cleaned between different salts and the feed solution changed. The DO experiments are the least soliciting and the intervention of the operato r is required only in the beginning and at the end of the run, assuming automatic data logging. Temperature control Transport parameters in hyperfiltration membranes are temperature sensitive. Preliminary data is required to perform th eoretical temperature corrections and these corrections can introduce additional errors in th e calculations of the transport parameters. The temperature control should be preferred to temp erature correction whenever is possible. In RO, elevated temperatures can be reached in th e water, especially at high operating pressure, therefore the use of a cooling system is ofte n necessary. In DO, the increase in the system temperature is less than few degrees, and the temperature can be controlled by maintaining constant ( 1OC) ambient temperature. Capital and operating costs The costs involved for running RO experime nts are considerably higher than for DO experiments. In this research, the costs of th e apparatus used to perform the RO experiments exceeded $10,000, whereas only approximately $1,500 was needed to procure the DO apparatus. However, the DO experiment re quires a test cell which is not commercially available and has to be custom fabricated. Th e design of the DO cell is relatively simple and inexpensive materials, such as acrylic, can be used. The energy consumption to perform a RO experiment is considerably higher than to perform a DO experiment.

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132 6.4 Factors controlling the salt permeability The order of the salt permeability among the si x studied salts is the same regardless the experiment type (DO or RO), the memb rane type (seawater, brackish water or nanofiltration), the membrane configuration (flat sheet or spiral wound), or the model chosen (Spiegler-Kedem or Kimura-Sourirajan). The order of the salt permeability is in perfect agreement with the lyotropic series which c onfirms the physicochemical nature of the transport mechanisms taking place in the membranes. The order of separation for strong electroly tes with common anion in hyperfiltration membranes can be explained by the different degrees of the hydration for the cations. Any parameter quantifying the hydration of the cation (hydrated radii, enthalpy of hydration or entropy of hydration) can be used for a r ough estimation of the salt permeability. Comparing the hydration parameter of the salt with th e hydration parameter of a salt with a known permeability, the permeability of the first salt can be estimated from plots similar to those presented in Figures 5.9, 5.11 or 5.12. If a mo re precise prediction of the salt permeability is desired, the relative free energy theory can be used, although it requires many more known values of the permeabilities for other salts. Th e prediction of the salt permeability based on the tabulated values of the physical or th ermodynamic properties of the salt and the known values of salt permeability of other salts can reduce significantly the experimental work especially when the salt permeability is required for a large number of salts. 6.5 Summary This work proves that the diffusion is the dominant transport process in hyperfiltration membranes. The equality of th e salt permeability in DO and RO experiments represents a significant finding which allows the selection of the most appropriate experiment and model to calculate salt permeability. This re search shows that the permeation of salts

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133 with a common anion is controlled by the cation hydration. Any parameter quantifying the cation hydration as well as the relative free en ergy can be used for prediction of a unknown salt permeability based on known sa lt permeability of other salts.

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134CHAPTER 7 RECOMMENDATIONS This research has shown that the concen tration at the membrane wall in direct osmosis is lower than the concentration in the bulk solution. The concentration at the membrane wall was calculated in this dissert ation based on the pure water permeability of the membrane, which was determined from revers e osmosis experiments. A new method of determining the concentration at the membrane wall which should not require additional RO experiments, has to be developed. The starti ng point in determining the equation which will allow the calculation of the concentration at the membrane wall in DO is to consider that at steady state, all the salt fluxes across the me mbrane are balanced. The resulting equation will be similar to the equation used to calculate th e concentration polarization factor in RO from the thin film theory. Another limitation of the DO research is th e consideration of the salt and water fluxes as independent in the membrane. The results of this dissertation confirmed this assumption, however further studies need to consider th e implications of a coupling between salt and water fluxes across the membrane. The coupling eff ect might be relevant for high salt fluxes, such as 1:1 salts in nanofiltration membranes. The Spiegler-Kedem model and the Kimura-S ourirajan model were selected for the membrane transport analysis in this disserta tion because they are widely applied in the literature. Other models which include both diffu sive and convective salt fluxes need to be explored. These models include solution-diffusi on-imperfection, the frictional model and the finely-porous model. The solution-diffusion-impe rfection model considers that water and salt are transported by diffusion and convection in the membrane pores and is most suitable for

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135 membranes with larger pores, such as na nofiltration membranes. The frictional model assumes that the driving forces for any species are balanced by the frictional forces exerted by the other components, including the membrane. The importance of the salt diffusive and convective fluxes can be determined by comp aring the friction coefficients between saltwater and salt-membrane. The finely-porous model includes the hindering effects of the diffusion and convection fluxes due to the very small size of the pores (less than 0.5 nm). An aspect that was not emphasized in th is research is the surface charge on the membranes. Some authors consider that the me mbrane surface charge plays a more important role in the mechanism of salt separation for NF membranes than for RO membranes. This research has to be extended to models that include the effects of the membrane surface charge, such as the Nernst-Plank model. This m odel describes the transport of ions across the membrane as a result of diffusion and convection, but the diffusive flux is considered to be due to both concentration and electrical potentia l gradients. The drawbacks of the model are that the membrane surface charge and the thic kness of the membrane skin layer need to be known. Calculating the concentration polarization by combining the thin film theory and Sherwood correlation lead to erroneous results in the case of seawater membrane in this research. It is believed that the use of the Sherwood correlation from th e literature might be inadequate. A more accurate dimensionless corre lation can be obtained if a term relating the Reynolds number and the salt and water permeati on rate are considered. The coefficients of such correlation have to be de termined experimentally for the specific test cell used. The experimental method of determining these empiri cal coefficients of correlation is described by Prabhakar and Ramani (1994) and Ramani (1992).

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136 The measurements of the zeta potential in the literature show that the membrane surface charge depends on the pH of the feed water. A common pattern for variation of surface charge with pH shows that at low pH the surface charge is positive and decreases with the increase of the pH range. A shift in th e sign of the charge occurs at pHs between 3 and 5 while at higher pHs, a negative charge increases with an increase in pH. Moreover, cellulose acetate membranes are subject to hydrol ysis at low pH which results in modification in the membrane water contents and the natu re of the water-polymer binding. Additional investigation is required to de termine the effects of the feed water pH on the transport properties of the membranes. In verifying the relative free energy theory, it was found that the chloride ion, which is negatively charged, was attracted to the membrane surface of all five membranes studied. According to the literature data, the membra ne surface charge is also negative and the attraction of the co-ion by the membrane su rface was explained by the co-ion/counter-ion dragging effect. In order to maintain soluti on electroneutrality, the co-ion which is attracted to the membrane, pulls the counter-ion, and th e two ions move together due the dragging effect. The investigation needs to be continued in two directions: first, the assumption made about the negative surface charges on all five memb ranes needs to be confirmed. This can be done by measuring the charge using a surf ace zeta potential method. Second, additional experiments with the same salts but positively charged membranes can test the validity of the cation-anion dragging effect. It was shown in this study that the salt pe rmeability increases with the increase in the salt diffusivity in infinite dilute solution. The plot of the salt permeability for 1:1 and 1:2 salts versus salt diffusivity in infinite dilution pres ents a significant ”shift “ up of the 1:1 salts compared to the 1:2 salts. Since the salt permea tion through the membrane is function of both

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137 diffusion and adsorption, the “shift” suggested that the partition coefficient of the salt between the feed solution phase and membrane pha se is different for 1:1 salts than for 1:2 salts. This assumption can be verified experime ntally by determining the partition coefficient for the 1:1 and 1:2 salts. Two methods are curren tly used in the literature to determine the solution-membrane partition coefficient: 1) by using an adsorption/desorption experiment and 2) by using a DO experiment and time the lag method. The findings of this research are limited to single solutions of strong electrolytes at relatively low concentrations, where they exist in dissociated form. The research needs to be extended to the following categories of solutes: 1) strong electrolytes in dilute solutions for salts with a common cation and different an ions; 2) strong electrolytes at higher concentrations; 3) weak electrolytes and non-el ectrolytes at varying concentrations; and 4) mixture of salts, also at varying concentrations Each category of solutes is described below: Strong electrolytes in dilute solutions for salts with a common cation and different anions. This research has prove d that for strong chlorides salts, the salt permeability in the membrane increases w ith the increase of salt diffusivity in water. However, some studies (Krinke 1988) have shown that although the diffusivity of nitrate salts is lower than of chloride salts in water, the salt permeability of nitrates is higher than the salt permeability of the chlorides. Therefore, the differences in the salt permeabilities in membrane for salts with common cation and different anions cannot be explained by the differences in the salt diffusivity in water. Strong electrolytes at high concentration. Due to electrostatic attraction of the oppositely charged ions at high concentrations, ion-pairs are formed. The factors controlling the salt permeabilities in such cases need to be investigated.

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138 Weak electrolytes and non-electrolytes. Weak electrolytes in solvent are partly dissociated and partly in their molecular form. Non-electrolytes, such as organic molecules, exist only in the molecular form. The neutral molecules do not hydrate in water and therefore, none of the thermodynamic parameters quantifying the hydration can be used to explain the relative order of permeation for those salts. Mixture of salts. The most important application of the RO processes is desalination of seawater and brackish water. These water sources contain among other components, mixture of inorganic salts. It has been shown that the concentration polarization for individual salts changes substantially with the presence of other salts (Srinivasan and Tien 1970). The equations of transport in membranes are complex for multicomponent systems with more than one anion and more than one cation. The Spiegle r-Kedem model is valid only for binary systems and it cannot be used for mixture of salts. One alternative is the use of Nernst -Plank model which for a mixture of n ions requires (3n+2) equations. Another option is the use of the artific ial neural network model described by Bowen et al. (2000).

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139REFERENCES Baker, R.W., 2000. Membrane Technology and Applications McGraw-Hill, Menlo Park. Baker, R.W. et al., 1991. Membrane Separati on Systems. Noyes Data Corporation, New Jersey. Belfort, G., 1984. Synthetic Membrane Processes. Academic Press, Orlando. Bhanushali, D., Kloos, S. and Bhattacharyya, D ., 2002. Solute transport in solvent-resistant nanofiltration membranes for non-aqueous system s: experimental results and the role of solute-solvent coupling. Journal of Membrane Science, 208: 343-359. Bhattacharya, S. and Hwang, S.T., 1997. Concen tration polarization, separation factor and Peclet number in membrane processes. Journal of Membrane Science, 132: 73-90. Bitter, J.G.A., 1991. Transport Mechanism in Membrane Separation processes. Plenum Press, New York. Bockris, J.O.M. and Reddy, A.K.N., 1970. Modern Electrochemistry. Vol I. Plenum, New York. Bowen, W.R., Jones, M.G.J., Welfoot, J.S. and Yousef, H.N.S., 2000. Predicting salt rejections at nanofiltration membrane using artificial neural networks. Desalination, 129: 147-162. Burgess, J., 1988. Ions in Solution. Basic Principles of Chemical Interactions. Ellis Horwood, Chichester. Carter, J.W., Hoyland, G. and Hasting, A. P.M., 1974. Concentration polarization in reverse osmosis flow systems under la minar conditions. Effect of surface roughness and fouling. Chemical Engineering Science, 29: 1651-1658. Chang, R., 2000. Physical Chemistry for the Chemical and Biological Sciences. University Science Books, Sausalito. Chaudry, M.A., 2002. Water and ions tran sport mechanism in hyperfiltration with symmetric cellulose acetate membranes. Journal of Membrane Science, 5204: 1-14. Childress, A.E. and Deshmukh, S.S., 1998. Effect of humic substances and anionic surfactants on the surface charge and performance of reverse osmosis membranes. Desalination, 118: 167-174.

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140 Childress, A.E. and Elimelech, M., 1996. E ffect of solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes. Journal of Membrane Science, 119: 253-268. Conway, B.E., 1981. Ionic Hydration in Chem istry and Biophysics. Elsevier Sceintific Publishing Company, Amsterdam. Cussler, E.L., 1997. Diffusion-Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge. Deshmukh, S.S. and Childress, A.E., 2001. Ze ta potential of commercial RO membranes: influence of source water type and ch emistry. Desalination, 140: 87-95. Diawara, C.K., Lo, S.M., Rumeau, M., Pontie M. and Sarr, O., 2003. A phenomenological mass transfer in nanofiltration of halide ions for selective deflourination of drinking water. Journal of Membrane Science, 219: 103-112. Dickson, J.M., Matsuura, T. and Blais, P., 19 75. Reverse osmosis separation of some organic and inorganic solutes in aqueous solutions using aromatic polyamide membranes. Journal of Applied Polymer Science, 19: 801-819. Elimelech, M., Zhu, X., Childress, A.E. and Hong, S., 1997. Role of membrane surface morphology in colloidal fouling of ce llulose acetate and composite aromatic polyamide reverse osmosis membranes. Jour nal of Membrane Science, 127: 101-109. Erdey-Gruz, T., 1974. Transport Phenoma in Aqueous Solutions Akademiai Kiado, Budapest. Fang, H.H.P. and Chian, E.S.K., 1975. Criterion of ion separation by reverse osmosis. Journal of Applied Polymer Science, 19: 2889-2895. Fang, H.H.P. and Chian, E.S.K., 1976. Remova l of dissolved solids by reverse osmosis. AICHE Symposium Series: Physical, chemical, wastewater treatment, 73(166): 137-143. Friedman, H.L., 1973. Water-A Compre hensive Treatise. Plenum, New York. Frommer, M.A., Murday, J.S. and Messalem, R.M ., 1973. Solubility and diffusivity of water and of salts in an aromatic polyamide fi lm. European Polymer Journal, 9: 367-373. Gekas, V. and Hallstorm, B., 1987. Mass transfer in the membrane concentration polarization layer under turbulent cross flow : I. Cr itical literature review and adaptation of existing Sherwood correlations to membra ne operations. Journal of Membrane Science, 30(2): 153-170. Gilron, J., Gara, N. and Kedem, O., 2001. Experimental analysis of negative salt rejection in nanofiltration membranes. Journal of Membrane Science, 185: 223-236.

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141 Glueckauf, E., 1976. The distribution of el ectrolytes between cellulose acetate membranes and aqueous solution. Desalination, 18: 155-172. Heyde, M.E., Peters, C.R. and Anderson, J.E ., 1974. Factors influencing revese osmosis rejection of inorganic solutes from aqueous solution. Journal off Colloid and Interface Science, 50(3): 467-487. Johnson, H.K., 1975. Reverse osmosis rejec tion of heavy metal cations. Desalination, 16: 205-224. Jonsson, G. and Benavente, J., 1992. Determina tion of some transport coefficients for the skin and porous layer of composite me mbrane. Journal of Membrane Science, 69: 29-42. Kessler, J.O. and Moody, C.D., 1976. Drinking water from sea water by forward osmosis. Desalination, 18(3): 297-306. Krinke, S.L., 1988. The Effect of Ion Species on Concentration Polarization. Master Thesis, University of South Florida. Lonsdale, H.K., Cross, B.P., Graber, F.M. and Milstead, C.E., 1971. Permeability of cellulose acetate membranes to selected solutes. Journal of Macromolecular Science-Part B:Physics., 5(1): 167-188. Lonsdale, H.K., Merten, U. and Riley, R.L., 19 65. Transport properties of cellulose acetate osmotic membranes. Journal of App lied Polymer Science, 9: 1341-1362. Mallevialle, J., Odendaal, P.E. and Wiesner, M.R. (Eds), 1996. Water Treatment Membrane Processes. McGraw-Hill. Marinas, B.J. and Selleck, R.E., 1992. Re verse osmosis treatment of multicomponent electrolyte solutions. Journal of Membrane Science, 72: 211-229. Mason, E.A. and Lonsdale, H.K ., 1990. Statistical-mechanical theory of membrane transport. Journal of Membrane Science, 51: 1-81. Mason, E.A., Wenndt, R.P. and Bresler, E.H., 197 2. Test of the Onsager relation for ideal gas trasport in membranes. Journal of Chemical Society. Faraday Transactions II., 68: 1938-1945. Matsuda, M. and Kamizawa, C., 1984. Precise measurement of membrane constants of cellulose acetate membranes by direct os mosis tests. Desalination, 49(3): 367-378. Matsuura, T., Pageau, L. and Sourirajan, S., 1975. Reverse osmosis separation of inorganic solutes in aqueous solutions using porous cellulose acetate membranes. Journal of Applied Polymer Science, 19: 179-198.

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142 McCray, S.B., Vilker, V.L. and Nobe, K. 1991. Reverse osmosis cellulose acetate membranes.II. Dependence of transport pr operties on acetyl content. Journal of Membranes Science, 59: 317-330. Mori, K. et al., 2000. Diffusional characteristics of sodium chloride in symmetrical cellulose acetate membranes measures by an unstead y-state dialysis method. Desalination, 127: 225-249. Mulder, M., 2003. Basic Principles of Membrane s Technology. Kluwer Academic Publishers, Dordrech. Petrotos, K., B., Peter C. Quantick, P.C. and Petropakis, H., 1999. Direct osmotic concentration of tomato juice in tubular membrane – module configuration. II. The effect of using clarified tomato juice on the process performance. Journal of Membrane Science, 160(2): 171-177. Petrotos, K.B. and Lazarides, H.N., 2001. Osmotic concentration of liquid foods. Journal of Food Engineering, 49(2-3): 201-206. Petrotos, K.B., Quantick, P. and Petropakis, H., 1998. A study of the direct osmotic concentration of tomato juice in tubular membrane – module configuration. I. The effect of certain basic process paramete rs on the process performance. Journal of Membrane Science, 150(1): 99-110. Pontie, M., Buisson, H., Diawara, C.K. and Essis-Tome, H., 2003. Studies of halide ions mass transfer in nanofiltration-applicatio n to selective deflourination of brackish drinking water. Desalination, 157: 127-134. Prabhakar, S. and Ramani, M.P.S., 1994. A new concept of mass transfer coefficient in reverse osmosis-practical applications. Jour nal of Membrane Science, 86: 145-154. Ramani, M.P.S., 1992. Mass transport mechan ism on the high-pressure side in reverse osmosis: an analysis. Chemical Engineering Science, 47(15-16): 4099-4105. Rautenbach, R. and Albrecht, R., 1989. Me mbrane Processes. John Wilet & Sons. Rutgers, A.J. and Hendrikx, Y., 1962. Ionic hy dration. Trans. Faraday. Soc., 58: 2184-2191. Sablani, S.S., Goosen, M.F.A., Al-belushi, R. and Wilf, M., 2001. Concentration polarization in ultrafiltration and reverse osmosis: a critical review. Desalination, 141: 269-289. Schaep, J., Van der Bruggen, B., Vandecasteele, C. and Wilms, D., 1998. Importance of ion size and charge in nanofiltration. Sepa ration and Purification Technology, 14: 155-162. Sherwood, T.K., Brian, P.L.T. and Fisher, R. E., 1967. Desalination by reverse osmosis. Industrial and Engineering Chemistry Fundamentals, 6(1): 1-12.

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143 Soltanieh, M. and Gill, W.N., 1981. Review of reverse osmosis membranes and transport models. Chemical Engineering Communications, 12: 279-363. Sourirajan, S., 1970. Reverse Osmosis. Academic Press, New York. Spiegler, K.S., 1966. Thermodynamics of hyperfiltration (Reverse Osmosis): criteria for efficient membranes. Desalination, 1: 311-326. Srinivasan, S. and Tien, C., 1970. A simplified method for the prediction of concentration polarization in reverse osmosis operation for multicomponent systems. Desalination, 7: 133-145. Strathmann, H.K. and Michaels, A.S., 1977. Po lymer-water interaction and its relation to reverse osmosis desalination efficiency. Desalination, 1: 311-326. Sutzkovere, I., Hasson, D. and Semiat, R., 2000. Simple technique for measuring the concentration polarization level in a re verse osmosis system. Desalination, 131: 117-127. Taniguchi, M. and Kimura, S., 2000. Estimation of transport parameters of RO membranes for seawater desalination. AIChE Journal, 46(10): 1967-1973. Taylor, J.R., 1997. An Introduction to Error An alysis. University Science Book, Sausalito. Urama, R.I. and Marinas, B.J., 1997. Mechanistic interpretation of solute permeation through a fully aromatic polyamide reverse os mosis membrane. Journal of Membrane Science, 123: 267-280. Van Gauwbergen, D. and Baeyens, J., 1998. Modeling reverse osmosis by irreversible thermodynamics. Separation and Puri fication Technology, 13: 117-128. Vrijenhoek, E.M., Hong, S. and Elimelech, M., 2001. Influence of membrane surface properties on initial rate of colloidal foul ing of reverse osmosis and nanofiltration membranes. Journal of Memb rane Science, 188: 115-128. Weast, R.C., 1967. Handbook of Physics and Chemistry. Chemical Rubber Pub. Co., Cleveland. Yazdani, K., 1991. Studies in Separation of I onic Species by Reverse Osmosis Membranes. Ph.D. Dissertation, University of South Florida.

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144 APPENDICES

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145APPENDIX A: DIAGRAMS OF THE TEST CELLS O-ringsSlit Solution in Solution out Fixing Screws Membrane Figure A. 1. DO test cell top view of the salt solution chamber. DI in DI out DI Flow Figure A. 2. DO test cell top view of the DI water chamber.

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146 APPENDIX A: (CONTINUED) O-ringsSlit Feed Concentrate Membrane Fixation Pin Figure A. 4. RO flat sheet cell bottom side. Cell Top Side Cell Bottom Side Mesh Spacer Membrane Figure A. 3. DO test cell – assemble view.

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147 APPENDIX A: (CONTINUED) Product out Product out Figure A. 5. RO flat sheet cell top side. Cell Top Side Cell Bottom Side Membrane Permeate Carrier Figure A. 6. RO flat sheet cell –assemble view.

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148 APPENDIX A: (CONTINUED) Membrane Envelope Membrane Product Carrier Retentate Product Flow Feed Flow Membrane Envelope Product Tube Tube Holes Figure A. 7. Diagram of a spiral wound membrane configuration.

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149APPENDIX B: EQUATIONS OF THE SALT FLUX IN DO Salt Solution (Feed) Side CS(CS)memCDI(CDI)memDI (Permeate) Side Membrane (CS)'mem(CDI)'mem Figure B. 2 Diagram of the salt concentrations across the membrane. Starting with Fick’s law of diffusion represented by Equation B.1, SdC JD dx (B.1) and using the approximation from Equation B.2 an d Equation B.3 in the case of a membrane ' DIs mem memCC dC dx (B.2) S DI memmem DIS mem memC C 1 CCK (B.3)

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150 APPENDIX B: (CONTINUED) Equation B.1 becomes Equation B.4: ssDIsDI mem memmem DODODD JCCCC KK (B.4) Using the approximation from Equation B.5 as well as the Equations B.6 and B.7 representing the variation of concentration in tim e in the solution vessel and in the DI vessel, respectively, Equation B.4 becomes Equation B.8: ss mCC (B.5) ss tt0CCt (B.6) DIDI tt0CCt (B.7) ssDI t0 DOD JCC()t K (B.8) sdn J Sdt (B.9) Equation B.8 is integrated in time from t = 0 to t = and considering (D/K )DO constant in time, as well as the definition of the molar flux presented in Equation B.9, it results Equation B.10 and Equation B.11 n tt t sDIt0 nt0t0 DO t0dnD (CC)dt()tdt SK (B.10) 2 sDIt0 DOND1 (CC)()() SK2 (B.11)

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151 APPENDIX B: (CONTINUED) Equation B.10 can be rearranged as Equa tion 12 which was used in calculating (D/K )DO in the diffusion runs: 2 DO sDIt0DN 1 K S(CC)()() 2 (B.12) The difference in the total number of moles diffused during a run was calculated using Equation B.13 and Equation B.14: tt0DIDIDIDIDIDI ttt0t0ttNNNCVCVCV (B.13) DI DI saltC (B.14) where (VDI )t=0 and (VDI )t= are the volume in the DI water vessel in the beginning and at the end of the experiment, respectively, DI is the conductivity of the DI water, and salt is the salt specific conductivity.

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152APPENDIX C: SALT AND WATER TRANSPORT IN DO Table C. 1 Comparison of salt permeability for all membranes at 0.05 molL-1 in direct osmosis experiments. (D/K )DO x10-7 (cms-1) Salt SE AD CG CK LiCl 4.51 1.5 67.1 118 NaCl 6.53 2.2 77.1 133 KCl 8.73 2.6 96.9 165 MgCl2 4.30 0.83 21.9 56.1 CaCl2 5.14 0.91 31.6 63.3 BaCl2 5.99 1.0 33.4 65.5 Table C. 2 Comparison of salt permeability at different concentration for chlorides for the SE membrane in direct osmosis experiments. (D/K )DO x cms-1) Salt Cs = 0.01 molL-1 Cs = 0.02 molL-1 Cs = 0.05 molL-1 Cs = 0.1 molL-1 Cs = 0.15 molL-1 Cs = 0.2 molL-1 LiCl 5.27 4.51 3.94 3.37 NaCl 6.75 6.58 6.53 6.13 4.59 3.82 KCl 9.17 8.84 8.73 8.08 7.90 7.02 MgCl2 5.98 4.30 3.74 CaCl2 6.72 5.14 4.36 BaCl2 5.99 Table C. 3 Comparison of salt permeability at differe nt concentration for acetates for the SE membrane in direct osmosis experiments. (D/K )DO x cms-1) Salt Cs = 0.05 molL-1 Cs = 0.1 molL-1 LiAc 4.46 3.29 NaAc 5.28 3.70 KAc 6.05 4.11 MgAc2 3.77 2.75 CaAc2 4.16 3.36

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153 APPENDIX C: (CONTINUED) Table C. 4 Comparison of salt permeability for chlorides and acetates at two concentrations for the SE membrane in direct osmosis experiments. (D/K )DO x cms-1) At Cs = 0.05 molL-1 (D/K )DO x cms-1) At Cs = 0.1 molL-1 Cation Chlorides Acetates Chlorides Acetates Li+ 4.51 4.46 3.94 3.29 Na+ 6.53 5.28 6.13 3.70 K+ 8.73 6.05 8.08 4.11 Mg+2 4.30 3.77 3.74 2.75 Ca+2 5.14 4.16 4.36 3.36 Table C. 5 Comparison of pure water flux for all membranes at 0.05 molL-1 in direct osmosis experiments. Jw, DO x 10-6 (gs-1cm-2) SE AD CG CK Salt CV (%) CV (%) CV (%) CV (%) LiCl 4.75 5.64 17.8 7.26 NaCl 5.45 7.18 18.5 5.27 KCl 4.91 2.7 7.55 15.1 18 0.7 5.36 21.2 MgCl2 6.95 11.7 31.3 18.1 CaCl2 7.02 11.5 31.3 17.9 BaCl2 6.98 0.02 10.5 3.7 31 0.1 17.4 0.7 Note: CV represents the coefficient of vari ation calculated as the standard deviation divided to the average. Table C. 6 Comparison of pure water flux at different concentration for chlorides for the SE membrane in direct osmosis experiments. Jw, DO x 10-6 (gs-1cm-2) Salt Cs = 0.01 molL-1 Cs = 0.02 molL-1 Cs = 0.05 molL-1 Cs = 0.1 molL-1 Cs = 0.15 molL-1 Cs = 0.2 molL-1 LiCl 1.80 4.75 6.75 8.75 NaCl 1.80 3.22 5.45 6.83 8.72 8.82 KCl 2.25 3.03 4.91 7.05 8.05 10.1 MgCl2 2.47 6.95 10.1 CaCl2 2.20 7.02 10.0 BaCl2 6.98

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154 APPENDIX C: (CONTINUED) Table C. 7 Comparison of pure water flux for chlorides and acetates at two concentrations for the SE membrane in direct osmosis experiments Jw, DO x 10-6 (gs-1cm-2) Salt Cs = 0.05 molL-1 CV (%) Cs = 0.1 molL-1 CV(%) LiCl 4.75 6.75 NaCl 5.45 6.83 KCL 4.91 7.05 LiAc 4.32 6.35 NaAc 4.02 6.60 KAc 4.07 6.7 6.90 0.9 MgCl2 6.95 10.1 CaCl2 7.02 10.0 MgAc2 6.68 9.48 CaAc2 6.57 0.7 9.58 0.9 Note: CV represents the coefficient of vari ation calculated as the standard deviation divided to the average.

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155APPENDIX D: SALT REJECTION COEFFICIENT IN RO Table D. 2 Average over pressure of salt rejection in RO experiments. R (%) Salts AD CG CK SW30 LiCl 99.56 84.52 58.99 99.38 NaCl 99.46 83.5 57.82 99.36 KCl 99.36 82.54 55.81 99.24 MgCl2 99.93 95.10 87.92 99.48 CaCl2 99.83 94.78 86.07 99.42 BaCl2 99.82 94.40 85.95 99.40

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156APPENDIX E: FILM THEORY AND SHERWOOD CORRELATION E.1 Film theory In RO membranes, the salt accumulates at the membrane surface, in the region called boundary layer where the concentration is higher than the concentration in the bulk, Cfeed The maximum value of the concentration in the boundary layer is at the membrane wall Cmem. Due to the differences in the concentrations, the salt diffuses from the boundary layer back to the bulk side. The diffusion is characterized by the diffusivity coefficient D (Figure E.1). Feed Side (high pressure) Permeate Side (low pressure) Membrane Cprod 0 d x Boundary layer Bulk feed JSJv Cfeed dC D dxCmem Cfeed Figure E.1 Schematic diagram of the salt fluxes across RO membranes. At steady state, the salt convective flux JvCfeed is balanced by the flux of salt that permeates the membrane JS and the salt diffusive flux from the membrane wall to the bulk (Equation E.1). The boundary conditions are given in Equation E.2.

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157 APPENDIX E: (CONTINUED) SvfeeddC JJCD dx (E.1) mem feedx0CC xdCC (E.2) Integrating Equation E.1 with the boundary conditions E.2 it results Equation E.3. The ratio d/D is called the mass transfer coefficient k. memp vv feedpCC JdJ expexp CCDk (E.3) E.2 Sherwood correlation The feed flow in the RO flat sheet cell is in laminar regime with a Reynold number of 667. This is in agreement with findings from the literature for flow in plate module configurations (Prabhakar and Ramani, 1994). In fully developed laminar flow when the concentration boundary layer is developing, the Sherwood correlation is given by Equation (E.4) (Belfort, 1984). 0.33 hd k0.186ReSc L (E.4) where Reynolds number Re = vdh/ with v = flow velocity (0.313 ms-1), dh = hydraulic diameter (1.98 x 10-3 m), = kinematic viscosity (9.27 x 10-7 m2s-1), Schmidt number Sc = /D, D = diffusivity coefficient (m2/s), and L is the length of the flow channel (0.146 m).

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158 APPENDIX F: CONCENTRATION AT THE MEMBRANE WALL FOR SE MEMBRANE AND CORRECTED SALT PERMEABILITIES IN DO Table F. 1 Concentration at the membrane wall for the SE membrane at different bulk concentrations in direct osmosis experiments. DO memC (molL-1) Salt Cs = 0.01 molL-1 Cs = 0.02 molL-1 Cs = 0.05 molL-1 Cs = 0.1 molL-1 Cs = 0.15 molL-1 Cs = 0.2 molL-1 LiCl 0.006 0.015 0.021 0.028 NaCl 0.006 0.010 0.017 0.022 0.028 0.028 KCl 0.007 0.010 0.016 0.022 0.026 0.032 LiAc 0.014 0.020 NaAc 0.013 0.021 KAc 0.013 0.022 MgCl2 0.005 0.022 0.032 CaCl2 0.005 0.022 0.032 BaCl2 0.022 MgAc2 0.021 0.030 CaAc2 0.021 0.030 Table F. 2 Corrected salt permeability at 0.05 molL-1 in direct osmosis experiments. (D/K )DO x 10-7 (cms-1) Salts SE AD CG CK LiCl 12 4.49 373 2211 NaCl 17 5.44 411 3383 KCl 29.3 7.20 516 4134 MgCl2 8.1 1.36 130 629 CaCl2 8.63 1.43 148 714 BaCl2 9.02 1.75 159 749

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159 APPENDIX F: (CONTINUED)Li+Na+K+Mg+2Ca+2 5 10 15 20 25 30 (D/K)DO x 10-7 (cm s-1)Cations Chlorides Acetates Figure F. 1 Comparison of salt permeability for chlorides and acetates at 0.05 molL-1 bulk solution concentration after correction in SE membrane in diffusion experiments. Li+Na+K+Mg+2Ca+2 0 5 10 15 20 (D/K)DO x 10-7 (cm s-1)Cations Chlorides Acetates Figure F. 2 Comparison of salt permeability for chlorides and acetates at 0.1 molL-1 bulk solution concentration after correction in SE membrane in diffusion experiments.

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160 APPENDIX F: (CONTINUED) 0.000.050.100.150.20 0 10 20 30 40 50 60 70 (D/K)DO x 10-7 (cm s-1)Solution Concentration Cs (mol L-1) LiCl NaCl KCl MgCl2 CaCl2 Figure F. 3 Variation of salt permeability with bulk solution concentration after correction in SE membrane for chlorides in diffusion experiments. 0.000.050.100.15 5 10 15 20 25 (D/K)DO x 10-7 (cm s-1)Solution Concentration Cs (mol L-1) LiAc NaAc KAc MgAc2 CaAc2 Figure F. 4 Variation of salt permeability with bulk solution concentration after correction in SE membrane for acetates in diffusion experiments.

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161 APPENDIX G: EXPERIMENTAL ERRORS Table G. 1 Experimental errors for direct osmosis experiments. Parameter Equation/Direct measurement Instrument Nr. (Table 3.1) Experimental error e S Direct measurement 2 0 % Direct measurement 8 0 % CDI, CS Direct measurement 3 1 % T Direct measurement 10 0.3 % mw Direct measurement 9 0 % Water Volume Vw Direct measurement 9 0 % Jw, DO Eq. (3.1) 0 % A' Same as A in Table G.2 0.45 % DO memC Eq. (5.3) 1.75 % N Eq. (B.13) 1 % (D/K DO Eq. (5.5) 3.75 % Table G. 2 Experimental errors for the first cas e of the SK model in RO flat sheet membrane experiments. Parameter Equation/Direct Measurement Instrument Nr. (Table 3.1) Experimental error Cprod Direct measurement 3 and 4 1 % Cfeed Direct measurement 4 1 % P Direct measurement 7 0.25 % Product volume Direct measurement 12 0.2 % Product flowrate QP Product volume/time 0.2 % Jv QP/S 0.2 % A Jv/ P 0.45 % C Cfeed-Cprod 2% Cavg (Cfeed+Cprod) 2% PRO (1) Eq. (2.10) 8.6 % 2 (1) Eq. (2.10) 5.6 % Jdiff/Jtotal (1) PRO C/(CprodJv) 12.8 % 1 (1) Eq. (2.9) 7.0 % Lp (1) Eq. (2.9) 8.3 % Note: (1) Denotes the parameters in the first case of the SK model.

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162 APPENDIX G: (CONTINUED) Table G. 3 Experimental errors for the sec ond case of the SK model in RO flat sheet membrane experiments. Parameter Equation/Direct Measurement Experimental error e max memC Eq. (4.7) 2.2 % C max memCCprod 3.2 % Cavg (max memC+ Cprod) 3.2 % PRO (2) Eq. (2.10) 9.1% 2 (2) Eq. (2.10) 4 % Jdiff/Jtotal (2) PRO C/(Cprod Jv) 13.5 % Notes: 1. (2) Denotes the parameters in the third case of the SK model. 2. CP, CF, P, Product volume, QP, Jw, JP, and A are the same as in table G.2. Table G. 4 Experimental errors for the third case of the SK model in RO flat sheet membrane experiments. Parameter Equation/Direct Measurement Instrument Nr. (Table 3.1) Experimental error Volume product Direct measurement 12 0.2 % Channel height h Direct measurement 2 1 % Channel length L Direct measurement 2 0 % Channel width l Direct measurement 2 0 % Channel cross Area hl 1 % dh 2hl/(h+l) 2 % Velocity v QF/hl 4 % k Eq. (4.8) 2.64 % k memC Eq. (4.9) 5.84 % C k memCCprod 6.84 % Cavg (k memC+ Cprod) 6.84 % PRO (3) Eq. (2.10) 10.4 % 2 (3) Eq. (2.10) 6.6 % Jdiff/Jtotal (3) PRO C/(Cprod Jv) 18.4 % 1 (3) Eq. (2.9) 6.2 % Lp (3) Eq. (2.9) 6.8 % Notes: 1. (3) Denotes the parameters in the third case of the SK model. 2. Cprod, Cfeed, P, QP, and Jv are the same as in Table G.2.

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163 APPENDIX G: (CONTINUED) Table G. 5 Experimental errors for KS mode l in RO flat sheet membrane experiments. Parameter Equation/Direct Measurement Experimental error R 1-Cprod/Cfeed 2 % Jv Eq. (2.13) 3.2 % Cmem Eq. (2.14) 2.5 % (D/K )RO Eq. (2.15) 8.7 % Note: Cprod, Cfeed, P, QP, Jv, and A are the same as in Table G.2. Table G. 6 Total error for the salt and water parameters in all experiments. Parameter Experimental error e Standard deviation of duplicates STD Total error E(*) A 0.5 % 12.3 % 13.1 % (D/K )DO 3.8 % 13.2 % 13.7 % (D/K )RO 8.7 % 16.6 % 18.7 % Jdiff/Jtotal (1) 12.8 % 11.1 % 16.9 % Jdiff/Jtotal (2) 13.5 % 11.9% 18 % Jdiff/Jtotal (3) 18.4 % 5.3 % 19.1 % Lp (1) 8.3 % 8.9 % 12.2 % Lp (3) 6.8 % 13.1 % 14.8 % PRO (1) 8.6 % 9.7 % 13 % PRO (2) 9.1 % 15.2 % 17.7 % PRO (3) 10.4 % 12.9 % 16.6 % 1 (1) 7.0 % 6.7 % 9.7 % 1 (3) 6.2 % 8.8 % 10.8 % 2 (1) 5.6 % 3.8 % 6.8 % 2 (2) 4 % 12.9 % 13.5 % 2 (3) 6.6 % 4.6 % 8.0 % Notes: 1. (1) Denotes the parameters in the second case of the SK model 2. (2) Denotes the parameters in the second case of the SK model. 3. (3) Denotes the parameters in the third case of the SK model. 4. (*) Calculated as 22E(%)e(%)STD(%) (Taylor, 1997). It does not include the operator’s error and the systematic errors.

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164APPENDIX H: PHYSICAL AND THERMODYNAMIC PROPERTIES OF IONS Table H. 1 Physical parameters of cations. Cation Ri () (1) Rh ()(1) Dw x10-5 (cm2s-1)(2) Dw x10-5 (cm2s-1)(3) Hcation (4) (kJmol-1) Scation (5) (kJmol-1) Li+ 0.60 3.82 1.37 1.06 515 119 Na+ 0.95 3.58 1.61 1.20 405 89 K+ 1.33 3.31 1.99 1.40 321 51 Mg2+ 0.65 4.28 1.25 0.92 1922 268 Ca2+ 0.99 4.12 1.34 0.97 1592 209 Ba2+ 1.35 4.04 1.39 0.99 1304 159 Notes: (1) (Conway, 1981) (2) For chloride salts (Sourirajan, 1970) (3) For acetate salts (Cussler, 1997) (4) (Burgess, 1988) (5) (Chang, 2000) Table H. 2 Hydration number cal culated from different methods. From Mobility(1) Cation Min Max From Activity(2) From Entropy(3) From Diffusion(3) From Water Transport(4) Li+ 3.5 7 7.1 5 5 22 Na+ 2 4 3.5 4 3 13 K+ 1.9 3 1 7 Mg2+ 10.5 13 13.7 13 9 36 Ca2+ 7.5 10.5 10 9 29 Ba2+ 5 9 8 8 28 Cl3 5 Notes: (1) (Conway, 1981) (2) (Bockris and Reddy, 1970) (3) (Burgess, 1988) (4) (Rutgers and Hendrikx, 1962)

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165APPENDIX I: FREE ENERGY PARAMETERS Table I. 1 The corrections of ionic radii, the parameter E, and the ionic free energy in the bulk solution. Cation S (1) m x 10-10 ES (1) mkJmol-1 Gs (1) kJmol-1 Li+ 0.89 762 -517 Na+ 0.89 762 -412 K+ 0.89 762 -338 Mg2+ 1.01 3124 -1907 Ca2+ 1.01 3124 -1594 Ba2+ 1.01 3124 -1321 Note: (1) [Friedman, 1973 #35] Table I. 2 The corrections of ionic radii and the parameter E at the membrane surface, the free energy at the membrane surface. Seawater membrane SE Cation mem (m x 10-10) Emem (mkcalmol-1 x 1010) Gmem (kcalmol-1) Li+ -118 Na+ -95 K+ 0.84 171 -78 Mg2+ -449 Ca2+ -373 Ba2+ 1.01 746 -316 Seawater membrane AD Cation mem (m x 10-10) Emem (mkJmol-1 x 1010) Gmem (kcalmol-1) Li+ -119 Na+ -96 K+ 0.86 174 -79 Mg2+ -449 Ca2+ -373 Ba2+ 1.01 745 -316 Brackish water membrane CG Cation mem (m x 10-10) Emem (mkJmol-1 x 1010) Gmem (kcalmol-1) Li+ -120 Na+ -97 K+ 0.87 177 -81 Mg2+ -449 Ca2+ -373 Ba2+ 1.01 745 -316

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166 APPENDIX I: (CONTINUED) Table I. 2 (continued) The corrections of ionic radii and the parameter E at the membrane surface, and the free energy at the membrane surface. Nanofiltration membrane CK Cation mem (m x 10-10) Emem (mkJmol-1 x 1010) Gmem (kcalmol-1) Li+ -121 Na+ -98 K+ 0.88 180 -81 Mg2+ -450 Ca2+ -374 Ba2+ 1.016 750 -317 Seawater membrane SW30 Cation mem (m x 10-10) Emem (mkJmol-1 x 1010) Gmem (kcalmol-1) Li+ -121 Na+ -98 K+ 0.88 179 -81 Mg2+ -449 Ca2+ -373 Ba2+ 1.01 744 -316

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ABOUT THE AUTHOR Silvana Melania Stefania Ghiu receive d her BSc in Physics in 1995 from the University of Bucharest, Romania, with a sp ecialization in Physics and Protection of the Environment. She received her first MSc degr ee in Atmospheric Physics in 1996 from the same university, and her second MSc in Envir onmental Science and Policy in 1997 from the Central European University, Hungary. She is the recipient of George Soros Foundation Fellowship for completion of MSc studies and Channabasappa Memorial Scholarsh ip offered by the International Desalination Association. During her PhD program at University of South Florida, she has authored two publications in Desalination Journal, and five articles in conference proceedings. She has presented papers or posters on RO desalination to nine conferences. Her research interests are in separation technologies with hyperfiltration membranes.


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Small and large signal modeling of MM-Wave MHEMT devices
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ABSTRACT This research effort advances millimeter-wave transistor modeling in a current RF/Microwave circuit simulator (Agilent's Advanced Design System-ADS) for small-signal noise and large signal simulations. The device modeled is a metamorphic High Electron Mobility Transistor (mHEMT) supplied by Raytheon RF components. Because of their structure, these new low noise devices are used in this work to test the abilities to accurately model in the sub 0.5dB noise figure territory and to study model prediction into W-band (75-110 GHz). New modeling issues discussed in this thesis involve the effects of noise modeling in relation to the small-signal model parameters. The noise modeling identifies two methods of extraction and how to determine good noise data. Other modeling topics addressed are the use of an advanced nonlinear model, and the ability to optimize for gain compression in the nonlinear model. Several measurement systems were used in the extraction and validation of this modeling effort. They consist of the ATN NP5 noise system, Maury Automated Tuner System, Agilent's IC-CAP, and Gateway's Special. The concept behind using these systems was to construct a complete modeling reference for a transistor and validate it against noise parameter and nonlinear measured data. Since the modeling work for this thesis is built on previous work, one goal has been to bring past USF field-effect transistor (FET) modeling efforts up to date and refine them for future use. The noise measurements were compared to results from Raytheon to validate the USF ATN noise parameter measurement system. Also the IC-CAP modeling system has been validated in measuring the test devices using the Maury load-pull system. Small-signal and noise modeling were accomplished using techniques standardized from several technical papers and prior USF Ph.D. work relative to the model extraction. The IC-CAP modeling software also provided a straightforward platform for large-signal model extraction that is documented in this thesis. Using optimization in ADS, a final nonlinear was created. Measured DC, S-parameter, noise parameters, harmonic power, TOI, load-pull, and efficiency measurements were shown to compare well with model data simulated in ADS. Temperature scaling was also executed using a linear approximation of model values over measured temperatures in the noise model. The results presented show that the models developed illustrate good fitting of the behavior of the mHEMT device.
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