A PHOTGGRAM‘NC STUDY OF EXTRACTSON FRCW‘. FORMWG mama DROPS Thesis {'92 the Degree 35 55%. S. MECHE‘GAH Eff-AW UMVERSWY Wiéééa's Tambc i969 LIBRARY Michigan State University A PHOTOGRAPHIC STUDY OF EXTRACTION FROM FORMING LIQUID DROPS BY William Tambo AN ABSTRACT Submitted to the College of Engineering Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE DEPARTMENT OF CHEMICAL ENGINEERING 1960 A PHDTOGRAPHIC STUDY OF EXTRACTION PROM FORHIIG LIQUID DROPS ABSTRACT A photographic tedhnique was used to investigate the mechanics of extraction from single drops during the period of drop formation. A toluene drop. saturated with picric acid and water, was formed at the tip of a glass nozzle immersed in stagnant water. The drop fonmation and the distribution of extracted colored solute in the water surrounding the drop during the formation period were recorded on 16 millimeter film at the rate of 24 and 32 photographic frames per second. The resulting negatives were analyzed by measurement, the use of microphotometer, and Observation. Physical measurements on the resulting fihm negatives showed that the transfer area generated was nearly identical to the rate which would have been generated if the drop had remained spherical in Shape during formation. optical measurements using a micro- photometer and Observation indicated that extracted solute remained in the water film immediately adjacent to the forming drop. The theories and previous work applying to extraction from single forming drops were reviewed. lbne of the theories adequately explained why the extracted solute remained close to the drop interface during formation. Some qualitative and semi-quantitative information was also obtained from the aforementioned photographs and from some additional photographs of drop formation in pulse flow and of drop coalescence which were taken as a supplement to this work. As the drop broke away from the nozzle, the solute, previously in the water film near the drop interface, was dispersed into the bulk water phase. As the drop rose. a vortex action was indicated which drew the extracted solute into a small area behind the rising drop leaving only a small portion of solute behind. Pulse flow over a forming drop rapidly disperses the extracted solvent through-out the bulk water phase. For this system not less than 0.1 percent of the total solute in the drop was extracted during coalescence. Included in this thesis are appropriate photographs made from the negatives which were analyzed. Hiscellaneous information including the hazards of the system studied, and optical theory. is appended. A PHOTOGRAPHIC STUDY OF EXTRACTIOR non PORIIIIG LIQUID DROPS BY William Tambo A THESIS Submitted to the College of Engineering _Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE DEPARTMENT OF CHEMICAL EBGIIBERIIG 1960 ' fl /4%/7rdV€d/'. /€ZWZZ¢//(7K yjkziézg Acknowledgements The funds for the project were provided by the Chemical Engineering Department of Michigan State University. Dr. Richard Zeleny of the Michigan State University Chemical Engineering Department, under whom this project was carried out, suggested this subject, provided some of the background and assisted in the mathematical developments. The author wishes to extend special thanks to Dr. Zeleny, for being allowed to proceed largely on his own initiative, and to the entire Chemical Engineering Department staff whose interest in the project and willingness to advise, were invaluable. TABLE OF CONTENTS Abstract 0 O O O O O O O O O O O O O O 0 Introduction . . . . . . . . . . . . . . Summary of Results . . . . . . . . . . . Theory and Literature Survey . . . . . . Special Techniques and Mathematical Considerations . . . . . . . . . Apparatus and Procedure . . . . . . . . Results and Conclusions . . . . . . . . Recommendations and Suggestions for Future work . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . Appendices . . . . . . . . . . . . . . . I. Derivations of Some Equations . . II. Preparation of Standard Solutions III. Hazards of Picric Acid and Toluene IV. Equilibrium Data '. . . . . . . . V. Optical Theory . . . . . . . . . VI. Data . . . . . . . . . . . . . . VII. Graphical Integrations). and Graphical .Results. . . Calculations page Page Page Page Page .page Page page page page page page page Page page Page page 36 52 64 85 89 91 92 101 102 105 115 Introduction With the purpose of furthering fundamental concepts of liquid-liquid extraction, several investigators have, in the past, studied extraction from single liquid drops rising or falling in an immiscible stagnant phase. ‘ The techniques which were employed by these investigators were somewhat similar. Briefly, a number of drops formed at the tip of a small nozzle were allowed to rise or fall through a column containing an immiscible stagnant phase of fluid. Solvent, originally present in the drop or the stagnant phase was transferred between phases. Column height was varied for different runs. Data taken included the number of drops rising in an interval of time, the volume of liquid making up these drops, the concentration of the drop fluid at the beginning and end of each run. and the concentration of the immiscible fluid at the beginning and end of each run. These data enabled the calculation of results which could usually be expressed graphically as percent solute extracted vs. column height. Results of these studies sometimes were in agreement concerning the extraction whiCh took place during the time a drop was rising and enabled investigators to fit assumed.mechanisms to the results with fair success. Little agreement, however, was found concerning the extraction which took place during the time a drop was being formed at the tip of a nozzle. The latter information, usually Obtained by extrapolation of a percent extraction vs. column height plot back to column height of zero, ranged from a major portion of extraction taking place during drop formation to a negligible portion of extraction taking place during drop formation. The most recent investigation of extraction from single drops was directed towards obtaining definite information about extraction during drop formation. .At least part of the technique employed was novel enough to be given special consideration. In this study, a number of drops were partially formed at a nozzle tip and then “instantaneously“ drawn back into the nozzle through a separate channel. By varying formation time and the extent to which a number of the drops were formed in several different runs and then analysing for the solute in the immiscible phase, an equation was developed which described the extraction which took place during drop formation as a function of formation rate. In the opinion of the author, however, this equation describes extraction from a number of drops as they were partially formed and withdrawn from the nozzle, not as they were formed with no interference. From this brief background concerning the study of extraction from single drops, it is apparent that further work in the area of drop formation would not be superfluous. Further study using techniques similar to those previously described would, however, be repetitious and would not add further enlightening facts to those conflicting facts already accumulated. Preliminary work by Zelenylindicated that photo- graphic methods might be employed to carry out a very exacting study of liquid-liquid extraction from single drops during the formation period. Such methods would allow direct Observation of what takes place at any instant and facilitate calculation of extraction rate from the drop at any instant. The purpose of this paper, then, is to develop the necessary photographic methods and mathematical expressions required to study liquid-liquid extraction from forming single drops and to apply these methods to a suitable system in order that rates and mechanisms may be determined for the drop formation period. SUMMARY OF RESULTS Photographic methods have been developed which enable an exacting study to be carried out of liquid- liquid extraction from single drops during the formation period. This development, along with the necessary techniques and mathematical considerations are found in the section of this thesis entitled ”Special Techniques and Mathematical Considerations." The mathematics involved in the development have an intrinsic value in that they may be used for other dynamic studies. The results of a study of the extraction of a colored solute from a liquid drop forming at the tip of a nozzle which is submerged in a stagnant liquid phase immiscible with respect to the drop is presented. This study has been made using the aforementioned methods. Toluene drops saturated with picric acid and water were formed at the tip of a glass nozzle immersed in dis- tifled water. The drop formation and the distribution of extracted colored solute in the water surrounding the drop during formation were recorded on 16 mm. film at the rate of 24 and 32 frames per second. Physical measurements on the film negative provided quantitative information regarding the volume rate of drop formation and the rate of transfer surface generation. The transfer surface is generated nearly as if the drop remained spherical during formation. Optical measurements provide information regarding extraction during the formation period. Within the scope of the methods used, no extraction can be observed during drop formation. It is concluded that the solute which is extracted remains close to the drop interface. Visual Observations indicate that upon break away this solute was dispersed into bulk water phase. Upon rising, a vortex action was indicated which drew the extracted solute into a small area behind the drop leaving only a small trail of solute. Qualitative and semi-quantitative results concerning extraction from a coalescing drop and a forming drop in pulse flow are presented by photographic prints. Limiting calculations show at least 0.1 percent and probably much more of the total solute present in the drop is extracted during coalescence. Pulse flow over a forming drop rapidly disperses the solute extracted from the forming drop into the water phase. Photographic prints of all runs are presented on pages 7?, 7e 79, v0, 31, t? .3 n4. Theory and Literature Survey The continued need for information concerning the fundamental mechanisms of extraction processes is well illustrated by the remarks appearing in a recent article by Handles and Baroné. The essence of these remarks follows: Although rates of mass transfer in an extraction device may be calculated in a manner similar to the calculation of heat transfer rates in a heat exchanger, the evaluation of certain factors in extraction devices presents difficulties. There is, for example, no simple relationship by which the contact area in an extraction device may be evaluated. Because, in an extraction device, flow is neither concurrent nor countercurrent, the evaluation of whatever driving force is available also presents problems. Further, information on transfer coefficients and their use in design calculations is sparce. With the purpose of Obtaining information about some fundamental mechanisms of liquid—liquid extraction, many studies have been carried out of extraction from single liquid drops rising or falling in a stagnant immiscible liquid phase. The value of such studies is based on the very reasonable premise that liquid-liquid extraction basically takes place in a drop-wise fashion and the understanding of extraction from single drops will contribute to the further understanding of all extraction processes. The value of this work is based on the same premise and therefore space will be devoted to the further elaboration on this concept. If a liquid-liquid extraction process in a packed column could be Observed in slow motion, one would see the lighter phase, assuming it is dispersed, enter the bottom of the column in the form of small droplets. These droplets would rise through the continuous phase until restrained by barriers formed by the packing. The barriers referred to act like inverted cups which, as more dispersed phase droplets are restrained or trapped, fill and subsequently overflow. The overflow of light dispersed phase from these barriers probably takes place one or two drops at a time, corresponding to the rate at which the dispersed phase is trapped. As overflow takes place, new droplets are formed which, further up the column, are trapped, repeating the process. Most likely as a result of a consideration similar to that just presented, it has been proposed10 that there exists three distinct stages in the life of a drop, 1. Drop formation 2. Drop movement 3. Drop coalescence In all previous investigations of extraction from single liquid drops rising or falling in an immiscible stagnant liquid phase*, an attempt was made to consider these three stages separately. Experimental means were divised to study each stage, and the resulting data was compared to predicted data based on various assumed mechanisms. The specific purpose of this work is to obtain quantitative information on the drop formation period in liquid-liquid extraction. The remaining portions of this section are, therefore, confined as much as possible to presenting the theory and previously Obtained information concerning extraction from single liquid drops during the formation period. For clarity, the remaining portion of this section is divided into three parts: the first is concerned with theoretical * Hereafter “extraction from single liquid drops" will be understood to mean "extraction from single liquid drops rising or falling in an immiscible stagnant liquid phase". 10 considerations, the second with previous experimental efforts, and the third with some comments and the basis for continued study. Rather than leave the reader with no background information on extraction in general and extraction from liquid drops in all stages, such information is included wherever it serves the development of the text. PART I - Theoretical Considerations A. General The theoretical development of extraction from single drops is best approached from.briefly considering the diffusion of a solute from one solvent to another which is immiscible in the first. In this consideration, the following schematic diagram4 will be used. The development will be recognized as the two film theory. 11 Phase _A_ Phase _B_ 1 direction of \\‘ direction of increasing mass concentration transfer interface In the two phases shown, the concentration of solute in phase B is less than that concentration of solute which would be in equilibrium with phase A. The concentration in the bulk of phase A is greater than the concentration at point i, the interface. The molal rate of diffusion at any instant in the B direction is given by (1) 5"“?! = ka(C -c) dt A 1A A where H 2 moles t s time a a area perpendicular to the direction of diffusion 12 kA = transfer coefficient for phase A CiA c molal concentration of solute at interface in phase A C = molal concentration of solute in the bulk of phase A If the volume of solvent in.A is constant then (2) VA dCA dt where Vt is the volume of solvent A. Because the rate of diffusion in both phases must be equal (3) v dCA —-—dt = kAa (Cm " CA) = (C13 " CB) kBa Bow, introducing m, the distribution coefficient so that CA. a mCB and C*iA = ”91B where CfA is the concentration of Phase A which would be in equilibrium with the concentration of Phase B and then substituting into (3) (4) VA ch a kAa (Cm ‘ CA) =' 1‘33 (C13 - CA") dt m Then writing an equation considering an over-all transfer coefficient and driving force, KA and (CA - CA*) respectively l3 (5) v; dcA = Kn“ ‘93*-— ca) 'HE' * Bquating the right hand sides of (4) and (5) and assuming equilibrium at interface or that Cu = C18 = Cut, (9A - CA.) = (CA - C13) + (C13- CA?) Substituting and rearranging (6) 1 = 1 + 1 or if equilibrium at interface is not assumed (7) 1 = _;_ + (R1) + 1 KA 3A mks where (R1) is the interfacial resistance. If m is large and equilibrium at the interface is assumed. Going back to equation (5) and assuming CfA constant and integrating'from CA = con to CA = CfA a where 0 refers to initial and f to final (9) 1n (QA* ' Cfa) KAat If the initial concentration of phase B is zero, 14 (10) ln__ can 3 K5“ C0A VA and if spheres are considered a = 3 where R is the ‘V3 'R' radius of the sphere, and (11) In C = Kat .31 0A R B. Liquid Drops Already Formed l. The Dispersed Phase The above approach was general save for one point where the quantity'a/Vh was set equal to 3/R for a sphere. low the consideration of extraction from.single liquid drops already formed will be combined with the above development. For this purpose the equation relating the overall mass transfer to the individual mass transfer coefficients and interfacial resistance will be rewritten. VKd "RH+ (Ri)+m1]i'; where d refers to the dispersed phase or drop and c the continuous phase of the system. In many systems in which extraction.from.fbrmed single liquid drop takes place 'uég is small enough.to be neglected and as a result little effort has been put forth in the determination of kc‘ Even though (R1) 15 is sometimes thought large enough to be significant, little experimental work has been put forth in its analysis. Further no theory which is adequate has been developed concerning (R1). Most studies previously made have been directed towards the determination of kd, and the theory on this subject is plentiful and will therefore be presented first. In all the theory to be presented, whether the drops are formed or forming, the dispersed phase is assumed to be small spherically shaped drops. This should be kept in mind. The simplest treatment of the dispersed phase is to assume complete mixing of the fluid within the drop right up to the interface. In this way no film can exist and the concentration throughout the drop is uniform. Then, kc is infinite or 1 is zero. This is c an oversimplified consideration and would probably hold true for very few situations in liquid - liquid extraction. A more reasonable but still extreme treatment is to assume that absolutely no circulation takes place within the drop. Mass transfer from.the interior of the drop to the interface would then have to take place by means of pure molecular diffusion. Differential equations 16 have been formulated4 and solved for this situation. These equations give at any time the concentration at any radius from the center of the drop, the total moles of solute which have crossed the interface of the drop, the average concentration of the drop and, for various size drops, the effective mass transfer coefficient, kd. The derivations of some of these equations are in Appendix I. Logically, if the above theorized mechanisms played a major part in extraction from single liquid drops already formed and rising, the actual situation would fall somewhere between, that is, incomplete mixing within the drop. With this reasoning, another treatment of dispersed phase resistance is to consider that the transfer of solvent takes place from elements which always maintain a fixed position with respect to the interface. New elements replace the old ones as the drop rises, and the old elements are dissipated in the center of the drop. Transfer of material from each element is so small that not enough concentration difference exists to cause mass transfer from the center of the drop. The energy required to remove the small surface elements and replace them with new elements is 17 obtained from drag friction. It is interesting to note that this treatment allows for diffusion in the volume close to the surface of the drop and mixing near the center. It would seem, for a rising drop, that the actual situation would involve the opposite physical means of transfer as the inside of the drop would be stagnant and circulation would be at the surface due to drag. The equations derived to describe extraction from a single liquid drop dictated by the above mechanism necessarily includes terms which take into account drop diameter and rate of rise16. This is so because frictional forces, a function of diameter, and rate of rise determine the length of time each of the elements is exposed to the interface of the drop. The film theory has been proposed to explain the mechanism by which extraction takes place from liquid drops. In the simplest treatment of the film theory a thin stagnant film of dispersed phase surrounds the main 'body of the drop.‘ The film is considered so thin the amount of solute required to establish a gradient across the film is negligible. Mixing takes place within the drop and, kd = %, where Dm is molecular diffusivity and x is the film thickness. 18 A modified film theory proposes two films, a laminar one and a turbulent one. A correlation has been worked out on this basis.13 An equation has been derived giving the concentra- tion within a drop at any time by predicting the circulation in a moving drop from fundamental equations of hydrodynamics and viscous flow.5 The last treatment of any consequence was to consider a “viscous” circulation inside the drop, that is, circulation but no turbulence. A mathematical expression for this physical situation was Obtained by considering diffusion from a cylinder of infinite length.2 B. Liquid Drops Already Formed 2. The Continuous Phase The various theories just presented were concerned with dispersed phase resistance. The continuous phase will now be considered. As previously pointed out, little effort has been set forth to verify any of the theory connected with continuous phase resistance in extraction from single drops. Most investigators have purposely chosen systems iniwhich 1 is so small compared to l/kd that-5%; could ‘MKE be neglected. Some effort has been devoted to analytical 19 and approximate relationships to describe the continuous phase resistance. Some of the considerations are similar to those discussed for dispersed phases resistance. As might be expected, the simplest treatment of continuous phase resistance is to assume complete mixing of the continuous phase. The resistance to transfer then is zero and kc is infinite. The opposite extreme, no circulation of the continuous phase at all, cannot be handled mathematically. By considering diffusion from the drop to a semiinfinite liquid of contact area equal to the surface of the drop, however, an equation has been derived which approximates this physical situation.14 This equation gives concentration at any point in the continuous phase as a function of time. A somewhat modified and more realistic model assumes complete mixing of the continuous phase save for a thin film around the drop. This will be recognized as the film theory and it is applicable to the continuous phase in the same way it is applicable to the dispersed phase. The surface renewal theory may also be applied to the continuous phase. As in the one of the preceeding treatments, however, mathematical development is possible 20 only when approached using the approximation of transfer to a semi-infinite liquid of contact area equal to the surface of the drop. C. Interfacial Resistance It is apparent, at this point, that some of the same theories which apply to the dispersed phase are suitable for treatment of the continuous phase. Such is not the case with interfacial resistance (R1). Inter- facial resistance is referred to very little in the literature. In fact, no conclusive evidence of its existence is supplied. Further, there have been found no attempts to treat, analytically or empirically as far as mathematics are concerned, how solute might be transferred across this resistance. D. Forming Liquid Drops 1. The Dispersed Phase Thus far the two film theory has been briefly reviewed and this theory has been qualitatively applied to extraction from already formed rising liquid drops. NOw, Ehc,same application of the two film theory will be applied specifically to extraction from forming liquid drops. 21 Beginning with the dispersed phase resistance, again, the simplest treatment is to assume complete mixing of the liquid in the drop and subsequently a uniform concentration throughout. In this case kd = 00 and Rig = o. This treatment is reasonable as fluid entering the drop might cause complete internal mixing. If the other extreme is assumed, that is no mixing of the liquid within the drop, then further assumptions must be made regarding what happens to the liquid entering the drop during formation. If it is assumed that this liquid enters the center of the drop, (this assumption is more in error as the drop becomes larger), and pushes old liquid uniformly outward from the center, then the following differential equation, which is derived in the appendix, is Obtained. 13—820 + ZD.Q_C.___U .19. = 66 3r2 r a: 4 r2 8r 5? Ho solution for this equation has been obtained. .Although the usual approach is to assume a product solution such as C = R x T where R is only a function of r and T is a function of t, this assumption, however, does not satisfy theboundary conditions of the physical prOblem. Changing variables in such a manner which allieviate this difficulty has also proven 22 unsatisfactory as the resulting expression is so complicated that attempts to rearrange the equation in such a manner that each term involves one independent variable is impossible. As a compromise between the aforementioned extremes, complete mixing is assumed.within the drop save for a thin film at the surface of the drop. The amount of solute required to effect a gradient across the film is so small that new film generated.by drop formation immediately reaches its steady state concentration gradient. Accounting for the variation of surface area, the bulk concentration is given by the equation4 x n = 00 ya c .= Co exp 9kdt 3 (9kd£@+ _ . (Zn + 3)n: The surface renewal theory, wherein' transfer takes place from surface elements which are continually removed and renewed by means of drop circulation can be applied to forming drops. The prOblem here is to determine an analytical relationship between the element exposure time and the drop formation time. To do this many assumptions regarding drop circulation have been made and these will not be here summarized. 23 The removal of these surface elements may be assumed to be brought about by means other than circulation... for example frictional drag forces and forces on the surface of the drop. D. Forming Liquid Drops 2. The Continuous Phase .Although most investigators have eliminated the need for consideration of the continuous phase resistance by choosing a system in which the solute strongly favors the continuous phase, it has been proposed10 that because of the motion of the incoming liquid in a forming drop, vigorous circulation is maintained within the drop eliminating the dispersed phase resistance entirely. The continuous phase would, on the other hand, remain stagnant and therefore present resistance. The resistance of the continuous phase, thus considered, is controlling. Considering diffusion to a semi-infinite liquid sham and accounting for new surface area by assuming that new surface is formed with a concentration gradient equal to that of the old surface, the following analytical expression for the continuous phase was derived: 24 is (tf) c __ __9__C_ = 2.34 D c c. v 1/3 E. Coalescence A word will be said about coalescence. This part of drop life has been most neglected as far as theory and experimental work is concerned. Most investigators have taken steps, though not always successfully, to avoid its effect in their data. When required a qualitative treatment has been given the subject by applying the film theory. PART II - Previous ExPerimental Efforts HOw that the various mechanisms for mass transfer from forming drops have been summarized, the most important analytically, the remainder of this section will be devoted to presenting previous studies of extraction from single liquid drops which directly pertain to extraction from single forming liquid drops. The first study carried out on extraction was presented in a paper prepared by Sherwood, Evans and Longcorlz. The equipment and experimental procedure involved in this study set the pattern for many following studies, and therefore, a detailed description 25 of the same is worthwhile. Drops of solvent containing acetic acid were introduced through a nozzle mounted vertically at the bottom end of a glass column filled with water. Drops of this solvent formed at the tip of a nozzle broke away and rose through the water. The solvent feed rate was controlled by maintaining a constant level in a feed tube which was attached to the nozzle. Solvent was fed to this feed tube from a buret so that the amount of solvent used could be recorded. The top of the aforementioned column consisted of a cork stopper the bottom end of which had been carved out to a conical receptical. A minute quantity of water ‘das forced into the bottom of the column during runs. IIn this way, the drops which had reached the top of the <:olumn were caught in the conical top and carried out avith the minute purge water into a glass measuring buret. A run consisted of recording the number of drops vehich rose during a predetermined time interval. After a run was completed, quantities of inlet and outlet Solvent and outlet water quantities were determined by lauret readings. Acetic acid contained in these solutions ‘was determined by titration. During a run, the number 26 of drops formed was. recorded. In this way the time it took a drop to rise and the volume of the drops formed could be calculated. The solvents used were benzene and methyl isobutyl ketone. Several different size nozzles were used to vary drop size. The column height could be varied by adjusting the position of the stopper in the bottom of the column. The nozzle was inserted through this stopper. All runs were carried out at 22 - 28° C. In the actual experimental work,drop size, column height, inlet concentration of acid in solvent and solvent feed rate were varied. Drop diameters were calculated on the basis of spherical drops and the amount of solvent fed. Drop diameter varied slightly compared to nozzle size indicating that the properties of the solution from which the drop was formed are an important factor in drop size. The most important result of this study is sumnarized by the graph on page 27, which shows a plot syiving percent extracted vs. column height for benzene and ketone. Data for this graph was obtained by ut by Kopinsky 1:ake place from the continuous phase to the drop. An (effort was made to cancel out the effects of the :Eormation period. .A detailed summary of this study is omitted because the article was not available. 2 Farmer carried out a study with acetic acid as ‘the solute in the dispersed phase with several dispersed 29 phase solvents, particularly CCl4. CC14 was heavier than the continuous phase, water, and, therefore, the data pertained to falling drops. Percent extracted was plotted vs. column height and an extrapolation to column height zero showed there was a variation with percent extracted during formation and formation time. No attempt was made to correlate. Licht and Conway9 studied falling drops and made an attempt to separate the three stages of drop life by including stop-cocks at various points in the column used. These stop-c0cks were closed at the end of a run, thus separating the sections of the column. Data from this study are presented in a plot similar to the that on page 27 . The extrapolation of this plot to column height zero indicated from 10 1:030 percent of the solute \das extracted during drop formation. This is lower than {Sherwood reported. Further information indicated that (irop size or drop formation time had little or no effect can the amount extracted during formation. Licht and Pasing10 studied a system of water, acetic acid and methyl isobutanol. water was the (dispersed phase. Similar to the Licht and Conway study, a column was used on which were located stop-cocks to 30 facilitate separation of the amount extracted during the three stages of drop life. In this study no variation of extraction during formation with formation time could be detected which agreed with some of the previous results. It was concluded that some unusual effect was present during formation which caused the amount extracted to be independent of time and drop size. Perhaps, the breaking away of the drop caused this effect. In this study, coalescence is separated from the other stages of drop life and the amount extracted during this stage was found to be independent of size or concentra- tion. The authors also take note that when extrapolating percent extractionmcolumn height curves, several smooth curves could be drawn to column height zero. This would invalidate this method of determining extraction during formation. Haritatoes and Liberman7 carried out an investi- gation in which acetic acid and valeric acid were solutes in a dispersed benzene phase. Water was the continuous phase. The usual extrapolation to column ‘height zero showed an increasing amount extracted during the formation period with an increased formation time. The authors contend that the column purge during 31 coalescence was inadequate in previous studies and this introduced error as the coalescence period was not eliminated. A study of the coalescence period stowed that extraction during coalescence was proportional to concentration and diameter. This is contrary to previous results. Further study of extraction from single drops was carried out at the University of Washington and was reported by West, Robinson, lorgenthaler, Beck and l!c(;regor.]’6 Again, a system of Benzene, acetic acid and water was used. The apparatus and experimental methods are so similar to that of Sherwood, Evans and Longcor that description of it would be repetitious. Despite the similarities in the work, results did not agree. The data of West when extrapolated to zero column height show only 14 to 20 percent extraction takes place during drOp formation as compared to the 40 percent obtained by extrapolating Sherwood's data to zero. Further work by west and associates12 showed that certain impurities in the benzene, acetic acid and water system would affect considerably the amount extracted. 32 It was concluded that dissolved tygon tubing affected Sherwood's results. Coulson and Skinner1 studied a system of benzene and water in which benzene was the dispersed phase. Solvents were used which enabled the experimenterStto neglect the continuous phase resistance. This study is important in that the data taken were specifically restricted to the formation period. This was accomplished by partially forming a number of drops at the end of a nozzle and rapidly ejecting these through an alternate opening in the nozzle. By titration of the continuous phase the amount extracted during various periods of formation could be obtained. Though this study was extensive a detailed summary is omitted (as the techniques were later improved upon by another .1nvestigator and another similar study made. Gregory4 carried out a study using acetic acid as 1:he solute with benzene as the dispersed phase and water ias the continuous phase. Apparatus similar to that used 13y Coulson and Skinner was used. The apparatus was 11mproved upon in that ejection was more rapid. .Again Cirops were partially formed at the tip of the nozzle and ‘then instantaneously withdrawn from the tip of the nozzle 33 through an alternate opening in the nozzle. By partially forming a number of drops to different degrees and obtaining data by titration of the immiscible phase, equations were worked up describing extraction during drop formation. The equation which best correlated the data obtained was ‘42 —LO ’3 £749.13) (e45) where k dispersed phase transfer an fl coefficient a nozzle velocity 2 diameter of the drop the density of the drop 2 diffusivity of solute in drop solvent fl a viscosity of the drop fluid o’bo< u Gregory concluded that at slow formation rates the extraction mechanism was diffusion and at fast fermation rates turbulence carried the solute to the surface of the drop. It is felt that this study and the resulting equations are concerned with a drop formed and ejected [and not a drop formed without interference. Other studies of drops which do not contain data :relative to extraction fron.forming drops were carried out by Garner and Skelland3, and Pike, Withers and Beaty11 and 8014. 34 PART III - Comments and Basis for Future Study The equations concerning drop formation are based on rigid assumptions. These assumptions, though necessary to facilitate mathematical development, are extreme. The equations, therefore, pertain to highly idealized mechanisms and probably do not describe actual situations satisfactorily. Previous investigators, because of limitations of experimental procedure, did not Obtain adequate data concerning drop formation. Results conflicted, theoretical equations could not be verifiedand empirical equations, in most cases, were not formulated. Though further study is indicated, it is apparent that new experimental methods are required if the already existing information is to be added to. The basis for a new method of studying extraction from single forming liquid drops is found in a study of extraction by Zeleny.l7 In this study the transfer of'a colored solute from one phase to another, the (phases flowing past each other counter currently in a horizontal extractor,, was studied using photographic methods. As a side light to this study, photographs were taken of rising and forming drops. These photographs 35 indicated that photographic methods could be developed which would make possible a very exacting study of extraction from single drops during the formation period, and, further, such photographic methods would enable visual observations of what is happening at any instant and measurements of extraction at any instant. This information would enable the formulation of empirical equations which would accurately describe extraction during drop formation. Also, the existing theoretical equations might, with this information, be verified or modified to describe the actual medhanimms of extraction. The development of the required photographic methods is found in the following section which is entitled “Special Techniques and Mathematical Considerations”. Special Techniques and.Hathematical Considerations The following section is a description of the means by which quantitative information is to be obtained by photographing, with a motion picture camera, extraction from a drop forming at the tip of a nozzle submerged in a liquid immiscible with respect to the drop. The techniques described and mathematical considerations made have an intrinsic value, in that they may be applied to other types of dynamic studies. The first stage of extraction from a single drop, as previously mentioned, is the formation of the drop or the generation of transfer interface. In experimental studies of liquid-liquid extraction from single drops this formation takes place at the tip of a nozzle which is immersed in a solute free liquid which is immiscible with respect to the solvent from which the drop is to be formed. Extraction from the forming drop takes place along the liquid—liquid interface. The extracted solute may logically be assumed to be arranged in a cloud-like fashion in the stagnant liquid surrounding the drop. This is schematically illustrated below. 37 Solution of immiscible .liquid and solute \\\\\\Forming drop of solvent and solute // . .Glass nozzle immersed i in stagnant liquid To solvent reservoir If a colored solute is used, the shape of this cloud may be recorded on a photograph providing, of course, the optimum film, filter, shutter SPEGd. lens opening, and exposure time are used. Obtaining a photograph of the drop during formation, however, provides only qualitative information. If quantitative information on liquid-liquid extraction from single forming drops is desired, the following data must somehow be obtained: vs 1. the rate of drop formation.unit time area 2. the rate of interface generation, ufiIf:time 3. the total extraction which has taken place at any time. 4. the concentration of the solute at any point around the forming drop. 38 If a motion picture camera is used which takes a known number of frames per second, the first two items are easily determined, providing some type of constant volume feeder is used for the purpose of introducing the solvent. It might be noted here that it would be no easy task to design a feeder with a calibration fine enough and a timer accurate enough to be sure at what rate the small amount of solvent which makes up the drop had been fed. With a camera, as will be demonstrated, only that the feeder does feed at a constant rate need be known. The camera provides the calibration and the timing device. As a drop is formed at the tip of a nozzle immersed in a stagnant liquid, symetry about an axis through the center of the nozzle is observed as illustrated.below. Central axis _, i e—-—-- H83 surement 39 If one measurement is made on the apparatus, such as shown above, a reference scale is then provided for the photograph which is to be taken and any projection thereof. I After a film has'been developed, several frames could be analyzed, say the fourth, eighth, sixteenth, and thirty-second, counted from the time the drop began to form. These represent, if the camera was taking 32 frames per second, one-eighth, one-fourth, one-half and one second respectively. The volume of the drop at any time interval may be calculated by assuming symmetry around a central axis and considering the following measurements on a single photographic frame: The cross-section of the circle for which D is the 2 diameter a TL§—. If D is a function of height, the 1 = H vo ume Innz dh , O 4 For each frame, the value of the integral may be determined by measurement and graphical integration as shown below: Volume h The surface area may be calculated for each frame also. Consider the following measurements: 40 The circumference of circle for which D is diameter = 1ro.- \ S If D is a function of S . the area 3 ‘jznpds. O For each frame, the value of the integral may be determined by measurement and graphical integration as shown below: Area 41 42 Once the value and surface area of the drop have been evaluated for several frames, a plot may be made and an exact or empirical equation fitted to the data which will represent the surface or volume at any time. It should be noted that the only assumption made is that of symmetry about a vertical axis passing through the center of the nozzle and drop. This same assumption will also be made in obtaining a concentration distribution of solute in the immiscible phase around the drop. The figures below show the nature of an extractor and standard cells which will be used for the study. 7— / / / / / j / STANDARD CELL / V / / TOP PORTlON OF EXTR ACTOR 43 An extractor with a rectangular cross section is shown. Metal sides are used on the extractor. Two parallel glass faces make up the front and badk of the unit. Shown next to the extractor is a standard cell. The faces of this cell are constructed of the same type of glass as the extractor, the same thickness and the same distance apart, DS = De° If a colored solute is used, various concentrations of solute and immiscible fluid can be photographed through the standard cell. The density of the film negative will depend on the concentration of solute only as, for each photograph,light source, lens opening, lens speed, film, filter, shutter speed and camera distance will be maintained constant. By comparing these film negatives by use of an optical densitometer a plot can be prepared of concentration vs. light transmission. This plot will look as follows: Concentration V 0 (percent light 100 transmission on film ———————’ 44 where the 0 percent light transmission point is for pure water, and 100 percent for an opaque medium. low if photographs are taken of a drop forming keeping all previously mentioned variables constant, various points in the immiscible fluid around the drop can'be compared for percent light transmission to the standard cell concentrations by means of the optical densitometer. For example see sketch below which represents a certain frame. Solute cloud Percent light trans- mission through this point observed and compared to concen- trations vs. percent transmission plot as shown above. forming drop / It should be noted that the comparison represents an average concentration which the microphotmeter "sees" compared to the concentration of the standard cell. Analyzing the photographs with the purpose of Obtaining point concentrations anywhere around the drop at any time is an involved procedure. Consider Figures 45 l, 2, 3, and 4 on pages 46 and 47 . For each photographic frame the area around the drop is to be mapped as shown in Figure l. The inter- sections of the lines 1, 2, 3, ..., with the lines A, B, C, ... represents points which will be read on the densitometer for percent light transmission. The mapping lines, in 3 dimensions, represent planes, and Figure 2 shows a cross section of the extractor in isometric represented by plane 4. The lines B, C, D... in Figure 2 represent the intersection of the planes B, C, D..., with plane 4. These lines also represent differential volumes through which percent light transmission will be measured. This is shown in Figure 3. It is clear that any points chosen for measurement can be represented by this mapping method. What is eventually desired from this analysis is an expression for concentration any point in the ”cloud" around the drop. First an expression will be Obtained for the concentration at any point on the numbered planes. Censider plane 4 for example, and say this expression can be represented by a series such as (1) C41. = a0 + alr + a2r2 + gr3 + a4r4 46 Aacpcre‘fiz TO BE READ FOR ‘1. LIGHT TRANSMISSION mh‘hh\ SOL UTE C LOUD DROP FIGURE 1" MAPPED DROP / PLANE A // 5.CD£F6”1 /// / SOLUTE /// q .. . FIGURE 2- DROP PROJECTED ON PLANE4 47 FIGURE 3" ELEMENT y /' r /‘L READING FOR Ml -// , MISSION / 0/ TRANS wax _{ A DROP OLOU 6::\ Lnuome THROUGH HERE FlGURE 4 ‘— VIEW. OF DROP CLOUD FROM TOP 48 where Cr4 is the concentration on plane 4 corresponding to a distance r away from the central axis as shown in Figure 4. a0, a,... and a4 are constants. (Again symmetry with respect to shape and concentration is assumed around the central axis.) If C4A is the average concentration the densitometer sees through element 4A, using the nomenclature in Figures 3 and 4, then, C4A = total moles of solvent in element LdXdY ‘ LdXdY - or L/2 L/2 __ 2 C4A = ZfCQL :3XdeZ = (2) E fC4r dz LdXdY O O The trigonometric transformations from Figure 4 give Z-= RSine X = R C086) and by division and rearrangement Sine z a x 0039 X Tana (3) dz = XSecze do 49 Substituting (1) and (3) into (2) PR??? C14 = 12‘ ZICIII' 59c Gde 0*- IZ=O 21 flFTTjfi" __ A'-4 C‘ :2? . M T Za‘(—L)5ec9c/€ A‘O Z=o which upon integration gives E' = _2_Z{Q.T«mevo< oz< mozE>m 0.233%: e do 2253.. also m U n¢ as: noes: mono sundae Have» Isoeussuom scaveEMOh mono Assam ca nuance Heuou x.mo cassava“ no even no 8 oeuoaoeua maaDMHd flbHaflfithdfib HHH manta 74 necessary to project the negatives on a mdcrofilm reader. Calculations. graphical .integrations and graphical results are found inwAppendix VII. The graphical results show that the constant volume feeder was functioning properly and that the surface area of the drop interface was generated nearly at the same rate as if the drop had remained spherical during formation. . The final volume of the coalescing drop. Photo- graphic Set 6, was determined by the means just described. Its rate of formation was determined by dividing its final volume by the number of seconds which elapsed between the beginning of formation and break away from the nozzle. This~calculation is shown in Appendix VII. The final volumes of the drops shown forming in Photograph Sets 3 and 4 and the drop in pulse flow, Photograph Set 5, were determined by direct measurement on the photographs. The rates were determined by dividing the final volume by the time elapsed between the beginning of formation until break away from the nozzle. The accuracy of the measurements involved was poor because of the size of the photographs and the 75 out-of—focus conditions in Photograph Sets 3 and 4. The calculation for this is shown in Appendix VII. Because the solute remained close to the drop interface and did not form a "cloud“ around the forming drop, it was not possible to determine the amount extracted by the means described in the section entitled ”Special Techniques and Mathematical Considerations". As an alternative, an estimate was made of the minimum amount extracted in the formation of the drops shown in Photograph Sets 1 and 2 and the coalescence of the drop shown in Photograph Set 6. This was done by measuring the area of the portion of the film representing solute left behind the drop and determining, using the standard cell photographs. the minimum amount of solute in the calculated volumes represented by this area. This is better explained in the calculation shown in Appendix VII. How much more solute than calculated could be in these calculated volumes is undetermined. no quantitative data on extraction were Obtained for the drops shown forming an Photograph Sets 3, 4 and 5. 76 By using Gregory's4 formula, page 33 and Equation ten on page 14, the amount of extraction expected from the drops shown forming in all photographic sets was predicted. The use of these equations involved several assumptions which are noted on the pages mentioned. A sample calculation for these predictions is found in Appendix v11 . Theplots of concentration vs. percent transmission made from the standard cell photographs are presented in Appendix VII. Also in Appendix VII are plots for two standard cell photographs, of percent transmission vs. distance from the side of the standard cell. These plots illustrate that the light source was uniform. From direct measurement on the photographs in Sets 1 and 2 at 84/24 and 163/24 of a second respectively, the motion during break-away which was not stopped by the camera was calculated. These calculations show that, while the camera shutter was open, (1/45 of a second) each drop moved approximately 0.059 inches upward. Because of the out-of=focus conditions in Photograph Sets 3 and 4, this movement could not be calculated for the drops shown forming in these sets. 77 Photograph Set 1 - Forming Drop Time given in 24ths of a second from beginning of for- mation. Camera speed--24 frames per second. Photographed through Kodak #35 filter f - 5.6. .\\ l T Photograph Set 2 - Forming Drop Time given in 24ths of a second from beginning of for- mation. Camera speed--24 frames per second. Photographed through Kodak #35 filter f s 5.6 133 78 79 Photograph Set 3 - Forming_nzgp Time given in 32nds of a second from beginning of for- mation. Camera speed—-32 frames per second. Photographed through Kodak #50 filter .. 2.8 .119... st 32 r _1_7..3__. 32 77 _, 32 179 80 Photograph Set 4 - Forming Drop Time given in 32nds of a second from beginning of for- mation. Camera speed—-32 frames per second. Photographed through Kodak #50 filter f - 2.8 197 32 203 32 —-§ ‘ghotograph Set 5 -4§orminngrop in Pulse Flow Direction of flow indicated. Time given in 32nds of a second from beginning of formation. Camera speed--32 frames per second. Photographed through Kodak #50 filter f - 2.8 81 82 Photggraph Set 6 = gpalescipg Drop Time given in 32nds of a second from first frame shown. Camera speed--32 frames per second. Time from' beginning of formation to break-away (not shown) 178/32 seconds. 19 Photographed through '33" Kodak # 50 filter f - 2.8 83 Photograph Set 7 - Standard Cells Concentrations given in grams Picric acid per liter. Camera speed—-24 frames per second. Photographed through Kodak #35 filter f - 5.6 "°*-~-.... . “0.0244 0.00609—o 0.0122 0.00244_n. ‘— 0.00975 0.000488-* 84 Photograph Set 8 - Standard Cells Concentrations given in grams Picric acid per liter. Camera speed--32 frames per second. Photographed through Kodak #50 filter f - 2.8 -— 0.0975 0.0122-* 'x-0.0488 0.00609* *— 0.0244 0.00249*- Recommendations and Suggestions for Future werk Although the results of this work leave much to be desired, it has been well illustrated that the photo- graphic methods presented are a rigorous means by which studies of extraction from single liquid drops may be carried out. If properly applied, these photographic methods presented leave nothing to speculation. Complete information, qualitative and quantitative, can be obtained on all phases of drop life using these methods. It is therefore recommended that a long range program be initiated in which extensive studies of drop-wise extraction be carried out utilizing the methods presented in this thesis. An outline of this program based on the experience derived from this work is presented. Program.0utline A. Equipment Procurement 1. 35 mm. vari-speed camera on a permanent basis 2. Film developing facilities in laboratory 3. Film reader in laboratory 86 Equipment design and fabrication l. flew extractor (easy to disassemble) 2. new constant volume feeder with no moving parts (pressure controlled) 3. camera mounting or housing Literature Search -.A search for systems which are suitable for photographic study Research - Each phase of drop—life for each system Should be studied separately. Finally the separate studies should be combined and correlated. Variables which.should be studied in the Research part of the program are listed below. 1. Drop size a. .At different rates of fermation b. From different size nozzles c. Under different fluid heads Extraction a. During formation (1). At different rates of formation (2). From different size nozzles b. During drop rise c. During coalescence after different distances of rise. 87 Correlations should be made on the basis of these variables and on the basis of the fluid properties involved. Another suggested topic of research is the circulation within the drop or the circulation in the continuous phase. This could be studied by photo- graphing systems in which both the drops and the continuous phase have a fine solid dispersed in them. This solid would show up on the resulting negatives and thereby indicate the circulation pattern. A few words should be said about difficulties encountered in this work. First, when the motion of the drop Va stopped and the fluid around the drop was stagnant as in formation and coalescence, the solute did not move out into the water phase as anticipated, but remained in the water layer adjacent to the drop interface. While the principle of obtaining extraction data by comparison using a microphotometer is sound, this phenomenon did not lend itself to analysis and the amount extracted from the drop during these phases of drop life could only be estimated. A different means to determine extraction during these periods is then required, A basis for this means is provided by 88 Photograph Sets 3 and 4 in which light of varying intensity could be seen through the drops which were forming. It is suggested that this light transmission could be a basis for determining the amount extracted from a drop during a given period. Rising drops might also be studied using this idea. A second difficulty, which was anticipated but not encountered, was the voluminous work and numerous calculations which would be required for complete analysis of extraction from single drops particularly using the methods described in this work. The use of a computer is vital if progress is to be made in the direction of correlation. Time should be allotted to programing and understanding operational procedure of the computer used before research is to be started. Third and last was the difficulty in understanding the mathematics and physical considerations involved in extraction from.single drops. To alleviate this, the investigator should have a background in the formulation and solution of differential equations, transport processes and viscous and turbulent flow in the boundfln! layer before attempting a literature search. Part of the degree course work taken should include this subject matter. 10. 11. 12. 89 BIBLIOGRAPHY Coulson, J; as, and Skinner, S. J., Chemical Engineering Science, 1, 197-211 (1952). Farmer, w. 8., “Controlling Variables in Liquid- Liquid Extraction from Signle Drops,“ CRIL - 635, U. 8. Atomic Energy Commission, 1949. Garner, F. 8., Skelland,.A. H. P., Industrial and Engineering,Chemist£y, 48, 51-8 (1956). Gregory, C. P., Jr., “Mass Transfer Between Forming Drops and a Continuous Phase,“ Ph.D. Thesis in Chemical Engineering, lassachusetts Institute of Technology, June, 1957. Hadamard, J., Comptes Rendus, 152, 1735-8 (1911). Handles,.A. E., Baron, T., A,.;. 92. g. JOurnal, 127-135, march, 1954. Haritatos, I. J., and Liberman, 14., ”Liquid-Liquid. Extraction in Drops,” n. S. Thesis in Chem. Eng., H.I.T., 1953. Kopinski, 5., "Mass Transfer in Liquid-Liquid Drop Systems,“ H. S. Thesis in Chemical Engineering, H.I.T., 1949. Lidht, W., Jr., and Conway, J. 8., Ipdustrial and Engineering Chemistry, 42, 1151-1157 (1950). Licht, W., Jr., and Pansing, W. P., Industrial and Engineerigg Chemistgy, 45, 1885-1896 (1953). Pike, F. P., Withers, W. T., Jr., and Beatty, K. C., Jr., “Some Mass Transfer Effects inside Drops in a Miniature Liquid-Liquid Spray Tower,“ north Carolina State College, Raleigh, I. C. Sherwood, T. K._, Evans, J. E., Ioncor, J. V. A., Industrial and Engineering Chemistgy, 31, 1144-1149 (1939). ‘ 13. 14. 15. 16. 17. 90 Sherwood, T. K., and Pigford, R. L., Absogption and.§xtraction, lew'York: HcGraw-Hill Book Company, Inc., 1952. So, W., ”Extraction from Single Drops,“ M. S. Thesis in Chem. Eng., W.I.T., 1955. West, F. B., Herrman, A. J., Chong, A. T., Thomas, L. E., Industrial and Engineering Chemistgy, 44, 625-31 (1952). West, P. B., Robinson, P. A., Horgenthaler, A. C., Jr., Beck, T. R., McGregor, D. K., Industrial and Engineering Chemisggy, 43, 234-238 (1949). Zeleny, R. A., "A Study of Eddy Diffusion in Liquid-Liquid Extraction," M. S. Thesis in Chemical Engineering, Worcester Polytechnic Institute, June, 1954. APPENDICES 92 APPENDIX I The Derivations and Solutions of Some Differential Equations Pertaining to Extraction from Single Liquid Drops A. Extraction from a forming liquid drop assuming mass transfer by diffusion only, liquid entering at the center of the drop, equilibrium at the interface and \constant\’interfacial composition. f 1. Coordinate system (spherical) 2. Nomenclature r = radius C1 = interface concentration D = diffusivity Co = initial concentration C = concentration t = time Rf = outer most drop V = drop volume radius fl . u = d t = rate of Ir indicates @ r volume change v = fluid velocity in ‘rwar indicates 6>r + or radical direction 3. Derivation using rate approach (1) input-output = accumulation 93 ( ) [(C/l/ragkoejk)-(C4/VA¢rAelHAr)]At 2 * [(ngf YA‘PV'AGL) -(—D%%y-A¢rae|Hm-)]4t = (C rafrAGAIr‘tm‘ )«(crsz raeavlt) Dividing both sides of equation (2) byaf.AO, er and at and using the definition of derivative, (3) a . a ‘25 .3. . ’ar'(’VC’)*Jr(D' <9?) at (C?) Carrying out the indicated differentiations in equation (3) and dividing both sides by r2, (4) “M10. «294/- ca_/_y.D3_g+__22s.- a; dr 1- ? ar 91, IfU' 34’ then /V=....‘-.L—l and 21/2. ..U at 411‘?‘ 2r 2m" and substituting into (4) and rearranging (5) ‘c 3.2.2.9. 2.9- u - 25'— D37.+ r av+ 2? 41wz 9!: i If C' defined as C' = , the equation may be Co’ Ci rewritten 94 r (6) D—L‘C + a—D— o 3...;— t- inc—’0 -u-——— 2. 3c, Dr‘ 9r 9 i A Q 1. £1 The usual way to solve such an equation is to assume a solution of the form C' = R . T where R is a function of r only and T is a function of t only. This assumption fails to satisfy a boundry condition of the physical problem which is: c'=0,r=n,t)o In this boundry condition R3 the outer most radius of the drop, is a function of time and this does not fulfill the specification that R be only a function of r. no solution for this equation has been found. B. Extraction from a liquid drop assuming mass transfer by diffusion only, equilibrium at the interface and a constant interfacial composition. 1. Coordinate system, same as previous. 2. EOmenclature, same as previous. 3. Derivation using rate approach (1) Input-output = accumulation 95 (2) [0' 933V4¢ V491,)-(-D%%PAQPAO|VN'V) At a (c'4¢"°°"1,_,,.)- (cyb¢y49 Av‘t) Following the same procedure as in previous derivation, ‘. 3 fl. V’ “aces-ever.» a If C' is defined as C' = ...—.... Co ' Ci 0 equation (3) becomes (4) ’ ‘l/ D(a%%+rac )= r 3!“ .5.’ t l) and these equations, (3) and (4), have the boundry conditions t = o, c = co, c' = 1 t = 00, c = Ci, c‘ = o r = R3 c 2 Ci' c' = 0 Equation (4) may then be solved with the following results n = 00 5) ( C' = Z 2L-l)n+1R .. Dnznzt. n = 1 nflr R2 nrtr Sine 96 (6) n (C - c )R 6 = Q g ...—.9 1- (1'172 1 3 n2 “ n = l J 2 2‘ Dn n t E2 R2 when 0 is total moles which have crossed interface. “=00 (7) E :3 C1 + 6 (CO _ C1) 2 1 n = 1 n.fl where E is the average concentration within the drop at time t. 11:00 22 (8) K ..Lué) 1 -Dn__12:_t ‘31-. " Z —— R n=1 nznz a Where K is the overall mass transfer coefficient. 97 APPEHDIX II The Preparation of Standard Picric.Acid-Water Solutions It was desired to prepare a standardized picric acid-water solution which could be diluted as needed to obtain various concentrations of picric acid in water for use in standard cells. This was done by first weighing out one gram of dried picric acid (Baker reagent grade) and dissolving this in one liter of water. Using a pipette,100 mls. of this solution was transferred to a clean 250 m1. Erlemeyer flask along with 10 m1. of wash alcbbol. This sample was titrated against 0.02 8 sodium hydroxide. This procedure was repeated three times with the following results: Gms./liter Titration Ml- saos picric acid 1 21.30 0.974 2 21.27 0.973 3 21.33 0.975 Sample galculation Titration 1 98 gormality Sodium gydroxide x golume Sodium gydroxide :- Iormality of picric acid soln. 0.02 x 21.30 “0 m1. lormality of picric acid solution Equivalent weight of picric acid :- 229 4.26 x 10'3 x 229 . gms./liter picric acid . 0.974 99 APPENDIX III The Hazardous Properties of Picric Acid and Toluene and Some Advisable Precautions to be Taken When Wbrking with these Compounds A. Picric Acid Picric acid is hazardous in two respects. First, it combines with most metals to form metal picrates which upon impact or rapid heating detonate. Dry picric acid itself will detonate when heated above 3000 C. It is therefore advisable to flush thoroughly with water all residue remaining after the acid has contacted metal. Further, any time crystals or a solu- tion of picric acid is discarded, it should be washed down a suitable drain with an abundance of water. Second, picric acid is toxic in nature. Exposure is usually from two sources, by skin contact with solution or crystals or inhalation of dust particles. Skin contact, particularly on the hands, usually results in transfer of the acid internally as a yellow stain results which is difficult to remove, but comes off slowly when food is transferred to the mouth. A primary symptom of poisoning is dermatitis around the mouth and nose (papules). Extreme poisoning is 100 internally injurious. It is, therefore, advisable to transfer crystals of picric acid with care, and if an extremely dusty variety is being used a dust filter mask should.be employed. Contact of a solution of picric acid with the skin should.be avoided. If the acid does get on the skin it should be washed off with water and an abrasive soap before the stain sets. B. Toluene Toluene is also hazardous in two respects. First, toluene vapors are flammable and toluene should never be transferred near an open flame. Second, because toluene is very volitile, inhal- ation is difficult to avoid. An excess of inhaled vapors results in poisoning, the first symptoms of which are similar to alcohol intoxication. Continued exposure results in internal injury. It is advisable to always transfer toluene under a hood or a well ventilated area. The above information was obtained from.the author's experience and Industrial Toxiology, by Laurence Fairhall. 101 a ..lvlolfi 1"-II4I . . ... o Etc , ... . TWIL ..4 I- -—9 . t . . o n , - -—-‘— »-c-o--Io_{r_.- ... a I o—o—O—r—o l .A. I .«.A. ...-“— »_—o b—v—o‘—7 ._ . i ...-....m. 61.. ... ..-,...- ....4. ...-.4... . , . T.,l M . . .6 .14 {11.4.9.IL‘6. I . .- 1+ -....l..ol|7..lu . . . v . o A . La —. o»-‘--.._.—.- 5.4—- c | 0 n . "T E -~A . ‘V—qvv—v'—“* § - A . ‘ o 1 .----..;— ...-~.n Q-.._. G 0 V I 1.--- I *4 102 APPENDIX‘V Optical Theory In this work no actuil reference need be made to optical theory as concentrations were to be determined by comparisons. - To make these comparisons easier, certain filters were put in front of the subject. The filters did not tramit light wave-lengths which were transmitted through picric acid-water solutions. For example, the kodak #35 Filter used would transait light ‘haVing. wave-lengths of 600 to 680 m’illinicronspwhile a, concentrated picric acid-water solution does not transmit light having a wave-length above 500 nill‘intonm. Thus, a solute cloud around the drop, photographed through a filter would appear light on the negative as little light would have reached the film. This light-r ness could be compared to a standard cell by means of a microphotometer . lo further knowledge then, is required of optical theory; however, the following is included. Ianbert's law is the basic equation forspectro- photometric - dens itonetric analysis. For Ionochronatic 103 light passing through a homogeneous absorbing medium: d1 = '-;- de Where I = Light intensity d1 = Change in intensity after passing through thickness dx of the medium B = a constant X = distance through the medium 'Upon integration of the above equation between the limits Io and I, corresponding to length 0 and 1, one obtains Where t a the fraction transmitted For a solution, - t1 1 ‘2 ' _ Where c c the concentration of the absorbing solute ' and; at a a constant Taking the log of both sides of the last equation In 'E =-0tc1 low defininglm% as the optical density, D, and (X as the extinction coefficient, 8, D a Ecl 104 For high accuracy in any analytical determination using optical methods, a high value of B is desirable. This is Obtained by varying the light filters in front of the subject until large values of E for any given concentration range exist. In this work, the use of the Kodak #35 or #50 filter mounted in 8 glass accomplished this end. 105 ‘APPEIDIX.VI Data: A. Nozzle Tip Diameter 1. lbzzle used for photograph sets 1 and 2 a. I.D. = 0.027“ b. O.D. = 0.041“ 2. ROzzle used for photograph sets 3,4,5, and 6. a. I.D. = 0.036" b. O.D. = 0.049” 106 na.a oa.a mm.o oh.o on.o mu.o oo.o . oo.o ov.o aon.o nne.o oea.o oo«.o onn.o n on no.H oo.a om.o oo.o oe.o ou.o oo.o A oa.e ma.o mo.o om.o mn.o oo.o a o.o oev.o owh.o oop.o oao.o omm.o a «a om.o om.o oo.o oe.o o~.o oo.o s -..- "-'- -"'- --‘-' --g' i a o poe.o oao.o oao.o cam.o onm.o n o op.o oo.o ov.o om.o o~.o oo.o a 'I-Iu' ----II- alal-Ial' "Illl- ....II a o onn.o oo¢.o omm.o omn.o n m ov.o on.o o~.o as.” oo.o n nonbsn u acosousnsoz annexe sq vacuum e :3onn as no manna codecoseo \/ 4 n x (Q. a you nmeumouonn Hon eusoaeuseeoz o>wusuoz Edam venuenoum .m 107 mm.~ om.a mm.s oe.e mH.H oo.H oo.o oe.o oo.o a on o ooa.o oo~.H .e¢.a om.e on.a oa.a oam.o o a om.e co.” ov.a o~.H oo.~ om.o oe.o o~.o oo.o s --- --- --- --- --- --- -- --- oo.o u o 86 84 mm; 3.4 H To ommd a mo --- --- --- --- --- --- -- --- oo.o s m~.~ om.H om.a om.a mo.a oa.o mn.o ma.o oo.o a o oon.o ooo.a oe~.a cam.a oom.a ~H.H ohm.o omm.o o om o>.e oo.a oe.e o~.H oo.a om.o oe.o o~.o oo.o : mm.H om.~ mm.a ma.a co.” om.o on.o oo.o n ooo.o oao.oc ooo.~ oo~.a oun.a HH.H oom.o omm.o e mm on.” oe.a om.” oo.H om.o oe.o ou.¢ 00.0 n m.H o~.a oo.a mm.o om.o oo.o m o oom.o ova.o oo.a oom.o omm.o a as o~.~ oo.a om.o ov.o ou.o oo.o n mv.s NH.H oo.H mm.o om.o oo.o m oo.o oom.o mm.o oo.H oam.o omm.o a an oN.H co.” om.o oe.o ou.o oo.o n Aoossdusoov a use aneumouosm sou euseeewsneoz o>eusm0l Edam vouoenoum 108 oH.H oo.o oh.o om.o m~.o o a oo.o ov.o e>.o oo.o m>.o m~.o a «a nm.o om.o oo.o ov.o o~.o oo.o : os.o ow4a::almaqd-Illmqu-Inlwa-o o -m o omv.o owm.o oem.o oh¢.o on~.o a ca om.o o-.o o-.o oa.o oH.H 00.0 n llll IIIII IIIII IOIII a oo.o ooa.o onn.o om~.o a a ~m.o o~.o oa.o oo.o n 0.30:.“ I Ufiflahfimflma 509030 and 0303“ G saonu as no enueu codeseawa N use sneuuouonm sou eusOEOMseee: e>aueuea Edam oeuuenoum .U 109 omo.H omm.a oom.s oma.a can.” omm.o oov.o ooo.o a can.” oom.H:u a oau.d can.” oma.aj ooa.o om«.o n n¢.H ov.a o«.H co.” om.o ov.o o~.o oo.o : om.a om.a mn.e no.” mm.o ov.o oo.o u o oom.o oaa.s om».~ o~H.H mm.o mu.o a an.” on.a oo.a om.o oe.o ou.o oo.o a mm.a ou.~ oma.o omm.o om.o oo.o a ....=_ _ ooo.o oom.o ooa.a ooH.H ooa.o om«.o a ou.~ co.” om.o o¢.o o~.o oo.o a m.H mm.d an.” oH.H mm.o mnqo o a ooo.o com.“ omm.o ooe.a oma.a oom.o om~.o a mu.“ o~.e oo.a om.o oe.o on.o oo.o n m~.H on.” mm.o mm. om.o oo.o . a o omoo oom.o oo.a oah.o om«.o n mo.H oo.a om.o o¢.o ou.o ooo.o 1-m mm.a oa.a mm.o mm.o oo.o u omo.o ooe.o ooo.a oom.o on~.o n oo.o om.o o¢.o o~.o oo.o a Aeosceunooe N new sensuouonm new auseaouseeoz 031.5002 Eda usual-own 110 on." ma.” me.a me.a oa.a oo.H om.o mm.o ov.o .oon.o ooo.o a o ovm.o oom.H oom.~ oom.~ omo.a ohm.a cow.“ ona.e. oop.o o.o a and mm.“ mm.” pe.a o¢.H on.“ oo.a om.p oo.o oe.o-o~.o oo.o : cc.“ om.u oo.~ m~.H om.a mm.a oa.o om.oo mm.o o~.o oo.o a oem.o oom.s oom.e ooe.~ ohm. omm.a omm.a oov.a ooa.a oop.o om~.o a oma oo.~ om.” oe.d o¢.a oa.a oo.~ om.o oo.o ov.o o~.o oo.o n mo.~ om.“ or.” ov.a m¢.~ oo.H om.o oo.o on.o ooo.o u o omm.o oe~.a omv.e ome.a owm.a oov.a oo~.a oom.o omu.o a one we.” oo.e cc.“ on.” oo.a om.o oc.o ov.o o«.o oo.o n 3.3 86 u... i: . . _ o om.o oH.H ~m.~ mv.a om.a av.” on.e om.o m«.o a cue no.~ oo.d o¢.H ou.e oo.a om.o oo.o oe.o o~.o oo.o a mo.~ on.” mv.a o~.a mo.a om.o oe.o on.o, o a o a om.a oe.H m¢.a o¢.a o~.a om.o n«.o n cos oo.a ov.a cu.” co.” om.o oo.o oo¢.o o~.o oo.o ,: ooo.a com.” com.” oo~.H owe.” oom.o omm.o omn.o o .u- o oom.o oNH.H can.” oom.a cow.” oom.a ooo.o om~.o a om om.~ ov.a ou.H oo.a om.o oo.o ov.o o~.o oo.o s Aoossausouv m use smeumouosm you museseuseee: o>ausmez sash oeuuofioum D. 111 Projected Film Negative Measurement for Photograph Set 6. 1. Drop diameter - 1.40” 2. Solute cloud diameter - 0.65” 3. HOzzle tip - 0.31" Photograph Measurement for Photograph Set 3. 1. Final diameter - 0.379" 2. lbzzle tip diameter - 0.106” Photograph Measurement for Photograph Set 4. 1. Final diameter - 0.441” 2. Nozzle tip diameter - 0.107" Photograph Measurement for Photograph Set 5. 1. Final diameter - 0.379“ 2. lbzzle tip diameter - 0.118" 112 - - m.a~ o.~n - .m\n M.” m.m o.m~ m.em m.vm :~\H v.” n.m a.ma o.m~ o.~m .m\m m.H ¢.m ~.o~ o.Hm m.¢m ~e\a - - ~.>H m.om - ;m\a Haoo pudendum no one. «was so«n0«2aseuu uncouom sown eenusu mhoooo.o evaoo.o mmvoo.o moooo.o mhooo.o umao.o ev~o.o uou«H\ueuum coaueuusoocoo s new neuumouosm .ne>«uemoz absounu coden«8nsnua panda usouuom I usoeeusnaez.aaoo Unevseum .m 113 1.. r nil - m.~ - _ - m.e H.ma - .m\m ~.N m.~ m.m m.m . o.m «.md m.Hm .N\H m.H m.m v m.m m.m m.o~ m.¢m nm\m H.N h.~ . m.m m.m N.m b.0m ¢.om ;v\H II 0.N .0 II m.m . m.mH II . .m\H dame Unevcsuu no «can sues coanmafimseuu usoohem scum menusu hqmmoo.o aomoo.o mnmoo.o Nuao.o vao.o mmqo.o memo.o Heu«H\eEde coaueuucousoo 4) l‘ w you smeuuouogm .~ g 114 I. Formation Times Photograph Set Formation Time (Seconds) 1 3.33 2 6.63 3 5.32 4 6.09 5 4.00 6 5.57 115 APPENDIX VII Calculations, Graphical Integrations and Graphical Results 116 118 V’I IA“ a... 120 ossao> no man ”sauna owoax o-oax emoa x owes x e-oax m-oa x m-oH x o-oa x o>em 0» uouuuu hm.H no.d nn .H 5H.H vMo.o Nbv.o v>~.o mnH.o mh.NH mo.HH Hm.oa. hm.m m~.¢ ha.m mm.d mm@.o mm mm ow ow mm on «H o sceeuo>soo nose» m.:« c nausea nouosasdam sue: geese so censuses ~.c« usouoe a mo aspen - uses AH pom smuuuoaozm. a pause sous .H a one 0 .m .¢ unease Bonn span pmusasoaeo use even 121 SON” OUfluhflfl NO eloax eloax cloak cloak cloak vloax N.um annual o>am 0» nouoeu soaeuo>cou c am.e hv.e ma.m vo.m me.~ mm.a nose» m.:e nmusmnma Hmuoaaseam mm.hs ~«.ha downs Ho.o no.e Hm.v sue: sauna no nonsense ~.s« eueoumu . me . ..z oo mm ;; n u «m ca . . «a we «seem - mafia .a new nmsumouonmv U nacho scum .m essao> wuoax cloak mtoafibuoax eloax OIOHx cloax oloax mflOHx @IOHX m0 .vu Hanuou Hm.H 0N.H ON.H mem.o who.o mam.o mvm.o vv~.o mmwo.o mmdo.o o>d on Hound“ _ . , moanuo>sou mesa» N.:H pmusmeoe ll . . soueaaseam om.ma m0.ma oo.oa ee.ma_ao.m. aa.m mo.m ea.~ em>.o ohu.o - sue: madam . . so censuses ~.ca I'll. 1“ w H . osooen e Omd OMH OOH om . cm on an NN OH N. n no nape“ - case an new smeumouonm. m sauna Bosh .N 122 m.uu deduce eloa x ona.o -. ganja-Iii Nmma meanness n ca x me.a x u.:« eons-nos mmm.o mum ensues @- n.c« nauseous . m an Hanan» «A x «A x NH vuoa x mv.a I n o x mm.H x ma.o I Houoeu scanue>cou A.< sense oomv oouoenoum as .uceseusueee oeuoofioum on» as mn.o one cannon on» no .n.H Heaven on» we aeo.o ones: m .sd deduce mloa x mm.a u mm.o I monounoum as n.:« a Heo.o m.s« on.o a amino so u.:« censuses 0:0 mne.o n Amino no nonsense N.s« .ccouee a no any vN\o us 4 guano Eoum mamasxm msazoaaom ca poueuumsdaa we mesa-uno euoooeu coaeuo>s00¢ «one oueuusm mo .uu Hanson eloax e oax enoax eloax cloak cloak cloak eloax o>a on Moscow -.w mm.n e~.m oo.¢ cm.u om.~ ab.a ooh.o soaeuo>cou a nose» n.:a censuses . . wouesassam mm.ma mv.ma vo.oa mm.ua am.m ma.m av.m av.~ nuaa chasm. . so censuses ~.se one one om oe oe an. «a as vacuum a «0 aspen - mass .m new nauseouonm. a ensue sous .v 123 24 125 I . 1 I114 4 I] 4 ‘1 dl-l J 111 . 1|! , 4 V 11 111‘: TM .. 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The estimation of percent of total solute extracted from the coalescing drop, Photograph Set 6. a) Projection Factor 0.31 measured inches = 0.049 actual inches 0.049 actual inches 1 measured inch = .0—31— 0.l58 actual inches ll 1 measured inch b) Drop volume Diameter of drop = 1.40 measured inches 1 1 Drop volume = 31rd 3 = 'g x’fl'(l.40 x 0.158)3 Drop volume 0.00580 cubic inches c) Grams of solute in drop Grams of picric acid in one liter of toluene saturated with water and picric acid, - 121 121 fig x 61% 3 x 0.0058 in.3 = 1.15 x 10"2 grams d) Grams of solvent in solute cloud Volume of cylinder which has a length equal to inside width of extractor and a diameter equal to the actual diameter of the solute cloud. 1102 x 1 -- 10.65 x 0.158)2 x 1 = 0.00826 4 4 cubic inches e) 130 Concentration of solute in this volume as determined from the standard cell Photograph Set 8 - > 0.0975 gms/liter f) Grams extracted from drop, ) l.3| x 10’53‘ms. 9) Percent of total solute in drop which was extracted. ’1-31 x 10-5 x 100 = > 0.114% 1.15 x 10"2 2. The determination of the final drop size and rate of formation of the drop shown in Photograph Set 3. a) b) 0) Enlargement factor 0.l06 measured inches = 0.049 actual inches 0.049 actual inches 0.106 1 measured inch 0.462 actual inches 1 measured inch Drop volume Diameter of drop = 0.379 measured inches 1 3 1 3 Drop volume = “517d - ‘6' TT' (0.379 x 0.462) Drop volume = 0.00279 1n.3 = 1.63 x 10’5 ft.3 Rate of formation 1.53 x 10 6 ft. .5 0.306 X 10 6 IL— 5.32 Sec Sec 131 3. Calculation of percent of total solute in drop extracted during formation for Photograph Set 1 using Gregory's formula, page 33 and formula 10 on page 14. a) Date and nomenclature /A( = viscosity of drop fluid - 3.76 x 10"4 mass ft. - Sec V = lnozzle velocity ---- 0.132 ft/Sec d = final drop diameter - 1.52 x 10‘2 ft. f = density of drop fluid - 54 #/ft.3 D = Diffusivity of picric acid in toluene --- - 2 5.59 x 10 5 5.5... hr The viscosity and the density of the drop fluid is taken as the viscosity and density of toluene at 25°C. from the 36th edition of The Handbook 2; ghemistgy and Physics. The diffusivity of picric acid in toluene was calculated from formula (23) on page 21 of Absorbtion and Extraction by Sherwood and Pigford, 2nd edition: k1 in this formula was taken for benzene. The nozzle velocity was obtained by dividing the formation rate by the nozzle channel cross section. b) lid .. 3.74v( 37":wa (555)-LO (p. 33) 132 f kd = 0.132 —- t- 3600 Sec Sec x .52. x 3.74 x -2 ft. -0.2 1.52x10 ft. x0.l32 ———Sec x 54 2%"! ) x 3.76 x 10"4 * ft.-Sec. - - .o 3.76 x 10 4-——i————— x 3600 339- 1 ft -5 hr. 2 54 -15— 5.59 x 10'5 -£EL— ft. x hr f . kd = 1.28 i":— c) Percent of total solute extracted: ,9 can a K = kd (p. 14) c x t3 ft. 3.34 In -§5 = __ d =..1.28 hr. x '3355 hr. C03 3 x 3 x 2 1.52 x 10“2 ft. c 1n -—SE = -0.496. .—£h = 0.626 133 %extracted = (1- 0.626) x 100 = 37.4% ‘2’ ”'Tl'h'lTuflfilLfijtflflflfijfihfllflfjflflflflflflfiyflfifil‘s