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Waldstein, Nathaniel A.
Analysis of pump oil and alkanes evaporation
h [electronic resource] /
by Nathaniel A. Waldstein.
[Tampa, Fla] :
b University of South Florida,
Title from PDF of title page.
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Thesis (M.S.M.E.)--University of South Florida, 2008.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
ABSTRACT: There are many products, including hard drives, which require trace amounts, on the order of several mg, of lubricants for proper operation. The following study investigated the evaporation rates of pump oil and several alkanes, which have a wide range of applications, using a thermogravimetric machine. Both static and dynamic temperature tests were conducted. The rate of evaporation of the test specimen was determined as the percentage of mass loss per unit time. Using the Arrhenius Equation, the activation energy of the evaporation process, Ea, can be calculated as the slope of the best fit line for a plot of the ln(k) vs. 1/T (where k represents the rate of the evaporation). These values were shown to have good agreement with the enthalpy of vaporization calculated from the Clausius Clapeyron Equation and with the activation energy calculated using the Freeman and Carroll Method. The alkanes were compared using the rate of evaporation and the amount of activation energy required for evaporation as model systems. Further investigations were conducted to determine the relationship of surface area of the evaporating liquid and the rate of evaporation. It is suggested that the surface area is a function that depends on the activation, bonding, and interfacial energies of the liquid. However, the wetting angle, which aids in the description of the surface area, depends on the surface energy. Subsequent modeling was conducted in an attempt to predict the evaporation characteristics of other lubricants for the purpose of comparison.
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Advisor: Alex Volinsky, Ph.D.
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
Analysis of Pump Oil and Alkanes Evaporation by Nathaniel A. Waldstein A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Alex Volinsky, Ph.D. Jose Porteiro, Ph.D. Muhammad Rahman, Ph.D. Date of Approval: November 19, 2008 Keywords: Arrhenius Equation, Ac tivation Energy, Evaporation Rates Copyright 2008, Nathaniel A. Waldstein
DEDICATION To my family, friends, and my advisor; fo r their encouragement made this possible.
ACKNOWLEDGEMENTS Above all else I would like to thank my a dvisor Dr. Alex A. Volinsky for his support, wisdom, and unrelenting patience to whom I ow e a great debt of gratitude. I would also like to thank my committee members Dr. Port eiro and Dr. Rahman for their time and advice. I am honored to have worked with Dr. Dirk C. Meyers group at TUD and am grateful to have been privileged to use thei r equipment and being supplied with samples. I would also like to th ank Seagate for supplying samples a nd give a special thanks to NSF for funding my research. Finally, I want to thank my fellow st udents as well as the faculty and staff in the Department of Mechanical Engineering at USF.
TABLE OF CONTENTS TABLE OF CONTENTS ..................................................................................................... i LIST OF TABLES .............................................................................................................. ii LIST OF FIGURES ........................................................................................................... iii ABSTRACT ...................................................................................................................... .. v CHAPTER 1 INTRODUCTION TO LIQUIDS EVAPORATION ................................... 1 1.1 Evaporation ............................................................................................................. 1 1.2 Arrhenius Equation ................................................................................................. 4 1.3 Clausius Clapeyron Equation .................................................................................. 7 1.4 Alkanes ................................................................................................................ 15 CHAPTER 2 EVAPORATI ON TEST METHODS ......................................................... 19 2.1 Testing methods .................................................................................................... 19 2.2 Testing procedure .................................................................................................. 22 CHAPTER 3 ALKANES AND OIL EVAPORATION RESULTS ................................. 23 3.1 Evaporation measurements ................................................................................... 23 3.1.1 Repeatab ility studi es ................................................................................................... .................... 23 3.1.2 Static testing .......................................................................................................... .......................... 39 3.1.3 Dynami c tes ting .............................................................................................................................. 48 3.2 Mixture testing ...................................................................................................... 54 3.3 Microchannel evaporation testing ......................................................................... 59 CHAPTER 4 SUMMARY A ND FUTURE WORK ........................................................ 65 4.1 Summary ............................................................................................................... 65 4.2 Modeling ............................................................................................................... 66 4.3 Testing technique improvements .......................................................................... 74 REFERENCES ................................................................................................................. 76 i
LIST OF TABLES Table 1. Antoine Constants and valid temperature range for alkanes. ............................. 13 Table 2. Heat of vaporization of alkanes from Troutons Rule. ....................................... 15 Table 3. Molecular formulas of alkanes.. ......................................................................... 17 Table 4. Activation energy, Ea, calcula ted for different heating rates from Arrhenius Plot. ............................................................................................ 27 Table 5. Repeatability comparison results for undecane. ................................................. 39 Table 6. Activation energies and pre-e xponential constants for all alkanes, obtained from static............................................................................................ 44 Table 7. Comparing Arrhenius to Antoine Equa tion for a heating rate of 10 C/min. ..... 51 Table 8. Comparing Arrhenius to Antoine Equa tion for a heating rate of 20 C/min. ..... 51 Table 9. Comparing Arrhenius to Antoine Equa tion for a heating rate of 30 C/min.. .... 52 Table 10. Average activation energies and preexponential constants fo r all alkanes. .... 52 Table 11. Propagated errors of the activation energies for all alkanes ............................. 54 Table 12. Comparison between mixtures and pure alkanes heated at 20 C/min ............. 57 Table 13. Comparison between mixtures and pure alkanes heated at 30 C/min ............. 57 ii
LIST OF FIGURES Figure 1. A typical Arrhenius Plot for the calculation of the activation energy, for the evaporation of undecane ................................................................... 6 Figure 2. Water phase diagram ....................................................................................... 11 Figure 3. Differences between straight ch ain and branched chain alkanes .................... 16 Figure 4. Example of the pump oil tes ting procedure, temperature profile ..................... 25 Figure 5. Example of the dynamic alkane tes ting procedure, temperature profile ........... 26 Figure 6. Heating rate dependency for undecane ............................................................. 28 Figure 7. Comparison of oil evaporation rate with and without air flow ......................... 29 Figure 8. Mass loss as a percentage of initial mass for each alkane ................................ 30 Figure 9. Example of wetting profile of three stages of oil ............................................ 32 Figure 10. Wetting profile of tetradecane in a pan ........................................................... 33 Figure 11. Wetting profile of pump oil in a pan ............................................................... 33 Figure 12. Superposition of the profil es of tridecane and pump oil ................................ 35 Figure 13. Evaporation process with respect to surface area ............................................ 36 Figure 14. Repeatability results for Arrhenius Plot undecane .......................................... 38 Figure 15. Static and dynamic Arrhenius Plot for hexadecane ......................................... 41 Figure 16. Static temperature testing for all alkanes ......................................................... 42 Figure 17. Drift test comparison for pump oil .................................................................. 46 Figure 18. Drift correction for pump oil ........................................................................... 47 iii
iv Figure 19. Arrhenius Plot of pump oil for calculating the activ ation energy ................... 48 Figure 20. Dynamic temperature testing for all alkanes ................................................... 50 Figure 21. Arrhenius Plot of specific mixtur es heated at a rate of 20 C/min .................. 55 Figure 22. Arrhenius Plot of specific mixtur es heated at a rate of 30 C/min .................. 56 Figure 23. Pictorial representation of microchannel testing fixtures ................................ 60 Figure 24. Microchannel fixt ures: a) Relative sizes b) Micrograph of a cross-section showing the microchannel dimensions ..................................... 61 Figure 25. Arrhenius plot for both threaded and non-threaded microchannels ................ 62 Figure 26. Rates of evaporation for thread ed and non-threaded microchannels ............. 63 Figure 27. Measured evaporation rates ve rsus temperature for all alkanes ...................... 72 Figure 28. Theoretical maximum evaporation rates for all alkanes .................................. 73 Figure 29. Mass of the alkanes versus time ...................................................................... 74
Analysis of Pump Oil and Alkanes Evaporation Nathaniel A. Waldstein ABSTRACT There are many products, including hard dr ives, which require trace amounts, on the order of several mg, of lubricants for proper operation. The following study investigated the evaporation ra tes of pump oil and several alkanes, which have a wide range of applications, using a thermograv imetric machine. Both static and dynamic temperature tests were conducted. The rate of evaporation of the test specimen was determined as the percentage of mass loss per unit time. Using th e Arrhenius Equation, the activation energy of th e evaporation process, Ea, can be calculated as the slope of the best fit line for a plot of the ln(k) vs. 1/T (where k represents the rate of th e evaporation). These values were shown to have good ag reement with the enthalpy of vaporization calculated from the Clausius Clapeyron Equation and with the activation energy calculated using the Freeman and Carroll Meth od. The alkanes were compared using the rate of evaporation and the amount of ac tivation energy required for evaporation as model systems. Further invest igations were conducted to determine the relationship of surface area of the evaporating liq uid and the rate of evaporati on. It is suggested that the surface area is a function that depends on the activation, bonding, and interfacial energies of the liquid. However, the wetting angle, which aids in the description of the surface area, depends on the surface energy. Subseque nt modeling was conducted in an attempt v
to predict the evaporation characteristics of other lubricants for the purpose of comparison. vi
CHAPTER 1 INTRODUCTION TO LIQUIDS EVAPORATION 1.1 Evaporation The conversion process from the liquid stat e to the gaseous state is what is known as evaporation. Liquids do not have to be heated to the boiling point in order for evaporation to occur [1-2]. The transiti on between the two states of matter is accomplished by molecules leaving the surface of the liquid. The molecules close to the surface of the liquid move in every possible direction at a range of varying speeds. The majority of molecules are inhibited by attractive forces within the liquid itself. Conversely, when the molecules have sufficien t kinetic energy and approach the surface, at or near normal, these molecules can es cape the liquid [1-2]. Although these molecules have broken through the surface of the liqui d, many molecules that have evaporated reenter the liquid as a result of molecular coll isions outside of the liquid. Specifically, the net vaporization is the rate at which a liqui d converts to a gas. Evaporation can account for significant mass losses in an exposed liquid . Since evaporation depends on kinetic energy it should be clear that as a liquid is heated, the amount of kinetic energy for indi vidual molecules incr eases the evaporation rate. Regardless of temperature, a liquid that is evaporating will always be absorbing the latent heat of vaporization. In other words, an evaporating liquid w ill continuously absorb energy that is utilized to break molecula r bonds to transform the liquid into a gas. 1
Molecules that successfully evaporate absorb large amounts of energy from the surrounding environment, without causing an increase in the temperature of the molecules. This results in a reduction of the temperatur e of the surroundings of an evaporating liquid. The rate at which the surrounding temperature reduces depends on several factors including the rate in which the molecules leave the surface of the liquid. Neglecting the contribution of ot her factors, an increase in the rate of molecules leaving the surface of the liquid will increase the extremity of the temperature reduction. Additionally, the molecules that remain with in the liquid have lo wer average kinetic energies which results in a reduction of the liquid temperature. Hence, evaporation is a cooling process and it is this phenome non that has been known and exploited for centuries. In fact, ancient Greeks and Romans used a method of hanging wet mats in windows and doorways to cool homes on hot summer days . Likewise, today similar processes to this have been incorporated in to many modern refrigeration systems and air conditioners. Since evaporation requires the breaking of molecular bonds it is considered to be an endothermic process [4-5]. Any change, be it physical or chemical, that absorbs energy is termed an endothermic process . How easily a liquid evaporates relates the strength of intermolecular bonds . Suffice to say that the stronger the bonding the slower the evaporation rate. These bond energi es represent the ener getic threshold that must be met in order to break the specifi c chemical bond. Since bond energies represent an amount of energy absorption they are always positive . Molecular structure dictates the strength of the bonds. Similar to bond ener gy, the amount of energy needed to be absorbed to initiate a chemical reaction, evaporation in this case, is known as the 2
activation energy . Lower activation energies generally correlate to faster reactions and higher activation energies corr elate to slower reactions. Evaporation rates differ for different li quids and in addition to the level of activation energy required, the ra te of evaporation is also de termined by such things as the concentration of the surrounding gas as well as the liquid it self, the flow speed of the surrounding gas, the temperature of the liquid and the surface area of the liquid exposed to the environment. If the su rrounding gas, generally air, ha s a high concentration of the evaporating liquid or of othe r substances the rate of ev aporation can be significantly reduced. Likewise, if there is a high concentra tion of other substances, impurities, in the liquid the rate of the evaporation will also be slowed. As a liquid evaporates it gains a higher concentration of solid matter and w ill hence have a slower evaporation rate. Hence, evaporation can alter the intrinsic properties of a liquid; mainly the viscosity, density and amount of substances with lowe r molecular weights . Since density is directly proportional to pressu re, it too has a significant infl uence on evaporation rates. When the gas in contact with the surface of the liquid increases its velocity, so does the evaporation rate, and vice versa. The quali ty of the surrounding gas also affects the evaporation rate. For example, if the air in contact with the surface of the liquid has a high humidity then the evaporation rate will be slower than if the air was dry. An increase in the temperature of an evaporating liquid wi ll greatly increase the rate of evaporation. Another very crucial factor in the rate of ev aporation is the surface area of the liquid, that is because evaporation is a surface phenomenon; and similar to temperature, an increase in the exposed surface area greatly increases the evaporation rate. 3
Since temperature is arguably the most im portant deciding factor of the rate of evaporation, it is worth discussing further. Wh en a liquid is at ambient pressure and at a temperature below the normal boiling point it wi ll wet the sides of the container. In this condition the liquid will evaporate slowly and relatively steadily. If the temperature is increased to the boiling point, tiny vapor bubbl es begin forming at the interface between the liquid and the container. The number of s ites in which these bubbles form increases as does the rate of evaporation. That is until a certain temperature is reached above the boiling point in which the evaporation rate is at a maximum and any increase in temperature from this will actually reduce th e rate. This holds true for a liquid that experiences a steady increase in temperature, but not a liquid that is vaporized by a dramatic increase in temperature . The ge neral rule when comparing different liquids is that the lower the boili ng point, the more rapid th e rate of evaporation. 1.2 Arrhenius Equation The Swedish born scientist, Svante Arrhenius (1859-1927), studied at the University of Uppsala and is considered by some to be one of the founders of modern physical chemistry . Arrhenius has been referred to as both a physicist and a chemist and it is in these capacities that he helped to revolutionize the science of chemistry. Some of his early writings investigat ed what is now called the greenhouse effect. In fact, in 1896 Arrhenius theorized the magnitude of the greenhouse effect in the London, Edinburgh, and Dublin Philosophical Magazine In this publication he stated: We are evaporating our coal mines into the air. He added that an increase of the CO2 concentrations by as little as a factor of two, would increase the average earths surface 4
temperature by about 5 C . Later in his career, in 1903, he became the first Swedish person to be awarded the Nobel Prize in chem istry for his works on the ionic theory of solution of salts . Several years prior to Arrhenius winning the Nobel Prize he worked on what would later become legacy and ear n him a right in the history of modern chemistry. Arrhenius noted that the majority of ch emical reactions need additional energy to continue. This energy, specifically heat energy, is added to a system until a predetermined threshold is reached and th e reaction commences. This threshold is a concept that was developed by Arrhenius a nd is referred to as the activation energy. Arrhenius further developed th ese concepts and combined supportive ideas to formulate the Arrhenius equation. Simply, th is equation relates the activa tion energy to the rate of the reaction process. Specifical ly, this equation was derived in order to adequately report the effects of temperature on the reaction ve locities of gases [8-9]. The Arrhenius Equation was originally derived from the wo rk of the Dutch chemist Jacobus Henricus van 't Hoff (1852 1911) . In order for Arrhenius to explain simple chemical reactions he viewed most processes as simple 1st order reactions that ha ve distinct temperature characteristics and obvious activation energi es. These reaction funda mentals are obtained by plotting the logarithm of the rate of the reaction against the inverse of the absolute temperature. This provides a model that relate s the reaction rate to temperature. One form of the Arrhenius Equation is an integrati on of the underlying differe ntial equation and is presented in the following empiricion: al express (1) 5
where is a constant that correlates to the rate of the reaction, is the activation energy of the reaction is the absolute temperature, is the universal gas constant (8.314472 ), and is the pre-exponential constant, which has the same units as the constant k. The units depend on the order of the reaction. For an nth order reaction, the shared units are However, in this investigati on the rate of evaporation was measured experimentally and has the units of mass per unit time as does the preexponential constant. Since the activation energy is in a nonlinear form in equation (1) problems arise during nonlinear regression. As a result, the logarithm of both sides of the equation is taken to yield: (2) -20 -18 -16 0.00240.00260.00280.003 60 100 140 y = -1.3158 6066.6x ln kT-1, K-1T, oC Figure 1. A typical Arrhenius Plot for th e calculation of th e activation energy, for the evaporation of undecane. If the activation energy, and the pre-exponential constant, are unchanging with temperature then a plot of against the inverse of will result in a straight line whose slope is proportional to the activation energy and offset is logarithm of the pre6
exponential constant . This can be seen if Figure 1 above. In this example, the slope of the linear best fit line multiplied by the nega tive of the universal gas constant provides an estimate of the activation energy of the evaporation. In th is case, the activation energy of the evaporation of undecane is 50.4 Likewise, taking the e xponential of the offset of the best fit line provides a value of the pre-exponential constant to be 0.27 If the plot is not linear as previously described, then the activation ener gy decreases with an increase in temperature [8-9]. 1.3 Clausius-Clapeyron Equation The Clausius-Clapeyron Equation is a well-known and frequently used formula that characterizes the phase tr ansition between two st ates of matter; liquid and gas in this case. Specifically it relates the heat of vaporization, or enthalpy of vaporization, to that of vapor pressure. This equation is named after the prominent German physicist and mathematician Rudolf Julius Emanuel Clausi us (1822 1888) and the French engineer and physicist Benot Paul mile Clapeyron (1799 1864) [11-12]. Both men are considered to be founders of the science of modern thermodynamics with their individual and contributing works on what is now know n as the second law of thermodynamics. Two very important terms should be de fined prior to continuing a discussion on the Clausius-Clapeyron Equation. The first of which has been used previously in this section, and that is the heat of vaporization. According to , the heat of vaporization is the amount of heat required to vaporize one gram of a liquid at its boiling point with no change in temperature. More generally, enthalpy is the amount of potential heat in a substance and it is proportional to pressu re and volume. Therefore, the heat of vaporization ( H) can be thought of as the energy re quirement for the transformation of a 7
given amount of substance, from the liqui d to the gaseous stat e. This value is conventionally measured at the normal boiling point of the substance. However, most tabulated values are adjusted to a temperature of 298 K. Vapor pressure is the particle pressure of a vapor at the surface of its parent liquid . To explain further, when a va por is in thermodynamic equilibrium with nonvapor phases then the pressure of this vapor is referred to as vapor pressure. Under certain circumstances, all liquids and even some solids have the propensity to evaporate and transform into the gaseous state. Likewi se, all gases, under similar circumstances, tend to condense to the origin al state, be it liquid or soli d. For a specific substance at a specific temperature there will exist a pre ssure at which the evaporated gas is thermodynamically in equilibrium with the condensed form (liquid or solid). This is known as the vapor pressure for the specific su bstance at that par ticular temperature. Volatile substances are those that have a high vapor pressure at near atmospheric pressures. The vapor pressure indicates the required pressure in order to have equilibrium, which relates the readiness of molecules to escape from the surface of the liquid. Therefore, this equilibrium pressure or vapor pressure is an indicator of the evaporation rate of a liquid. Understanding these terms it is now necessa ry to establish a relationship between the heat of vaporization and what is referred to as the behavior of a fluid . The most basic relationship approximating the behavior of real fl uids was established by the Dutch physicist and Nobe l laureate Johannes Diderik van der Waals (1837 1923) . The van der Waals equation c red in the following form: an be repsente (3) 8
where both and are characteristics of the specific substance. Instead of now iteratively relating the pVT behavior to th at of the heat of vaporiza tion, a more often used method that provides a relationship betw een the heat of vaporization ( ) to that of the temperature dependence of the vapor pressure ( ) will follow. First it should be noted that equation (3 ) is considered to be valid in a singlecomponent system (one substance) at equi librium between vapor and liquid. Analyzing the Gibbs energies in this situation reveals that the differential Gi bbs energies of the saturated liquid and the saturated vapor ar bolically: e equal. Sym (4) The total differential Gibbs energy is provided by the following relationship: (5) where is the molar entropy, is the molar volume, is the temperature, and is the vapor pressure. Combining these two equations provides a relationship between the heat of vaporization and the derivative of the vapor pressure with respect to the temperature along the saturation curve. This relationship is better known as the Clapeyron Equation and the empirical form and its derivation is as follows: 9
(6) From this equation it can be determined that when both the heat of vaporization and the change in volume are positive, the vapor pressure will always increase with increasing temperature . Integration of the Clapeyron Equation provides an exact relationship that relates the dependence of the vapor pressure on the temper ature, in a certain range. This range is the region from the triple poi nt temperature to that of the critical temperature. This region can be viewed on a phase diagram of the substance. To explain, a phase diagram is a plot of pr essure against temperature that illustrates the conditions for which a given phase of the substance exists . Figure 2 shows an example of a phase diagram for water. On this plot there are two important points: the triple point (A) and the critical point (C). The triple point determ ines the necessary temp erature and pressure needed for all three phases to coexist. The cr itical point, on the othe r hand, specifies at what temperature and pressure the substance must be in order for a phase boundary to no longer exist. Considering a closed system composed of liquid and vapor that is heated; as the temperature increases the density of the liquid reduces and the density of the vapor increases. The temperature at which the two de nsities are equal is the critical point. The heat of vaporization is zero at and beyond the critical point and the liquid state cannot exist passed it . 10
Soli d Li q ui d Pressure (atm) 1.0 D B A C Temperature (C) 0 C 100 C Gas Figure 2. Water phase diagram. Returning to the specifics of the Clapey ron Equation; a reduction in the pressure the culminating effects of the behavior of the liquid phase becomes increasingly insignificant. Understanding th is is the basis of the Cl ausius-Clapeyron Equation. The Clausius-Clapeyron Equation is a rather restrictive yet useful method of relating the heat of vaporization to that of vap d tae following form: por r essure ankes th (7) where C is a constant of integr ation. A key simplification inhere nt to this equation is that the volume of the vapor is formulated by the ideal gas equation of st ate and this volume is significant enough, as compared to the volume of the liquid, that the latter has been neglected. As previously stated, this equati on is often used to estimate the relationship between the heat of vaporiza tion and the vapor pressure, and a quick survey of equation (7) should relate the ea se of these estimations and conve y its convention. A result that is 11
inherent to this equation is that for temp eratures below the normal boiling point, the calculated heat of vaporization will always be higher than the corre ct values, with an associated error of less than 5% . Taking a differential form of the Clausius-Clapeyron Equation: (8) and integrating this with the assumption that the heat of vapori zation is a constant provides: (9) where A is a constant of integration and the variable is constant. Since the logarithm of the vapor pressure is only linear in small ra nge of temperatures, equation (9) will not exactly describe the behavior of a substance . There are numerous semi-empirical equations that modify the righ t-hand side of equation (9); a review of which can be found in . However, the form of this equati on, originally published by Antoine , that was used in this research t akesthe following form: (10) where p is the vapor pressure (mm Hg), T is the temperature (K), and the variables A, B, C, D, and E are all constants specific to substances and are valid within a determined temperature range. This form of the Antoine Equation is more expanded than the general form, but both provide accurate representati ons of substances over a large range of temperatures as shown in . The constants of the Antoine Equatio n, or Antoine Constants, are known and tabulated for many substances and tabulated valu es were used in this research for the six 12
n-alkanes. However, the pump oil that was investigated is was of an unknown composition. Therefore the constants are not ta bulated and this approach was not used with the pump oil The Antoine constants of the n-alkanes were obtained from  and can be found in Table 1; along with the valid temperature ranges, and names of each nalkane studied. Table 1. Antoine Constants and valid temperature range for alkanes. Alkanes A B C D E Range (K) Undecane 82.923 -5608.5 -27.327 1.05E-02 7.09E-13 247.6 638.8 Dodecane -5.6532 -3469.8 9.0272 -2.32E-02 1.12E-05 263.6 658.2 Tridecane 49.239 -4964.9 -13.769 -2.11E-09 2.59E-06 267.8 675.8 Tetradecane 106.11 -7346.1 -35.195 1.24E-02 -8.40E-13 279.0 692.4 Pentadecane 116.52 -8041 -38.799 1.34E-02 -4.44E-13 283.1 706.8 Hexadecane 99.109 -7533.3 -32.251 1.05E-02 1.23E-12 291.3 720.6 From Table 1 it can be seen that the maximu m low temperature that is considered valid for all the alkanes is 291.3 K or about 18.2 C. Similarly, the minimum high temperature that is valid for all the alka nes is 638.8 K or about 365.7 C. This means that as long as testing is done between 18 and 366 C, the approx imations of the vapor pressure for all of the alkanes are valid and reasonably accura te. Since the vapor pressures are first estimated then used in the Clausius-Cla peyron Equation to calculate the heat of vaporization, this implies that the values of heat of vaporization are also valid and accurate within this temperature range. Another method for estimating the heat of vaporization is to use Troutons Rule [22-23]. Troutons Rule is a rough approximation and is mainly used as a quick reference to ensure results are close to expected valu es. Suppose there is a liquid vapor system in 13
equilibrium and the vapor pressure is allowed to reach 1 atm. At this point the liquid will boil and completely transform into a vapor onc e it has absorbed the heat of vaporization and the temperature at which this occurs is its normal boiling temperature. The approximate relationship between the normal bo iling point and the heat of vaporization is known as Troutons Rule and is as follows: (11) or, (12) where is the normal boiling point of the subs tance. Since all the alkanes have well documented characteristics it is possible to gain rough estimates of the heat of vaporization of each individual alkane base d on the tabulated values of the normal boiling temperatures. Table 3 lists each alkane and their corresponding boiling temperature obtained from  and the h eat of vaporization es timated by use of Troutons Rule. 14
Table 2. Heat of vaporizatno es from rouons Rule. io f alkan Tt H Alkanes Undecane 195.5 41.2 Dodecane 216.0 43.0 Tridecane 234.0 44.6 Tetradecane 253.5 46.3 Pentadecane 270.5 47.8 Hexadecane 287.0 49.2 1.4 Alkanes Alkanes are organic compounds that only contain carbon and hydrogen atoms. They can sometimes be referred to as aliphatic compounds or paraffins. Alkanes are considered to be a non-functional group due to a relative unreactive nature and do not experience many chemical r eactions. All bonds between both carbon atoms (C-C) and carbon and hydrogen atoms (C-H) in alkanes are referred to as single, sigma ( ) bonds . Sigma bonds are formed fr om the overlapping of atomic orbitals. The total overlap of the bonding orbitals is propor tional to the strength of a bond. The two main sources of alkanes are crude oil and coal. The primary uses of alkanes ar e for fuels. The majority of alkanes are known as acyclic and acyclic ma terials are classically divided into two separate subcategories: straight chains and branched chains. Straight chains are aptly named because they are a straight series of carbon atoms connected to one another. Branched chains, on the other hand, have other connective groups of chains of carbon atoms that extend off of the original chain. These connectiv e groups are commonly 15
referred to as side chains or simply branches Figure 3 illustrates both straight chain and branched chain alkanes. All of the alkanes that were tested are straight chain molecules. Straight chain Branched chain b ranch Figure 3. Differences between straight chain and branched chain alkanes. In addition to acyclic, alkanes can be cycl ic in that the carbon atoms form rings. These specific alkanes are termed cycloalkanes and since they are of a different type of alkane as the research samples they will not be further discussed, but a review of these types of alkanes can be found in . The formulas and structures of alkane s are another example of distinctive characteristics. In a given compound alka nes contain the maximu m number of hydrogen atoms in connection with carbon atoms. It is for this reason that alkanes are deemed saturated compounds, because they are saturated with hydrogen atoms. Table 2 shows the list of alkanes of this investigation and the associated molecular formula. The formulas increase one CH2 unit for every successive alkane. Table 2 is known as a homologous series and each separate mol ecule is known as a homolog. The general formulation for alkanes is CnH2n+2 . 16
Table 3. Molecular formulas of alkanes. Alkanes Molecular formula Condensed formula Molecular Weight Undecane C11H 156 24CH3(CH2)9CH3 Dodecane C12H26CH3(CH2)10CH3170 Tridecane C13H28CH (CH) CH3184 32 11 T 1430 32 12 3etradecane C H CH (CH) CH 198 P 1532 32 13 3entadecane C H CH (CH) CH 212 Hexadecane C1634 32 14 3H CH (CH) CH 226 There are also nhysical and other compounds. As mentioned, alkanes cons ist of only C-C and C-H bonds of which the C-C nd ch t he intermolecular attractions are cr eated by London dispersion (LD) forces . When c may p chemical properties that set alkanes apart from bonds are nonpolar and the C-H are e ssentially nonpolar. This means that the molecules are nonpolar and as such are solubl e in nonpolar solvents, like other alkanes, and are immiscible in polar so lvents, like water. The C-H bond is a fairly strong bond a since it is considered nonpolar it makes the alkane molecu les less reactive than polar molecules. Alkanes are less dense than water at room temperature and as a result are characterized as hydrophobic compounds. Alkanes are generally chemically inert, whi allows for stability over long pe riods of time. Alkanes also ha ve the propensity to reac with oxygen or burn when presented with a source of ignition; hence, alkanes are used as fuels. Another characteristic of alkanes resulti ng from the nonpolarity of the molecules is that t ompared to polar intermolecular attraction forces, hydrogen bonding and ionic bonding, LD forces are considerab ly weaker. Fluctuations in electron densities generate transient dipoles, which are responsible for th e LD forces. As the molecule increases in 17
18 e r, t room lar a size so does the significance of the effect of the LD forces. Generally, the lower the molecular weight of the alkanes, the smaller th e total intermolecular forces are, and if th total forces are small enough, the alkanes will be a gas at room temperature. Howeve larger molecules inherently have a larger total of intermolecular forces which are necessary for alkanes to be liquids at room temperature. Higher molecular weights result in even greater total intermolecular forces a nd the resulting alkanes will be solids a temperature. As the molecular weight incr eases, the intermolecular forces increase resulting in a higher boili ng point and melting point. C onversely, branched molecules often boil and melt at significantly lower temperatures due to decreased intermolecu forces. This also means that less energy is required by branched molecules to complete phase transition.
CHAPTER 2 EVAPORATION TEST METHODS 2.1 Testing methods There are a number of ways to measure th e evaporation rates of substances. When measuring characteristics of a substance, or substances, the testi ng variable that is deemed most important is what dictates th e method of measurement. In the case of the evaporation rate of liquids th ere are three main variables of importance which are: the mperature of the substance, the amount of substance, and the vapor pressure of the evaporated liquid. The following is a f some of th e more popular methods of determining evaporation rates from these three approaches. If the testing vari e most important then a ermodynamic pr inciple of evaporative cooling follows. In this app liquid This information can then be used to determine the specific latent heat of the substance. Latent heat is the te quick re view o able of temperature is determined to be th method that conforms to the th roach a cloth or gauze pad is dipped into a container of the testing sample. The pad is usually wrapped around a thermocouple prior to the submersi on because the will begin evaporating as soon as it is removed from the container. As soon as the thermocouple and soaked gauze pad are rem oved from the container the liquid begins evaporating and as discussed in section 1.1 it will also begin cooling. Monitoring the cooling rate of the substance, exposed to normal ambient conditions, provides a temperature profile of the ev aporation process of the subs tance. 19
amount of energy absorbed during a phase tran sition, evaporation in this case. Knowing such tabulated variables as th e density of the vapor, the th ermal conductivity of the liquid and the vapor, and together with an understanding of the temperature profile will give the specific latent heat of the substance directly. The amount of energy absorbed during a phase change is equal to the specific latent heat of the substance multiplied by the mass of the sample. Since bond energies can be thoug ht of as the amount of energy required to break the intermolecular attractions of a subs tance than this is a good indication of the heat of vaporization and can be representative of the evaporat ion rate. This procedure is very cost effective because the only re quired equipment is a thermocouple and a computer. For repeatable results, the testing must be done in the same ambient conditions for every test. For example, the temperature, quality, and velocity of the air in the lab must be maintained constant during testi ng. For more information on this type of evaporation testing please see [4-5]. Another approach focuses on the quantity of the sample, or more precisely, the amount of loss of the sample with resp ect to time. This methodology follows the principles of thermogravimetrics to estimate the evaporation rate of the sample. This can be achieved by a number of techniques and by several different testing apparatuses. In temperature. The mass is measured with a hi ghly sensitive device th at can detect minor changes, on the order of 0.1 g sensitivity . When the substance is a liquid the mass loss represents the amount of the sample that is being evaporated and when the substance is a solid the mass loss represents the amount of the sample that is sublimated. As a result general, this approach measures the mass lo ss of the sample continuously with time and of monitoring the time lapse in addition to mass loss, the recorded mass loss is easily 20
transformed into a rate of phase transfor mation (evaporation or sublimation). Depe on the particular setup, this type of te nding sti ng can be done in a vacuum or in a sealed chambe 5, y le 26] a ximations of the evaporation rate of the samples. This procedure is less costly than the ther ly r with or without a purging gas. Rega rdless of setup, as before, conditions must remain constant between testing runs to ensure repeatability and ultimately comparability between samples. This approach requires ex pensive instrumentation and licensed data analyzing software. For further information on this specific testing approach see [10, 2 32]. Yet another way to determine a compounds spec ific evaporation rate is to directl measure the vapor pressure of the evaporated liquid. This approach assumes that a liquid vapor system in equilibrium will provide necessary information of the evaporation process. In this method the sample must be in a closed liquid vapor or solid vapor system. The closed system is then evacuated of the trapped air creating a vacuum. As the samp evaporates in the vacuum chamber, the vapor pressure can be measured directly by a couple of different means; which depend on the particular testing arrangement. In [ wire fed into the vapor portion of the vac uum chamber will change its resistance as the vapor pressure changes. This changing resist ance can be calibrated by known substances to give accurate readings of the changing vapor pressure. Once an accurate vapor pressure profile is obtained, the use of the Clausius-Clapeyron equa tion will provide valid appro mogravimetric approach, but requires the ability to create a vacuum. However, since the testing is done in a nd the readings are taken from a vacuum, then it is very easy to maintain constant environmental conditions between testing and is the most readi 21
22 lkane perature profile and th e differential temperatures were recorded. hermocouples were utilized to measure the temperature of the empty pan and the pan nce, as well as the temperature inside the heating hambe ed and comparable approach; in terms of direct m easurements. A good review of this approach can be found in [26-27]. 2.2 Testing procedure All testing followed the same procedure and used the same testing equipment. Samples were taken from storage containers using a p200 micropipette, 9 mg for a testing and 20-25 mg samples were drawn for pump oil tests. The micropipette was then used to inject the samples into aluminum pans and the pans were then placed onto a microbalance. The pan with the sample was ba lanced with an empty identical aluminum pan and the microbalance was zeroed. The pa rticular microbalance used in this experimentation has a reso lution of 0.001 mg, a range of 500 mg, and a maximum gross sample weight limit of 1 g. The pans were then heated inside a heating chamber with a programmable tem T that contained the sample substa cr. The chamber is isolated from the at mosphere and the inside temperature is us as a baseline temperature. The difference in temperature of the two pans was then used to accurately determine the temperature of the sa mple to within 1 C. The temperatures and the weight of the sample were measured continuously throughout testing runs. The testing runs were concluded when the sample was completely evaporated or until the heating program ended. The equipment used during testing was highly accurate proved to be a very good comparative tool for the evaporation of different substances
CHAPTER 3 ALKANES AND OIL EVAPORATION RESULTS veral interest is not obtained. As a result, without proven repeat ability results of different testing runs and between differe nt samples cannot be compared. 3.1.1 Repeatability studies The most important factors of evaporation measurements have been determined by mos ate vapor s g s constants between testing cycles with the exception of the vapor pressures and molecular weight which depend on the particular substance being tested. 3.1 Evaporation measurements Evaporation measurements, regardless of the testing approach, depend on se very important factors. These factors must be held as constant as possible to ensure repeatability between testing and compar ability between results. Without proven repeatable testing the resu lts are invalid and a good unde rstanding of the process of t of the literature, sp ecifically [25, 28-31], and our ow n testing. These factors are the initial mass of the samples, the exposed surface area of the samples, the heating r of the testing procedure, the flow rate of the surrounding gase s (if applicable), the pressure produced by the evaporative process, the molecular weight of the substance being tested, and the temperature (both the range and the specific temperatures durin testing). The majority of these factors can be readily maintained a 24
The heating rate and temperature are the eas iest of the factors to keep constant between testing. For a lot of te sting apparatuses a testing r un must first be established prior to testing. This acts as the blueprint of testing that the instrument will follow until stopped or the procedure has run its course. The instrument must have certain inputs from the use ng es. ny s eating and co oling rates constant at 20 C/min and 30 C/min, respectively. The pum p oil was either e xperiencing standard pan eva d s pe r such as to what temp erature should the sample be heated or cooled to, at what rate should this be done, should the sample be held isothermal after reaching this temperature, and if so, for how long, etc. On ce the user has determined these inputs a testing procedure has been established and is entered into the computer. If this procedure provides satisfying results then it can become the procedural guidelin es for all the testi and thus the heating rates and temperatures will be the same for the testing of all sampl Figure 4 illustrates a sample portion of th e testing procedure utilized for the ma tests of the pump oil in different arrange ments. The testing was done for over 70 hour while varying the temperatures but keeping the h poration or was evaporated from micr o-fluidic channels. As Figure 4 shows, the temperature was held isothermal after each te mperature increase or decrease for a perio of 1 hour. This allowed enough time for the temperature to stabilize before increasing or decreasing. This is crucial for sampling static temperatures rather than dynamic or rapid fluctuations of temperature. Conversely, Figure 5 demonstrates what has been deemed a static testing. Figure 4 shows a rather ra pid increase in temperature to effectively evaporate the sample completely in a short am ount of time. The time dur ation of this ty of testing was generally around 10 minutes. It should be noted that both Figure 4 and Figure 5 are plots of the sample temperat ure with time, not the instrumentation 24
temperature. As a result there are distinct nonlinearities in these two graphs. In Figure 4, just after a temperature increase or decrea se, obvious temperature oscillations can be seen. This is due to a fluctuating sample te mperature prior to stabilization at the set isothermal temperature. Figure 5, however, has two regions of the graph that are nonlinear. The first region is occurs in the fi rst minute of testing a nd this nonlinearity is due to the thermal inertia of the sample. In other words, there is a time delay between heating the sample and the sample temp erature increasing. Th e second region of nonlinearity occurs at about 6 minutes, for this example, and this correlates to when the sample mass is 10 20% of the initial mass, depending on the alkane. Once the sample has been evaporated completely, the temp erature increase of the instrumentation increases more proportionally with the em pty pan resulting in a nonlinearity and a subsequent change in slope. 60 100 140 51015202530T, oCFigure 4. Example of the pump oil test ing procedure, temperature profile. 180 t, hours 25
0 100 200 024681 0T, oCt, min Figure 5. Example of the dynamic alkane testing procedure, temperature profile The heating rate also has a profound eff ect on the accuracy of the calculated activa if the heating rate is too slow then the values of the activation energies are not as repeatable [25, 28-31]. From this it can be expected th at different heating rates will result in different values of activation energy. However, when the heating rate is above 10 C/min, for example, the activation energi es will have less deviation. Table 4 displays just that for some of the alkanes tested. As Table 4 shows, the heating rates used for different testing notice how as the rate increases the conformity of the activation energy calculations becomes more acute. tion energies. In general, when a sample is heated using a particular procedure, 26
Table 4. Alkanes activation energy, calculated for different heating rates Heating rate (C/min) Undecane from the Arrhenius Plot. Dodecane Tridecane 0.5 51.7 50.1 50.7 1.0 58.2 57.9 59.4 3.0 55.2 56.6 56.3 5.0 56.7 54.4 55.2 10.0 52.7 54.0 54.5 20.0 53.0 56.1 54.9 30.0 51.8 54.4 55.1 As discussed in section 1.1, the heating rate also affects the rate of evaporation. It sho will evaporat nderstand the dependence of the rate of evaporation to that of the heati ng rate. ass was kept revely the same for e.5 mg. H ensure co etween t percentage ofs loss is prefach te st was conducted in a burn-like procedure in which the temperature was ram the same value of 200 C, but with varying heating rates. The result for undecane can be seen in Figure 5. As expected, faster heating rates result in lessor the sample to completely evaporate. uld be obvious that the higher the rate of temperature incr ease the faster the sample e. A series of testing was completed to better u The initial m nformity b lati esting the ach test 0 owever, to eE mas rred. ped to time f 27
0.2 0.5 deg/min 0.4 0.6 0.8 1 1.0 deg/min 3.0 deg/min 5.0 deg/min 10.0 deg/min 20.0 deg/min 30.0 deg/minmass frtiont, min 01000200030004000500060007000 0 20406080100act, sec Figure 6. Heating rate dependence for undecane. The flow rate of the surrounding air also has a dramatic impact on the overall evaporation process. For example, Figure 7 shows the difference between the same test with and without a cooling fan on. The testi ng sample was the pump oil and the air flow rate of the fan was approximately 25 mL/mi n, and the temperature testing procedure was the same for both tests. Figure 7 illustrates a distinct difference in the use of a fan to increase the speed ction 1.1, the low rate of the air in co ntact with the exposed liquid greatly affects the rate of the of the surrounding air. As previously mentioned in se f evaporation. Using the linear be st fitting lines from Figure 6, it can be determined that activation energy without air flow is about 83.6 and with air flow is approximately 59.6 This equates to a 24 reduction in the amount of energy needed to break the intermolecular attractions in order for the liquid to evaporate. The pre-exponential constant is reduced by an even greater am ount. With the 25 mL/min air flow the pre28
exponential constant is approximately 6.9 and without the air fl ow the pre-ex constant is closer to 1.4e-4 ponential This demonstrates just how si gnificant the flow rate of the surrounding air is to the characteristics of evaporation. -28 -26 -24 -22 -20 No air flow y = 1,928 10051x With air flow 0,0024 0,0025 0,0026 y = -8,9103 7165,2xk lnT-1, K-1 Figure 7. Comparison of oil evaporatio n rate with and without air flow. As previously mentioned, the initial mass of the sample is a very important factor when attempting to obtain repeatable testing results. To ensure repeatable initial masses a micropipette was used. After several testi ng iterations the lack of accuracy of the micropipette was made evident. It was necessa ry to reset the micropipette each time prior to use. However, setting the micropipette to the same value every time did not result in the same amount of liquid being retained. It was initial thought that the micropipette was taking the same volume of liquid each time, but due to density changes between samples the amount of mass changed. This may in fact be true, but upon further inspection, using the same alkane resulted in different initi al mass measurements. To better explain, a series of constant mass testing was conducte d in which each alkane was tested numerous times using the same micropipette value prior to obtaining the sample. This was repeated 29
for every alkane. The results for undecane, for example, were a maximum value of 9.4 mg a minimum value of 8.1 mg with an averag e value of 9.0 mg and a standard deviation of 0.5 mg. These variations in initial mass, however small, would ultimately result in erroneous calculations of the activation energies of the alka nes. To combat this proble the data were analyzed by using the amount of mass reduction as a percentage of the initial mass per unit time. Simply dividing the instantaneous mass measurement by the initial mass reading provides the percentage of the initial mass remaining at a specific time. This was done for all the testing of the alkanes and th e pump oil. Figure 8 shows a graphical representation of this correction result. In this figu re there is a plot of the ma loss as a percentage of the initial mass vers us time for every alkane. The alkanes were ramped to the same high temperature at a rate of 20 C/min and this testing procedure was constant for each testing cycle. Figure 8 provides a good estimation of comparison the different alkanes evaporation rates. m ss of 0 0.4 0.8 200 600 1000 261 01 4 Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecanes frtiont, minmasact, sec Figure 8. Mass loss as a percentage of initial mass for each alkane. 30
Finally, the surface area of th e exposed liquid is a very important factor that must be controlled to promote repeatability and to compare final results. The exposed surface area was relatively the same for each alkane and the pump oil because all testing was done in aluminum pans of the exact same di mensions. Through repeated use the pans did become slightly deformed changing the ove rall shape of the opening of the pan. This change in dimension was determined to have very little effect on the exposed surface area. In order to estimate the surface area of the liquid in th e pan, the pan dimensions, the wetting angle, and the height difference between the liquid at the inner sides of the pan, and the c ed from e man s the le. So e enter of the pan must all be known. The pan dimensions are easily obtain thufacturers data or can be physically measured. The pans that were used had an inner diameter of 5 mm and an inner height of 1.5 mm. The wett ing angle came from a profile measurement using an optical microscope. The profiles were measured by focusing the image of the sample surface in th e microscope and noting the position of the lens. The sample was then incrementally move d and as the changes in the focal length were recorded an estimate of the profile of the liquids were obtained. The scanning of liquid surface was conducted from the liquid pa n interface of one side of the pan to the other. From this profile the height differen ce between the liquid at the sides of the pan and the center of the pan could easily be calculated. It is important to take note of another simplifying assumption that was used in the ca lculation of the exposed surface area. This simplification is that due to close molecula r composition and densitie s of the alkanes it has been assumed that the deviation in wetti ng properties between them is negligib to gain an average representation of the we tting profiles of the al kanes, tridecane was used to calculate the wetti ng angle and exposed surface area. Tridecane was used becaus 31
the average density of the alkanes is 0.758 and the average molecular weight is 191 whereas tridecane has a density of 0.756 and a molecular weight of 184 Figure 9. Example of wetting prof ile of three stages of oil. Fig Figure 9 is a picture of the pump oil in the test pans. From left to ri ght in Figure 9 is an example of fresh oil, oxidized oi l, and burnt oil. Fresh oil is oil that was taken directly from its container and injected into the pan, oxidized oil is o il that has been run through a series of heat treatments but has not completely evaporat e and burnt oil is oil that experienced a rapid increase in temperature and what is left insi de the pan are carbon deposits. ure 10 shows the recorded profile from the optical microscope of tridecane with the center point of the pan being at 2.5 mm and 0 mm and 5 mm representing the inner surfaces of the pan walls. The recorded data points for the prof ile have been fitted with a fourth order polynomial and the e quation can be found in Figure 10. From Figure 10 it can be determined that the minimum he ight of tridecane is 0.60 mm and a maximum of 1.12 mm. Figure 11 illustrates a similar resu lt for the pump oil. The profile of the pump oil yields a maximum height of 1.41 mm and a minimum height of 0.53 mm. 32
0 0.5 1 1.5 012345Tridecane height, mm Y = M0 + M1*x + ... M8*x8 + M9*x9 1.1279 M0 -0.58684 M1 0.27293 M2 -0.062981 M3 0.0063814 M4 0.99536 R 0.60 mm Length along the diameter, mm Figure 10. Wetting profile of tridecane in a pan. 0 0.5 1 1.5 012345Pump oil height, mmLength along the diameter, mm Y = M0 + M1*x + ... M8*x8 + M9*x9 1.4108 M0 M1 -0.98182 0.4363 M2 M3 -0.099013 M4 0.010213 0.99845 R 0.53 mm Figure 11. Wetting profile of pump oil in a pan. 33
The wetting angles for these two substances we re estimated from an averaging of angles. In this method the lowest point of the liquid profile is selected as a reference point. The angle between this point and the next is de termined by simple trigonometric identities. The angle of between the second point and the third point is then f ound. This is repeated until the angle between the last two points is recorded. The summation of these angles is recorded and the average is calculated. This process is repeated for both sides of the minimum point and for both liquids. The average of each side was then averaged with the other to give an overall average estimate of the wetting angle for the two liquids. Using this approach, the wetting angles for tridecane and the pump oil are 10.55 and 17.71, respectively. As expected the sample with the higher molecular weight, density, and viscosity has the higher wetting angle. To be tter express the difference in the measured wetting angles of tr ure 12 is displays the profile of tridecane and pump oil superimposed onto the same plot. Notice the similarity of the overall shape of the two profiles, but they differ in angle and minimum height of the liquid. These nonconformities are due to the differences between the surface energies and densities of the two liquids. idecane and pump oil Figure 12 was constructed. Fig 34
0 0.5 1 012345 1.5 Tridecane Pump oilight f liquis, mmLength along diameter, mmFigure 12. Superposition of the profil es of tridecane and pump oil. Another important characteristic that can be evaluated from the profile of the liquids is the exposed surface area. This is done by revolving the fourth order polynomials around the center point (2.5 mm) and using the following equation fro : Heod m (13) where represents the surf ace area of the revolution of the function between points and From this method the exposed surf ace areas were estimated to be 24.0 mm2 and 70.6 mm2 for tridecane and the pump oil, respec tively. These calculations represent a good estimation of the respective initial surface areas. During the evaporation the liquids evaporate uniformly over the exposed su rface area until the center of the liquid completely evaporates. This portion of the sample is the first to completely evaporate because it has the least amount of substance. After the cente r has evaporated the liquid continues to wet the sides of the pan and begins to evaporate as a ring of liquid. Figure 13 35
illustrates this process of evaporation that is dependent on the exposed surface area. In this figure the dotted line represents the expos ed surface of the liquid that is evaporating and the solid line is the pan. Notice how the rate of evaporation will vary based on the amount of remaining liquid through the he ight of the wetting liquid, h and h and that the wetting angles, and '' should remain the same throughout the evaporation process. Figure 13. Evaporation process wi th respect to surface area. This implies that the exposed surface area from which the liquid is evaporating is not a constant throughout the evaporation process and is in stead some function of the wetting angle and the amount of f evaporation will rein relatively constant u r resembles s been Partially evaporated Completely evaporated Initialevaporation h '' h' liquid. Based on this analysis, the rate o ntil the profile of the liquid in the con ma taine that of the partially evaporated state from Figure 13 and then the rate of evaporation will reduce with time until the liquid is completely evaporated. This can be accounted for if testing is stopped when the mass loss is equa l to the estimated mass of the cylinder of liquid with a height of h. This is approxi mated by finding the volume of the cylinder of liquid and multiplying this value by the density of the sample. Once this mass ha evaporated then the partial evaporation c ondition from Figure 13 begins and the rate changes significantly. If the wetting angles were assumed to be constant throughout the evaporation process then the volume of the li quid that is wetting the pans will also be 36
constant. Using the previously calculated wetting angles and th e height difference between the maximum and minimum heights of the liquid surface, the area of a two dimensional right triangle can be found from trigonometry. These tr iangles were then revolved around the inner surface of the pa ns, which resulted in the volumetric calculations of 0.16 mm2 and 0.78 mm2 for tridecane and the oil, respectively. Multiplying these volume calculations by the re spective liquid densities results in a good estimati e liquids co tting reg were found to be 0.12 mg and 0.67 mg for tridecane and the oil, respectively. These masses correlate to 1.33 and 2. of in itial massese and the oil. Since these masses are such a small percentage of the initial masses of the liquids it is very difficult to determine from the data when the partial evaporation conditions are active. Additionally, since there is so little liquid remaining in the pans at that moment and the remainder is evaporated very rapidly and the affect it has on the overall evaporation rate can be neglected. Understanding how essentia l factors like the initial mass of the sample, surface area, heating rate of the sample, flow rate of air, and the temper ature can vary between testing cycles is key for establishing repeat able testing procedures. These factors were held paramount in establishing all testing procedures. To test the repeatability of the alkane testing three und ecane burn tests were compared. Th e results can be seen in Figure 14. The three tests experienced the same maxi mum temperature and were heated at the same rate. It can be assumed that all three tests had the same exposed surface area and no air flow. Since all three example runs were conducted using the same substance, the on of the mass of th ntai ned inside the we ions. These masses % 39 % the of tridecan liquid is at a relatively high temperature, ne ar the boiling point of the substance, the 37
molecular weight remained constant through te sting. The factors that proved to be v cumbersome to maintain as constants thr ough testing cycles were the initial mass and initial temperatures of the samples. ery -22.4 -22 -21.6 -21.2 0.00310.003150.00320.003250.0033 y = 0.066781 6854.8x y = -0.4086 6706.4x y = -0.24417 6750.4xln-1-1 kT K Figure 14. Repeatability results fo r Arrhenius Plot of undecane. Regulating the initial masses was performed by an iterative process involving the micropipette and numerous weight measuremen ts. An initial amount of the sample, in this case undecane, was taken from its origin al container by use of the micropipette. This value was then measured and recorded. The subs equent tests gained the initial mass in the same way however, if the initial mass of less th an or greater than the first test by as little as 0.1 mg then an iterative process of adding and subtracting mass was conducted to gain conformity in the measurements. The initial temperature was an easier variab le to control. Essentially all the initial samples were at the same ambient room temperature, since they require no special storage conditions. The instrumentation setup used was allowed to cool to the same temperature prior to start of a new test. These initial instrumentation temperatures were 38
all within 0.2 C of each other. Table 5 lists the test run and the a ssociated initial masses (M he r each test run. Table 5. Repeatability compar ison results for undecane. Undecane Mi (mg) Ti (C) A i) and temperatures (Ti). Additionally, Table 5 lists the pre-exponential values and t calculated activation energy values fo Ea Test 1 9.19 26.3 1.1 55.8 Test 2 9.13 26.1 0.7 54.6 Test 3 9.17 26.2 0.8 54.9 Table 5 relates the importance of the initial ma ss and initial temperature on the calculated activation energy. From the table the lowest initial mass coinci ded with the lowest initial temperature, which resulted in the lo west calculated activation energy and preexponentia the lues of Static testing, as it has been termed in this investigation, is a method of testing samples over a long period of time at the same temperature. The intent of this type of testing is to provide long is othermal periods between incremental increases and decreases in temperature to allow for distinguishing be tween transient change s in the evaporation l constant. Likewise, the highest measured initial mass coincided with highest initial temperature which, as expected, resulted in the highest calculated va the activation energy and pre-exponential constant. Table 5 also demonstrates the remarkable differences in the pre-exponen tial constant stemming from very small changes in initial conditions. However, thes e variations in calculated values can be considered negligibly small and as a result th e testing conducted in th is investigation has been deemed valid and repeatable. 3.1.2 Static testing 39
rates and actual rates at specific temperat ures. As the temperature is increased and decreased the evaporation characteristics ar e recorded during the isothermal periods. Increases and decreases in temperature during st atic testing were done at a very low rate, which was pro thod of testing proved e de e ctics of nes at lower level temperatures (25 -75 C). This is very im portanse of th nature of static testing. With thnt pros of th nes su lower ds, molecular boiling temperatures, as compared to the pump oil, the low temperature data points were generally too scatte red to retrieve any useful re sults from a more rapid form evaporating and a faster heating rate results in noisy data at lower to atmospheric levels. phenomenon can better be described by compar ing the static and dynamic test results for against the inverse of the absolute temper ature. The unfilled circles represents data the data points become less uniform and begin to fan out altering the slope of the linear fit line. grammed by the instrumenta tion to be 0.001 C/min. This me to be very ffective at fini ng th haracteris au the alka y t bec e ve r e inhere pertie e alka ch as ensitie weights, and of testing. This is due, in part to the fact that once the alkanes are exposed they begin This is why the static testing procedures were introduced; to give a more complete explanation of the evaporation rates of the alkanes for a wider temperature range. This one of the alkanes. Figure 15 is such a plot of the logarithm of the evaporation rate collected from dynamic testing of hexadecane. Notice how as the temperature decreases 40
Figure 15. Static and dynamic Ar rhenius Plot for hexadecane. Since the slope of this line is directly rela ted to the activation en ergy, then another means of collecting the lower temperature data is necessary for a more adequate and comp representation of the evaporat ion rate from room temperature and above. This makes static testing an ideal approach for collecti ng these data. The sample begins testing at room temperature (25 C), where it remains for an extended period of time then it is heated to a slightly higher temperature and again held isothermal. This is repeated u predetermined temperature, the temperature at which dynamic testing has been deemed valid (usually 60 -75 C), is reached. This data is then recorded and analyzed by means o the Arrhe lete ntil a f nius equation, just as done with dyna mic testing data. The total collection of data is then graphed in the same Arrhenius Pl ot and linear lines are fitted to the separate data to approximate the activation energies for low and high temperature level evaporation. This type of plot, as shown by Figure 15, provides an expected result: at lower temperatures the molecules require more energy to be broken than at higher temperatures. From Figure 15 it can be determined that the activation energy for -28 -24 -20 -16 0.0022 0.0026 0.003 Dynamic testing Static testing y = 1.8941 8736.2x y = 5.6973 10136x ln kT-1, K-1 41
hexadecane is about 16.0% higher at a temperature range between 25 C and 75 C than at higher temperatures. Once static testing was determined to be an appropriate means of determining the overall evaporation characteristics of the alkane s, all the alkanes were tested with this method. Figure 16 shows the resulting Arrhen ius Plot for all the alkanes. There are several interesting results that can be observed in this figure. Most notably is the shifting down and to the left for the higher molecular we ight alkanes. This shifting has a two part explanation. The downward shifting is repres entative of an increase in the activation energy of the alkanes, as can be seen in Figure 16. This is expected because as the molecular weig ties. ht increases between alkanes so do some essential molecular proper -28 -24 -20 0.00260.00280.0030.00320.0034 Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecane in This ln kT-1, K-1Figure 16. Static temperature testing for all alkanes. The density, the molecular weight, and th e boiling temperature all increase with ascending alkane order. As disc ussed earlier in this work, an increase in such material properties requires a greater en ergy to break the intermolecula r attractions. As seen Figure 16, the shift to the left also seems to increase with ascending alkane order. 42
shifting represents an increase in the maximu m temperature of the valid static testing range. In other words, the higher the alkane ranking the higher the static temperature can be reco r he or the testing itself. The other explanation is that the data we re not isolated for the same temperature range for each alkane, but rather for the entire valid range specific to each individual alkane. This in effect alters the slope of the linear fitt ed line by averaging the lower temperature data with those of the more elevated temperature data. However, after creating similar plots for the truncated ra nges a similar phenomenon is present. This unexpected result is ultimately explained by the sporadic nature of data obtained from static testing. rded and remain a valid and accura te representation of the evaporation rate characteristics. The activati on energies and pre-exponential constants were calculated from the linear best fit lines of the data presented in Figure 16 and the results are displayed in Table 6. It is interesting to not e that all the offsets of the Arrhenius Plots were positive numbers resulti ng in large values of the pr e-exponential cons tants. Also, the fact that the activation en ergies do not increase incrementally as expected, is rathe peculiar. This could be a result of one of two things, or a combination of the two. T first possible explanation is that there are errors in the testing, from either the parameters 43
Table 6. Activation energies and pre-exponent ial constants for all alkanes, obtain Alkanes A ed from static testing. Ea Undecane 5317 79.5 Dodecane 316.4 74.5 Tridecane 61.21 72.2 Tetradecane 2623 85.4 Pentadecane 3575 89.3 Hexadecane 182.9 82.9 Even though there are these unexpected fluctu ations, there still are some fundamental relationships that can be learne d from the static testing of al kanes. Primarily, static testing of alkanes is only valid in the low temper ature range. In addition to this, the energy required to break intermolecular attractions is greater at lower temperatures. To further explain the latter relation, an averaging of the calculated values of the activation energies for higher heating rates for dynamic testi ng was done. These averages were then compared to the static values for the corres ponding alkanes. The percentage of increa of the activation energies was then obtained for each alkane by this method. Taking the mean value of se the percentage increase in activation energy for the alkanes resulted in 25.7 %. This means that, on aver age, the required activation energy at lower temperatures is 25% greater than what is necessary at highe r temperatures. This correlates to a slower evaporation rate at lower temperatures, as can be expected. If these results were to be generalized to all liquids then it could be stated that liquids near room temperature require 25% more energy to break intermolecula r attractions (evaporate) than at elevated temperatures. 44
ery different conclusions. First, due in larg of the inherterial properties of the oil static testing proved to be the only ethod of nding how the oil evaporates. Dynamic testing, in other words, evaporation of this oicause rapating the oi uced very little retrievable data. Als g rate ahe maximump erature were set too high the oil would sim e carbon deposits on the instrumentation. Therefore, static testing was preferred and for the pump oil the testing was usually over he s f e er, the aluminum pans were ke pt empty in the drift tests. The theory Static testing of the pum p oil was conducted in a similar fashion, but resulted in v e part viable m ent ma unde rsta is not a valid approach for defining the l. This is be idly he l prod o, if the heatin nd/or t tem ply burn and leav 60 hours. Testing over such a long time has se veral benefits and hindrances. The major benefit of testing for such a long period of tim e is that a lot of good usable data can be calculated. Also, long testing pe riods provide a chance to fluctuate the temperature to many different settings gaining a more complete estimate of the evaporation characteristics of the oil. The main negative result of such testing is in the accuracy of the instrumentation itself. When testing evaporation over such a long period of time t instrumentation used would suffer from drift. Instrumentation drift is a loss of calibration that stems from the use of the instrument. As an instrument is used it tends to become les accurate with time, hence the need for freque nt recalibration. However, since testing o this type cannot be stopped to recalibrate the instrumentation; measurements must be taken continuously. To account for instrument ation drift a series of drift tests were conducted to determine to what extent the instrument was reducing in accuracy over th testing period. For drift testing the testing procedure remained exactly the same as the normal testing. Howev 45
behind this logic is that at the temperatures that were be ing tested the aluminum would not be losing mass, or at least not a meas urable amount. Conducting these tests resulted in an observed mass loss of the empty pans on the order of 0.5 mg over a 64 hour perio The extent of this drift can be seen in Fi gure 17 which is a graph of the measured mas loss of the oil as compared to the drift resu lts for two test runs. All testing experien the same temperature controlling procedure a nd all other conditions were maintained as constants. Figure 17 shows a total measured mass loss for the pump oil as about 0. for the 64 hour testing. The drift testing resulted in a fictitious mass loss around 0.34 mg which would be a significant percentage of the measured mass loss for oil. Also notice from Figure 17 that the mass loss due to drift is represented by a relatively zero sloped line until about hour 4. That is why drift correc tions are not needed for the static testin of the alkanes, because they evaporated well within a few hours. d. s ced 83 mg g 50 100 150 200 0 1 3 0 oCt, hours 2 5 1 041 1051,5 1052 1050816243240485664T,mass, mgt, sec Figure 17. Drift test comparison for pump oil. Em p t y p ans Temperature profile Mass 46
Correcting for drift is necessary prior to an alyzing the data. To do this the mass loss due to drift is simply subtracted from the measur ed mass loss of the oil. Since the fictitious mass losses were recorded as nega tive values, as a result of drift test calibrations prior to testing, the magnitudes of the drift mass loss are added to th at of the measured oil mass losses continuously for the entire testing peri od. The series of drifti ng tests never resulte in the exact same total mass loss, but the resu lts were close in valu e and the overall shape of the mass loss curve. A function was linearly fi tted to the instrument drift data and was then subtracted from the measured mass loss profile for the pump oil. The result can clearly be seen in Figure 18, in which the m easured and the actual, after correction, mass losses are plotted with respect to time, temp erature, and mass. Notice that the mass loss profile of the oil maintains a very similar shape but is increased in magnitude. This increase is a result of drift corrections of the measured data and ac d counts for the loss of calibration of the instrumentation over the complete testing cycle. 50 100 150 200 2 2,5 3 3,5 08 1 041,6 1052,4 1050816243240485664T, oCmass, mgt, sec t, hours Figure 18. Drift correction for pump oil. Measured Correcte d Temperature profile 47
After the pump oil data was corrected the activation energy was then calculated. The method of calculatio n utilized the Arrhenius Equation and the related Arrhenius Plot for the corrected pump oil data can be seen in Figure 19. As usual a linear best fit line was drawn through the data points in order to obtain information on the slope and offset of the Arrhenius plot. From this informati on the activation energy of the pump oil was calculated to be 83.6 and the pre-exponentia l constant to be 6.9 -25 -24 -23 -22 -21 0,002350,002450,002550,00265 y = 1,928 10051xln kT-1, K-1 Figure 19. Arrhenius Plot of pump oil for calculating the activation energy. 3.1.3 Dynamic testing Dynamic testing is the measurement of th e mass loss of a sample with respect to time while experiencing a continuous increase in temperature. The heating rates for the series of dynamic tests were 0.5, 1, 3, 5, 10, 20, and 30 C/min. All the alkanes were heated to a maximum temperature of 300 C at these varying rates. Needless to say that all of the alkanes completely evaporated well before the maximum temperature was reached. In fact the testing usually lasted less than 15 minutes. As mentioned in the previous section, result ble data for higher s from dynamic testi ng proved to provide sta 48
teatures, generally over 60 C. The main difference between dynamic testing and static testing is that in dynamic testing the temperature of the sample is rapidly changing allowing no time for it to stabi lize in temperature. As a re sult, dynamic testing never ha an isothermal condition. Just as in the other testing proce dures the temperature and mass loss were recorded continuously throughout the testing. Likewise, the recorded data was analyzed by means of the Arrhenius Equation and were plotted to estimate the ar best mper s slopes and the offsets of the line fit lines. Figure 20 is such a graph, displaying the collected data and the linear fitted curves to that data for all th e alkanes. There is once again a pattern of shifting between the alkanes. Figure 20 shows a distinct shift downward and to the left for ascending alkanes. The shifting in the downward direction is an expected result as it represents an increase in the re quired activation energy to break intermolecular bonds in the increasing order of such propert ies as molecular weight and boiling point. As in static testing the shifting to the left is related to the valid te mperature range of the data. Although all the alkanes were tested under the same conditions and experienced the same the alkanes. From Figure 20 it can be dedu ced that the lower the melting point, for instance, the better the low temperature data. Here better refers to data that is more consistently repeatable and is m in Figure 19 that the Arrhenius Plots for dod ecane and tridecane are almost on top of each other, whereas the other alkanes have more significant spacing between them. This could boiling point, density an d molecular weight. temperatures, the amount of scatter in the lower temperature data varied between ore uniform for temperatures less than 60 C. Also notice be because of all the alkanes, dodecane and tr idecane have the closet tabulated values of 49
-23 -15 Undecane Dodecane -21 -19 -17 0,0022 0,0026 0,003 0,0034 Tridecane Tetradecane Pentadecane Hexadecaneln-1-1 Figure 20. Dynamic temperature testing for all alkanes. Tables 7, 8, and 9 display the resulting calculations derived from Figure 20. Eac table lists the alkane tested and the asso ciated activation energy calculated from the Arrhenius equation. Additionally, the heat of vaporization was calcula ted by means of the Antoine equation for comparative purposes. Table 7 has been compiled from data collected at the lowest acceptable heating rate, 10 C/min. Acceptable in this case is defined by a heating rate that gives consistently repeatable results. Table 8 represent data collected from a 20 C/min heating ra te and Table 9 was made from the data measured with a 30 C/min heating rate. These tables show that the measured values for each alkane are in close proxim ity to each other, within 3-4 kT Kh s the Similarly, the theoretical values of the heat of vaporization from the Anto ines Equation are within a similar range for each alkane. Notice from the three tab les and comparison of the two calculation methods reveals good agreement. 50
Table 7. Comparing Arrhenius to Antoine E quation results for a heating rate of 10 C/min. Alkanes Ea H Undecane 52.67 52.01 Dodecane 54.04 53.67 Tridecane 54.55 53.17 Tetradecane 57.06 59.57 Pentadecane 79.31 78.90 Hexadecane 73.39 74.46 Table 8. Comparing Arrhenius to Antoine E quation results for a heating rate of 20 C/min. Alkanes Ea H Undecane 52.95 52.08 Dodecane 56.10 57.75 Tridecane 54.91 56.46 Tetradecane 51.27 53.00 Pentadecane 73.81 77.38 Hexadecane 67.45 69.75 51
Table 9. Comparing Arrhenius to Antoine E quation results for a heating rate of 30 C/min. Alkanes Ea H Undecane 51.78 51.22 Dodecane 54.40 56.83 Tridecane 55.14 54.16 Tetradecane 52.60 54.42 Pentadecane 67.99 68.99 Hexadecane 70.33 71.72 etermined for all testing of higher heati ng rates, 10 C/min ater. Since dynamic testing proved to be mo ean values are very good representations of the actual able 10, which have been estimated w lity of 9 Table 10. Average activation energies and pre-exponential constants for all alkanes. E The mean values of the activation ener gies and pre-exponen tial constants were d and gre re consistently repeatable, these m values. The resulting values can be seen in T ith a reliabi 5%. Alkanes a A Undecane 52.5 0.74 0.46 0.11 Dodecane 54.8 1.32 0.45 0.19 Tridecane 54.9 0.36 0.22 0.04 Tetradecane 53.6 3.64 0.12 0.12 Pentadecane 70.9 4.95 9.25 10.46 Hexadecane 70.4 3.57 4.35 4.01 In addition to the mentioned statistical analysis of the measured data, an error analysis of the instrumentation was also conducted. The instrumentation used for the testing, as mentioned in the testing procedure section of this work, was found to be very precise. 52
T calculation of the activation ener gies is as follows. It was first noted that the activation energy can be written as a function of both e of the sample. The following empirical equation was used: he propagation of errors from the measured variables of mass and temperature to the the mass and tem peratur (14) where the ratio of mass, m, to tim ion is kg/sec, T is the ature, R is the gas constant (8.314472 J mol-1 K-1) and A is the preexpone is e, t, repres en ts the rate of evaporat absolute temper ntial constant found from the previously presented Arrhenius equations. Using th equation in association with th e chain rule in order to obta in the maximum possible error in the activation energy provides: (15 which can be simplified as: ) which m and T are the m s and temperatures, respectively and m and T are errors associated with the mass and temeasurements. The mass error was found to be 0.001 mg aeratu fou C. This means that a mass measurement of era men sult in the recorded values of m 0.001 m ropagate through the calculation of the activa tion energy and as a result must be accounted for. It should (16) perature m easured masse nd the temp re error was nd to be 0.3 m and a temp ture meas ure t of T will re g and T 0.3 C, respec tively. These errors will p to be noted that the error resulting from temp erature measurements dominates the total propagated error for the activation energy, t hus the mass error could be neglected for simplicity, but was not in the following erro r analysis. Equation (14) was used to 53
calculate the activation energy as a function of mass and temperature. Then equation (1 was used to calculate the instrumentation error inherent to th e calculation of the activation energy, also as a func tion of mass and temperature. Th e ratio of these errors to that of the activation energies were taken 6) o for all the alkanes for both the s es. The resulting maximum percentage errors an es and both testing regimes nge Alkanes amic Testing t provide the percentage error. This was done tatic and dynamic testing regim d activation erro rs for all alkan can be seen in Table 11. Notice that as it was re lated in the procedure section of this work the precision of the testing equipment was f ound to be very high and resulted in a ra of estimated instrumentati on errors of 013 0.30 %. Table 11. Propagated errors of the ac tivation energies for all alkanes. Static Testing Dyn Ea (%) Ea (%) Undecane 79.5 .13 0.253 0.11 0.135 52.5 0 Dodecane 74.5 54 0.268 0.11 0.152 .8 0.15 Tridecane 72.2 4. 0.12 0.162 59 0.16 0.285 Tetradecane 85.4 53.6 0.16 0.300 0.11 0.133 Pentadecane 89.3 70.9 0.15 0.210 0.12 0.137 Hexadecane 82.9 0.13 0.152 70.4 0.18 0.255 3.2 Mixtures testing A series of testing cycles that were not of pure alkanes but rather a mixture of them were conducted and rightfully termed mi xtures testing. The procedures for these tests were the same as the dynamic testi ng previously described. However, the only difference was in the samples being tested. Mixture testing consis ted of taking equal 54
volumetric portions of two separate alkanes and thoroughly mixing them in a beaker. Once these alkanes were mixed the 50-50 mixtur e was then transferred from the the aluminum testing pans via the micropipet te. The data was then processed as before using the Arrhenius Equation and constructi ng the plots. Figure 21 and 22 are two Arrhenius Plots constructed from the mixture data for a heating rate of 20 C/min C/min, respectively. In both plots it is easy to see that there is very little spacing between mixtures, unlike what was observed for pure substances. It also seems that regardless of heating rate the mixtures exhi bit evaporation characteristics that most closely resemble that of pure undecane. A re sulting hy beaker to and 30 pothesis is th at the molecularly lighter s The slopes of these linear fitt icantly below ane and, to a lesser extent, below that of pure undecan pecifieems to reduce the requirednerg verc ermolecular attractions below that of the values calculated for the pure components of ixture. ubstance evaporates first. That is except for the undecane and tridecane mixtures. ed lie e ns are signif thato c mixture s f pure tec rid e. This s o activation e y needd to o me int the m -23 -21 -17 0,0026 0,003 0,0034 -19 Undecane and doddecane Undecane and tridecane y 81,1x = -1,3159 61 y = -2,586 5808,3x Undecane and tetradecane y = -1,0527 6329xlnFigure 21. Arrhenius Plot of specific mixt ures heated at a rate of 20 C/min. kT-1, K-1 55
-23 -19 -17 -21 0,0024 0,0028 0,0032 Undecane and dodecane Undecane and tridecane Undecane and tetradecane y = -1,4346 6140,6x y = -2,671 5736,4x y = -1,4744 6128,7x ln kT-1, K-1 Figure 22. Arrhenius Plot of specific mi xtures heated a rate of 30 C/min. To further elaborate on the results of alka ne mixtures Tables 12 and 13 have been constructed. These tables pres ent the calculated activation en ergies and pre-exponential constants for both pure testing and of mixtures. Included in the mixture data are the averaged values of the activation energies and pre-exponential constants between the two pure substances found in the specific mixtur es. The second values, after the commas, are these averaged calculations. Table 12 represents data retrieved from the 20 C/min testing and Table 13 was constructed from the 30 C/min data. 56
Table 12. Comparison between mixtures and pure alkanes heated at 20 C/min. Alkanes Ea A Undecane 52.95 0.54 Dodecane 56.10 0.63 Tridecane 54.91 0.23 Tetradecane 51.27 0.05 Un & Do mix 51.39, 54.53 0.27, 0.59 Un & Tri mix 48.29, 53.93 0.08, 0.39 Un & Tetra mix 52.62, 52.11 0.35, 0.30 Table 13. Comparison between mixtures and pure alkanes heated at 30 C/min. Alkanes Ea A Undecane 51.78 0.37 Dodecane 54.40 0.37 Tridecane 55.14 0.26 Tetradecane 52.60 0.07 Un & Do mix 51.06, 53.09 0.24, 0.37 Un & Tri mix 47.70, 53.46 0.07, 0.32 Un & Tetra mix 50.96, 52.19 0.23, 0.22 Comparing the tabulated valu es in Table 12, the following observations are made: the calculated values of the activation en ergy of the undecane-dodecane and undecanetetradecane mixtures are close to the origina lly calculated value of pure undecane, so it seems that the earlier stated hypothesis, that th e molecularly lighter substances evaporates first, has some merit. However, the undecan e-tridecane mixture resulted in a reduced activation energy that is less than that of pure undecane. The undecane-dodecane and undecane-tetradecane mixtures also have close approximations with the average 57
ac tetradecane has the close to the c veragetion energy. This mixture also has a clos ation betwcalculate veraged values of the pre-exponential constaecane-dod mixture resulted in a value of the preexponential constant that is roughly half of the average value a mixture resulted in a value closer to tivation energies of the pure substances. It should, however nted that the undecane beo of activa a er estimat a lculated a e e appr oxim een th d and nt. The und ecane nd the undecane-tridecane th Comparing the results presented in T ws sim th the alculated values of the undecane-dodecan e and the undecane-tetradecane mixtures tridecane mixture resulted in a reduced value activation energy, below that of pure undecane. Undecane-d undecan cane mixtures also resulted in reasonably close approf both thetion energ pre-exponential constants to that of the average values. On the other hand, the values calculated for the undecane-tridecane m s than th average pre-exponen From this an ng e mre of alkanes will reduce the activation energy needed to break intermolecular attractions and the prea e average. a ble 13 sho ilar results. Bo c resulted in activation energies close to that of pure undecane, whereas the undecaneof the de odecane and e-te tra ximations o activa ies and ixture were les at of the averag e activation energy and tial constant. alysis the followi conclusions ar ade: a mixtu exponential constant. The extent of this reduction depends on the properties of the components of the mixture and the proportion of the mixture. It can be generalized that the reduction of the activation energy is dom inated by the component of the mixture that has the weaker intermolecular bonds. That is, the mixture resultant values will most closely resemble that of the component with the lower boiling point, density, and molecular weight. This proves the hypothesis that the molecularly lighter substances of 58
mixture will evaporate first. The change in the pre-exponential constant for mixtures is much more significant than that of the act ivation energies. While in some cases the activation energy of a mixture can be r oughly estimated as the average of the components, this is not always true and larg e errors can result from averaging. Since the change in the pre-expon ential constant is great er with mixtures this rule is even more applicable for these calculations. Another important observation that should be made from these two figures is dramatic difference in the reported values of the pre-expon ential constants between t static and dynamic testing. The pre-exponen tial constant, often referred to as the frequency factor, is directly related to the frequency of the rate of the reaction. The frequency factor is equal to the collision frequency multiplied by the steric factor. T steric factor is the ratio of th e observed frequency factor to th at of the calculated colli frequency. Therefore, the frequency fact or, or the pre-exponential constant, is proportional to the collision frequency, which re presents the average number of collis between reacting molecules for a un the he he sion ions it of time. This implies that for static testing there are ignific se santly more molecular collisions duri ng evaporation than that which is observed for dynamic testing. 3.3 Microchannel evaporation testing With the increasing popularity of MEMS de vices, testing was also conducted to measure the evaporation rate of the pump o il in simulated micro-fluidic channel. The microchannel tests were designed using all aluminum parts, which consisted of a cylindrical reservoir and either a screw thread ed or non-threaded plug for the reservoir. 59
Non-threaded Threaded Figure 23. Pictorial representation of microchannel testing fixtures. Figure 23 is a dimensionless pictorial repr esentation of the design of the testing fixture used to simulate micr o-fluidic channels. On the left side of Figure 23 is the nonthreaded microchannel which is a mating pair of smooth aluminum cylinders. The pump oil is first put into the reservoir and then the plug is pressed into the reservoir. This limits evaporation to only a thin ring of exposed oil at the top of the reservoir. On the right sid of Figure 23 is an illus Oil reservoir e tration of the thread ed microchannel simulation. In this setup the e the re servoir and the plug is set into place within the reservoir. reads and the reservoir has internal threads. After the oil is in place, the plug is th oil is again put insid However, in this setup the plug has external th readed into the reservoir. This limits the evaporation to only a small opening at the top of the rese rvoir, unlike the non-threaded setup, but in this design the evaporating oil has to m ove through the mating threads which is analogous to a micro-fluidic channel. 60
Figure 24. Microchannel fixtures: a) Relative sizes; b) Micrograph of a crosssection showing the microchannel dimensions. Figure 24a shows both of the microchannel setu ps and relates the relative size of the designs as compared to a 1 Eu ro coin. Figure 24b is a pictur e of a cross sectional c the threaded an be seen een culating for these values results in an activation energy of 55.8 a) b) 200 m ut of design. As mentioned, this desi gn simulates micro-flui dic channels and c in Figure 24b, which shows an equilateral triangular channel with a 200 m side These two designs were utilized to gain a better understanding of the nature of evaporation from micro-fluidic channels. The actual testing followed the same procedure as for the static testing of the pump oil descri bed in a previous section of this work. The collected data was then analyzed, as before, using the Arrhenius Equation to calculate the activation energy and pre-exponential consta nt for the two setups. Figure 25 is the Arrhenius Plot for both conditions with a linear best fit through the data for each. As s in Figure 25, the threaded design has a much steeper slope than that of the non-threaded design and as a result is expected to ha ve higher activation en ergies. The subtle differences of these designs produced dramatically different offsets between the two and this would correlate to very different values of the pre-exponential constants. Cal and 104.5 for the 61
non-threaded and threaded de signs, respectively. Likewise, the pre-exponen tial constants were found to be respectively 1e-4 Hz and 30.8 Hz for the non-threaded and threaded designs. -23 y = -9,2053 6713,8x -25 -29 -27 0,00220,00230,00240,00250,00260,0027 Non-threaded Threaded y = 3,4274 12566xln kFigure 25. Arrhenius Plot for both threaded and non-threaded microchannels. is non-T-1, K-1 As expected, the required activation energy to break intermolecular attractions of the pump oil while in a threaded microchannel is much greater than the previously tested open surface. However, the non-threaded microchannel the required ac tivation energy is much less than that of the open surface and is in fact less than the open surface that exposed to a 25 mL/min flow rate of air. Th is created many questions during analysis and to help explain what is happening a comparis on graph of the actual evaporation rates was constructed. Figure 26 is a plot of the evaporation rate ( kg/s) of the threaded and threaded microchannel designs against the temperatures (C) that the samples were exposed to. The data collected during testi ng was fitted with exponential equations which are provided in Figure 26. Th e overall slope of th e non-threaded design is much steeper 62
than that of the threaded one relating th at the non-threaded design evaporates much faster. 0 6080100120140160180 5 10-121 10-111,5 10-112 10-11 Non-threaded Threaded y = 3,1591e-13 e^(0,023594x) y = 1,4354e-15 e^(0,05225x)Rate, kg/sT, oC Figure 26. Rates of evaporation for th readed and non-threaded microchannels. After an examination of Figure 23 it should be clear that the thr eaded microchannel did not begin to evaporate u expected result because the pump oil did not begin to evaporate until similarly elevated temperatures and the microchannel has a dram atic reduction of exposed surface area. So the same is true for the non-threaded micr ochannel, but the data provides different results. The reason for this is because as the non-threaded pl ug rests in the reservoir it displaces the oil and pushes it up along the sides of the rese rvoir. In addition to this displacement there are capillary forces that can generally be quite significant at these small scales and add to the displacing force of the plug. This condition has been theorized to create a pooling effect of the oil on top of the plug greatly increasing the exposed surface area from what is expected. This layer of oil on top of the plug then evaporates as in the case of an open surface, but this surface area is greater than that of the aluminum ntil the temperatur e had reached almost 100 C. This is an 63
64 l annel is that of the threaded design. pans used previously. Therefor e, the most reliable and representative data of an actua microch
CHAPTER 4 SUMMARY AND FUTURE WORK .1 Summary The evaporation characteristics have been investigated for alkanes and a pump oil. Understanding how a substance will evaporat e can be very useful for comparative purposes for the selection of the best lubricant for particular a pplications. It is possible to measure both the evaporation rate and the ac tivation energy directly. Either of these qualitative results can be used as a compar ative tool between different substances. The study of the six alkanes resulted in activation energies between 50 and 70 4 whereas e pump oil investigation yi elded results closer to 84 th These values are a result of dynamic testing, which produces lower and more consistent calculations of the activation energies of the alkanes. The alkanes were found to have activati on energies between 72 and 89 for static testing. The pre-expone ntial constant changed even more significantly between te sting procedures. Sta c testing yielded pr e-exponential constants on the order of several kHz, while dynamic test ing resulted in values were in the mHz range. This means that there is a higher fre quency of molecular col lisions during static testing than for dynamic testing. Evaporation was also analyzed for pump oil in an air flow of 25 mL/min. The resul ting calculation of the activat ion energy turn out to be 59.6 ti 65
, which as expected is a less than the va lues calculated without an air flow. Additionally, a study of the evaporation rate of the pump oil in a microchannel was conducted and resulted in an activation energy of 104 The factors that contribute most to variation of the cal culation of these results are the exposed surface area, the heating rate, the flow rate erties themselves such ar weight and boiling point. It was observed that a mixture of equal consistently result in the averaging of the evaporation rates. T uld t 4.2 Modeling odeling of the rate of evaporation can be very cumbersome because of such non-co rs like the surface area which can significantly change with time. of air, and of course the substa nce prop as density, molecul proportions of alkanes did not his is because the change in compositi on is not directly proportional to the change in the entropy of the liquid mixture. The test ing helped to prove the theory that in a mixture of alkanes the molecularly lighter substance will evaporate first resulting in calculations close to a pure samp le of the lighter substance. Future investigations sho be conducted to gain a further understanding of the importance of the roles that differen factors have on evaporation. From this adde d information modeling of evaporation is possible and could provide a quick comparative tool of the eva poration of new lubricants. The m nstant contributo Once a specific model has been established it is only valid for the conditions examined during the derivation of the model. For this reason the modeling of evaporation must be generalized and take into account such factors. This type of modeling is discussed further in this section by means of four different approaches. Th ese models are derived from similar setups as used in this work, specifica lly the surface evaporation of a sample inside 66
an open ended container. For the investiga tion and modeling of ev aporation for dro see [34-37]. id sam plets Beverley et al.  measured and deri ved subsequent models for pure liquids with a range of vapor pressures (0.1 500 To rr). Liquples were investigated while partially filling an open ended cylinder that was encompassed by a vertical flowing gas stream. The actual evaporation rates were m easured as the amount of mass loss from the container per unit time. First they determined the theoretical ma ximum rate at which the liquids could evaporate. This is accomplished by neglecting such hindering factors as the stagnate layer of gases that forms on the surface of an ev aporating liquid inhibi ting evaporation. Also the liquids were assumed to be in constant equilibrium, that is, the number of molecules that are hitting and condensing on the surface of the liquid is equal to the number that is evaporating. From this the theoretical maximum evaporation in a vacuum is: (17) where P is the vapor pressure of the liquid, M is the molecular weight of the liquid, R is d T is the absolute temp erature. The units of the evaporation flux, Jmax, ar the gas constant, an e ; which relates the number of moles of a liquid evaporating per second per area of exposed liquid surface. Unders tanding that the maximum can never be reached in practice, a better representation of the real evaporation process was derived. Building from the theoretical maximum Be verley et al. conducted tests intended to measure the initial evaporation rates, where the height of the st agnate gaseous layer remains constant, and of more volatile liquids, where this height increases with time. T following relationship between the mass, m, and time, t, is: he 67
(18) where m is the initial mass of the liquid at time zero, h is the total inner height of the sample tube, is the density of the liquid, D is th e vapor diffusion coefficient, A is the surface area of the liquid, and z is the co rrection factor. This model accounts for variations in the evaporati on rates of liquids and has b een used to determine these evaporation rates with an accuracy of a few percent. Pichon et al.  have studied the eva poration of organic po llutants and have formulated a model describing the rate. The testing method was accomplished by means of thermogravimetric analysis and takes into account the effect of temperature, total external pressure, and heati ng rates. Testing was conducted with a constant flow of Nitrogen, in a temperature range of 20 800 C, and with varying heating rates. The model itself is a mathematical represen tation of non-isothermal evaporation. It was observed that the density of the flux of the pollutants, jfl, was non-uniform on the surface of the liquids. Th is lead to 19) d se f each other. 0 t the evaluation of the rate of evaporation, k, for the entire surface of the liquids to be: ( where r is the radius of the container and the integration is taken fr om the center of the container, where r is zero, to the outer edge where r is th e maximum value R. The authors note that in this model accur acy depends on the accuracy of the liqui surface area measurement. The calculated areas and what have been termed as adjusted areas differed 20 30 %, generally, but can be as much as 148 % . Even though the variations in the calculation of the surf ace area were significant, the observed and predicted values of the evaporation ra tes were within 10 % o 68
Xia et al.  studied th investigation was operties of surfaces and interfaces of complex liquids. This investigation was carried out to gain a better understanding of the molecular mechanisms associated with interfacial phenomena. The data of this work was obtained by anal yzing liquid films on crys talline substrates. The model of this approach stems from the Hertz-Knudsen-Langmuir equation for the net evaporation rate . It is an app lication of the transition state theory, which showed good agreement with experiments. Making certain assumptions the transition state theory provides the following expre ssion to describe the evaporation rate: e evaporation rates of liquid n-alkane films. This of the thermodynamic, st ructural, and compositional pr where is the transmission coefficient, N is Avogadros number, (20) Ae iil: rees of freedom are unaffected in the transformation from the e s for a is the free volum per molecule in the liquid, Q and Q+ are the partition functions for internal degrees of freedom of a molecule in the liquid a nd activated complex, respectively, and E+ is the activation energy for evaporation. The author s often made the following two simplifying assumptions while applying this mode (1 ) the molecular deg liquid phase to the transition phase, Qi and Qi + are equal, and (2) E+ = Ev, which identifies the activation energy of evaporation with th energy of evaporation. This approach yielded many results including the knowledge that molecular evaporation mechanisms are c ooperative and sequential in na ture. Evaporation was also determined to be accompanied by marked molecular conformational changes. Another important conclusion made by these authors is that the energy required to transport a molecule inside the liquid to the liquidto-vapor transitional region account 69
significant amount of the total en ergy required to transport a mo lecule inside the l the vapor state. Stiver et al.  presents three separate models for determining the rate of evaporation of spilled hydrocarbons and petrol eum mixtures. The three methods are tray evaporation, gas stripping, and distillation. Tray evaporation is the evaporation from the iquid to is ly e liquid at a known and/or measured rate. f evaporation can be determined by the following expr surface of a liquid and since it is the approach most alike to that previously discussed, it is the only configuration deemed appropriate. In this configuration the sample liquid placed into a tray, ensuring uniform thickness, and the weight of the tray is continuous monitored. The tray itself is placed inside a wind tunnel and air is passed over th From this c onfiguration the rate o ession: (21) where P is the vapor pressure of the liquid (Pa), a is the area of the spilled liquid (m ), is the mass transfer coefficient under the prevailing wind conditions 2 and k is the molar flux of the liquid This technique and associated model ha s been described as ideal for measuring the rate of evaporation of crude oils by the authors. The authors also note the biggest hurdle that must be overcome when analyzing the evaporati on rates of crude oils and hydrocarbons is linked to multi-component sy stems. Multi-component systems, also known as mixtures, are inherently difficult to express the vapor pressu re as a function of the changing composition of the mixture. Ev en with this hindrance the authors have reported good agreement between predicted and observed rates of evaporation. 70
The data collected from testing can be used to compare models and to provide valuable information on the actual evaporation rate of the sample substance. The raw data these includes continuous measurements of the mass of the sample. If the derivative of data were taken with respect to the recorded time then the result is a series of data accounting for the amount of mass loss per time. This is the best represen tative of the rate of evaporation for a substance under the conditio ns of the tests. The evaporation rate is expected to change with changing temperature, and the form of th e relationship of the rate of evaporation to the te mperature of any given substance can be assumed to have the form: (22) where is a constant of proportiona lity. Equation (19) is both separable and linear in the following form: = 0 (23 Multiplying both sides of the equation by the integrating factor of gives: ) (24) Integrating both sides of the equation (21) and rearranging to a more convenient form yields: (25) the relationship of the ev aporation rate with respect to te mperature is valid and the values can be seen in Figure 27. The data points in this figure have been exponentially fitted and Graphing the evaporation rates against the temp erature reveals that th is assumed form of of and can be found from such a graph. The evaporation rates for all of the alkanes 71
the associated equations are include d to provide estimations of the and values for each alkane. As can be expected, the slope of these lines increase with an increase in temperature. The changes in the slopes are al so more dramatic at higher temperatures fo the molecularly lighter substances. r 0 4 10-88 10-81,2 10-7y = 1,7893e-10 e^(0,045714x) y = 8,481e-11 e^(0,045836x) y = 5,8015e-11 e^(0,042817x) Undecane y = 5,2456e-11 e^(0,040089x) Dodecane 40 80 120160200 Tridecane Tetradecane y = 2,8983e-11 e^(0,039771x) y = 2,293e-11 e^(0,037658x)rateg/sPentadecane Hexadecane k Figure 27. Measured evaporation rates ve These evaporation rates cared to the theoretical maximum rates of ate was derived from evaporation in a va molecular weight of the a conversion factor to change the units to kg/s. The surface area was previo molecular weights of the alkanes ted in an earlier section. Figure 28 presents the results of the calculation of the maximum evaporation rates of all the alkanes. This is similar to Figure 24, however the rates are much greater than what was T, oCrsus temperature fo r all alkanes. an be comp evaporation for comparative purps eal maximum evaporation r oes. The thoretic cuum and ha s been calculated from equation (14). This equation provides an estimate of the molar flux and must be multiplied by the surface area, the substance, a nd usly determined to be 24 mm2, or 2.4e-5 m2, and the have been tabula 72
recorded from experimentations. Note that the theoretical maximum rate of evaporatio for hexadecane is close to the measured value of evaporation rate of undecane. n 0 4080120160200 4 10-58 10-50,00012 Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecane y = 1,0806e-07 e^(0,040925x) y = 3,5375e-08 e^(0,044468x) y = 1,4771e-08 e^(0,046664x) y = 3,3884e-09 e^(0,052455x) y = 1,0369e-09 e^(0,056529x) y = 4,1862e-10 e^(0,058789x)max rate, kg/sT, oC Figure 28. Theoretical maximum evap oration rates for all alkanes. The previous analysis provides a m eans of understanding how the rate of evap (26) which is a 3 order polynomial and the coefficients are found experimentally and vary based on the units used for the mass measurem ents and between alkanes. Figure 29 is a graph of the recorded mass of the alkanes against time. Fitting a 3 order polynomial to these data provides a means of estimating th e coefficients needed to understand how the mass changes with time between the alkane s under the same temperature profiles. oration changes with temperature, but additional information of evaporation is needed to develop a more encompassing model. The change of the mass of the sample with respect to time, as the temperature is increased, has been found from analyzing the data collected throughout tes ting. The mass of the sample as a function of time was observed to take the following form: rd rd 73
0 2 4 6 8 10 Undecane Dodecane Tridecane Tetradecane Pentadecane 0 100200300400 Hexadecanemass, mgt, sec Figure 29. Mass of the alkanes versus time. Any model that is used to predict the evapor ation rate of a substance must take into account the dependency that the mass has on time as well as the dependency that the rate has on temperature. The best model for pred icting evaporation rates would incorporate both of these essentia l characteristics. 4.3 Testing technique improvements After conducting a series of experiments and undertaking this investigative work it has been concluded that there are some asp ects of the testing tec hniques that can and should be improved upon such factors as initial mass and initial temperatu re insrumental to in the future. As mentioned previously re, of both the sample and equipment, at able results. The initial mass of th producing consistently repeat e samples can be monitored with the equipment used in this investigation however a greater accuracy of initial sample retrieval is needed. As discu ssed, the micropipettes used to retrieve the samples showed a significant variation between repeated measured sample masses. With 74
75 a more accurate micropipette, or other samp ling means, would result in less iterative process for setting up tests. This is important so that the evaporation of the sample be measured at room temperature prior to an extended exposure time to ambient conditions. Another initial condition that proved to be imperative to repeatab ility is the initial temperature of the instrumentation. This wa s controlled between tests by allowing for a long resting period of the equipment to ensure a stabilization of the temperature with ambient conditions. To reduce the downtime of the equipment means of controlled cooling could be enacted. This could be done by the attaching of fins or running cooling lines to the equipment cooling. also ing a coil of wire above a sample holder all inside tube. Once a vacuum is created in the tube and heat is applied the resistance of the coil ge in vapor pressure. This would be done simulta ples. ular or by less invasive means such as evaporative Replacing the equipment or constructing a dditional testing appa ratuses could improve the testing technique. If the testing were done inside a vacuum then the partial pressures could be measured directly a nd results would not rely on theoretical estimations. This could be done by hav a of wire will change as a func tion of the chan neously with a constant measuring of the mass of the sample. This apparatus determines the vapor pressure by the Langmui r method and together with measuring the mass loss would provide more accurate results of the evaporation rate of a substance. Since this apparatus requires the testing of a sample in a vacuum then the maximum possible evaporation ra tes would be recorded and compared between different sam These results could then be compared to the testing results of this study to determine the environmental effects on the rate of evaporat ion. Additional information on this partic type of apparatus can be found in .
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