MASS TRANSFER FROM SINGLE FORMING DROPS BY George Rusin A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1964 ABSTRACT MASS TRANSFER FROM SINGLE FORMING DROPS by George Rusin A photographic technique has been used to study the mechanism of extraction of a colored solute, picric acid, from a drop of toluene forming in water. Relationships were developed to relate the "dark- ness" of a photographic image of the drop to the total amount of extracted acid and to the distribution of this acid over the surface at any instant during drop formation. The data were compared with values calculated from several theoretical equations. The results of this investigation reveal that contrary to most theoretical models the dominating factor affecting mass transfer was tangential flow around the drops. The viscous drag of the circulating fluid within a forming drop caused tangential convection currents in the continuous phase atthe drop surface. The convection currents originated at the top of the drop and moved down over the drop surface carrying the extracted acid to- ward the capillary tip used to form the drop. Simultaneously, adsorbed surface active impurities were swept down toward the capillary tip where they accumulated at the interface in the form of a film and re- tarded the motion at this part of the drop. As the drop grew, the film George Rusin of impurities progressively extended over the drop area until the entire surface became motionless. Consequently, early in the life- time of a forming drop most of the surface was exposed to the cleaning effect of the tangential convection currents resulting in rates of extraction greater than predicted by any of the models. Later in the lifetime of a drop the resistance to mass transfer due to the film of adsorbed surface active impurities plus the retarding effect of the film on the tangential convection currents resulted in extraction rates lower than predicted theoretically. ACKNOWLEDGEMENT The author wishes to express his sincere appreciation to Dr. Donald K. Anderson and Dr. Richard A. Zeleny for their valuable guidance throughout the course of this work. The author is indebted to the Division of Engineering Research and the Dow Chemical Company for providing financial support. Thanks are extended to William B. Clippinger who assisted in the design and fabrication of the laboratory apparatus necessary for this research. ii TAB LE OF CONTENTS ACKNOWLEDGEMENT .................................... LIST OF TABLES ....................................... LIST OF FIGURES ........................................ INTRODUCTION .......................................... Previous Investigations on Mass Transfer from Single Drops Present Method of Investigation of Mass Transfer from Individual Drops THEORETICAL MODELS ON MASS TRANSFER FROM FORMING DROPS ..................................... Mass Transfer by Diffusion Mass Transfer by Diffusion and Convection Determination of N by Considering a Volume Element in Space APPARATUS ............................................ EXPERIMENTAL PROCEDURE ............................ Preparation of Chemicals and Solutions Procedure for Taking Data Film Processing and Optical Density Measurements ANALYSIS OF DATA .................................... Determination of the Total Amount of Extracted Acid from Optical Density Measurements Through the DrOp Image Experimental Determination of Solute Distribution Over the Drop Surface Theoretical Determination of Solute Distribution Over the Drop Surface Calculation of the Overall Mass Transfer Coefficient Effect of Dispersed Phase Resistance on Mass Transfer iii 12 12 16 23 26 31 31 33 33 36 36 47 49 50 52 TABLE OF CONTENTS (continued) Theoretical Calculations Based on the Assumption that Only the Picrate Ions Absorb Light SUMMARY OF RESULTS ................................. DISCUSSION OF RESULTS ................................. DISCUSSION OF EXPERIMENTAL ERROR .................. CONCLUSIONS ........................................... NOMENCLATURE ........................................ BIBLIOGRAPHY ......................................... APPENDIX A: An Estimate of the Upper Limit for the Ratio of the Amount of Picric Acid Extracted During the Formation and Withdrawal of a Drop to the Amount of Acid Extracted During Formation According to Jacob's Data ....... tf(tf- t)1/2’ APPENDIX B: Evaluation of the Integral [ T dt ...... 0 1: APPENDIX C: Calculation of the Fraction of Picric Acid Ionized in Water at 26.70C ................ APPENDIX D: Distribution of Picric Acid Between Water and Toluene at 25°C ...................... APPENDIX E: Experimental Data ....................... APPENDIX F: Calibration Curves ....................... iv Page 54 57 73 80 83 85 88 91 93 94 95 LIST OF TABLES Table Page 1 Comparison of the True and Experimental Average Concentrations of Aqueous Solutions of Picric Acid in a Three Compartment Cell ..................... 39 2 Diffusivity of Picric Acid in Water ................. 53 3 Summary of Data ................................ 59 Figure 10. 11. 12. 13. LIST OF FIGURES Drop forming device of Coulson and Skinner ........ Coordinate system for a forming drOp according to Michels' model ................................ Apparatus used to photograph the forming drops ..... Plunger drive ................................... Three compartment standard cell calibration curve of picric acid in water ........................... Coordinate system for determining the total amount of extracted picric acid .......................... Coordinate system for determining the distribution of the extracted acid over a drop surface ........... Coordinate system for determining the theoretical distribution of the extracted picric acid over a drOp surface ......................................... Comparison of the total amount of picric acid extracted to the amount of the acid ionized according to Coulson and Skinner's model ................... Comparison of the experimental data with that predicted theoretically using the spectroquality toluene as the drOp phase ......................... Comparison of the experimental data with that predicted theoretically using the spectroquality toluene as the dr0p phase ......................... Comparison of theoretical and experimental overall mass transfer coefficients using the distilled toluene as the drop phase ................................ Comparison of theoretical and experimental overall mass transfer coefficients using the spectroquality toluene as the drop phase ......................... vi 20 28 29 38 46 48 49 56 64 65 66 67 Figure 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. LIST OF FIGURES (continued) Experimentally determined distribution of the extracted solute over the drop surface for drOp sets 1, 2, and 3 ................................. Experimentally determined distribution of the extracted solute over the drop surface for drop sets 4 and 5 ......................................... Experimentally determined distribution of the extracted solute over the drop surface for drop sets 6, 8, and 10 .................................... Experimentally determined distribution of the extracted solute over the drop surface for drop set 12 Theoretical distribution of the extracted solute over the drop surface for the drops which were nearly spherical in shape ............................... Comparison of the data of the present work with Jacob's data and with that predicted theoretically ..... Schematic diagram of a forming drop .............. Standard cell calibration curve of picric acid in water for drop sets 1 through 6 ........................ Standard cell calibration curve of picric acid in water for drop sets 8 and 12 excepting the primed numbered drops ................................. Standard cell calibration curve of picric acid in water for drop set 10 excepting the primed numbered drops .......................................... Standard cell calibration curve of picric acid in water for the drops with primed numbers ........... Standard cell calibration curve of picric acid in toluene ......................................... vii Page 68 69 70 71 72 74 76 141 142 143 144 145 INTRODUCTION Liquid-liquid extraction is used a great deal in the chemical and petroleum process industries. Liquid-liquid extraction is the method in which two immiscible liquids are contacted with one another in order to facilitate the transfer of a solute from one phase to the other. Contacting is accomplished by dispersing one phase into the other in the form of drops. Three stages of extraction are recognized during the time of contact between the two phases. The first stage is con- cerned with the extraction that occurs while the drops form. The second stage involves the extraction during movement of the drops through the continuous phase. The third stage deals with the extrac- tion during coalescence of the drops. The present work is concerned with the mechanism of extraction during drop formation. Previous Investigations on Mass Transfer from Single Drops Among the early investigators on mass transfer from single drops were Sherwood, Evans, and Longcor (24). They studied the aqueous extraction of acetic acid from methyl isobutyl ketone drops and from benzene drops in columns of various heights. A series of drops were formed at a constant rate at the bottom of each column and col- lected in a measuring burette at the top. The total acid which was ex- tracted during formation, drop rise, and coalescence was measured. A plot of the logarithm of the fraction of unextracted acid versus column height resulted in a straight line. By extrapolating the line to zero column height, it was found that 45 percent of the acetic acid was extracted from the ketone drops and 40 percent from the benzene drops during formation. Licht and Conway (15) designed an apparatus to separate the extraction that occurs during drop formation and drop fall from that of coalescence. Several drops of a acetic acid-water solution were formed at the top of an extraction column, allowed to fall through methyl isobutyl ketone and collected at the bottom. At the bottom of the column, the drops passed through a stopcock which was closed after the last drOp was collected. A plot of the percent acid extracted during drop fall and formation versus column height was made. The percent extracted during formation was obtained by extrapolating the data to zero column height. A value of eight percent was obtained from the intercept. This value was much less than that obtained by Sherwood, Evans, and Longcor. The explanation given for the difference between the results was that the direction of extraction was different. It was sug- gested that the acetic acid formed hydrogen bonds with the water molecules. Consequently, the hydrogen bond offered a resistance to transfer of acetic acid from the water drops to the ketone phase. The percent extraction during drop formation was independent of drop size for drop sizes of O. 406 centimeters and O. 342 centime- ters in diameter. Also, the amount of solute extracted in a given column height was independent of drop formation time. West, et a1. (26), with an apparatus similar to that of Sherwood and co-workers (24), attempted to reproduce the results of the water- acetic acid-benzene system. They obtained 14-20 percent acid extracted during drop formation using the same plot. The discrepency between the results of the two investigations was attributed to differences in the purity of the benzene that was used. Later work by West, Herman, Chong, and Thomas (27) showed that this discrepency was due primarily to the use of Tygon tubing in the feed line of the apparatus. The acetic acid-benzene solution ex- tracted plasticizers from the tubing as it flowed to the drop forming device. The extraction efficiency was found to increase manyfold on the addition of a few percent of various alcohols to the benzene solu- tion. It was postulated that the impurities extracted from the Tygon tube concentrated at the water-benzene surface and acted as an inter- facial barrier. The alcohols served to displace or destroy this barrier. It was proposed that the barrier might interfere with mass transfer in two ways: by direct resistance to penetration by solute molecules; or by altering the mechanism of extraction by changing the fluid dynamics at the interface. Licht and Pansing (16) showed that the extrapolation procedure in the previous work was in error. Their data showed that the plot of the logarithm of the fraction unextracted or an equivalent variable versus column height resulted in a relatively straight line only over a given range of column heights. Part of the data was taken from the water-acetic acid-benzene system which was studied by the previous investigators (24, 26). The data also indicated that the amount of extraction during drop formation was independent of drop formation time. However, they noted that with a 25-fold variation in drop formation time (0. 4 to 10. 0 seconds) that this was questionable. They concluded that the amount of extraction during drop formation was too small to be accurately determined by their experimental technique. Garner and Skelland (5) investigated the extraction of acetic acid from nitrobenzene drops to water in a small column. Twenty to fifty drops at the same formation time were formed in the continuous phase and fell a distance of 4 to 5 millimeters before leaving the bot - tom of the column through a capillary exit. The amount of acid which was transferred to the water phase was considered as the acid extracted during formation. The fraction of extracted solute increased only two fold over a 25-fold increase in formation time (2. O to 50. 0 seconds). For a given time of formation, the fraction extracted increased with a decrease in the internal diameter of the nozzle tips used to form the drops. The smaller inside diameters gave greater linear flow in the nozzle causing more turbulence in the forming drops. Transfer of propionic acid and benzoic acid from water to form- ing benzene drops was studied by Coulson and Skinner (4). Referring to Figure 1, a benzene drop was formed on nozzle (A), and then re- moved through tubing (B). The tWo way stopcock (C) prevented the benzene from entering the exit tube during formation. After formation the stopcock was closed and the hydrostatic head of the continuous phase forced the drop out of the system. Since the amount of acid extracted from one drop was too small to be measured, this procedure was /\0 Figure 1. Drop forming device of Coulson and Skinner. repeated for a large number of drops holding the time of formation constant. This apparatus was operated manually for formation times greater than 3. 4 seconds. An automatic device was used for shorter formation times. Extraction was found to increase over a formation plus withdrawal time range of 0.515 to 14.1 seconds, but for times greater than 5 seconds, the increase was very small. Overall mass transfer coef- ficients based on the average area exposed during drop formation decreased with an increase of formation time and were independent of the drop size. Other investigators studied gas absorption by forming drops. Work in this area, although it is not specifically liquid-liquid extrac- tion, is directly applicable to the study of the mechanism of mass transfer in forming drops. Whitman, et a1. (28) investigated the absorption of carbon dioxide by forming drops of water in a small column of constant height. A series of drops were formed at a fixed formation rate at the top of the column and collected under a kerosene seal at the bottom. A plot of formation time versus the total amount of gas absorbed per unit volume of drop gave a straight line. Extrapolation of the data to zero formation time gave the amount of gas absorbed during the free fall of the drops. Assuming this to be constant, the gas absorbed during formation was calculated by subtracting this constant value from the total amount absorbed. Groothius and Kramers (7) studied the absorption of sulphur dioxide by individual drops of water. Their data were correlated by an equation which was based on the assumption that molecular diffusion within the drop controlled mass transfer. The equation was m(t) D t = l V(c* - c) 4/3 —d () o 2 Trr where m = amount of sulphur dioxide absorbed after t seconds (g) 3 V = volume of drop (cm ) c"< = concentration of the solute in the liquid phase at the boundary (g/cm3) c = initial concentration of the solute in the liquid drop (g/cm 3) Dd = diffusion coefficient of the solute (cmZ/sec) t = time of formation (sec) r6 = V/A for the forming drops, assumed constant A = surface area of a drop (cmz) Baird (1) compared the results of Coulson and Skinner (4) and of Groothius and Kramers (7) with an equation proposed by Ilkovic (14) and fully derived by MacGillavry and Rideal (17). The equation was de- veloped in the interest of studying the diffusion-controlled current in a dropping mercury electrode. The model for the derivation was a sphere growing at a constant volume rate and transfer of solute being controlled by diffusion in one of the phases. The solute diffused to— ward the drop surface where the concentration was zero. The mass of solute m that diffused in time t was given by /2 V2/3t1/2 1 m=3.57cD (2) where c is the concentration of the solute at the interface in the phase in which diffusion was the mechanism of mass transfer. The value of the partition coefficient was used to determine in which phase diffusion controlled. The data of Coulson and Skinner and of Groothius and Kramers showed a mean deviation of 18 percent about a straight line logarithmic /2 2/3t1/2. plot of m/c D1 versus V Present Method of Investigation of Mass Transfer From Individual Drops In the present investigation, the yellow solute picric acid was extracted from a toluene drop forming in a stagnant water phase. The drop was formed on a capillary tip positioned at the center of a column of square cross section. Glass windows in the sides of the column enabled motion pictures to be taken of the forming drop. Since the color of picric acid is much deeper in water than in toluene, the photographic image of the drop darkened as the acid was transferred from the toluene phase to the water phase. The images of the forming drop were trans- ferred from the film to glass photographic plates. Optical density measurements (the degree of ”darkness" of the image) were then taken from the images with a microphotometer and compared with optical density measurements of solutions of known concentrations. The total amount of picric acid which was extracted and the distribution of the extracted acid over the drop surface were determined from the measurements. This method was developed through the efforts of this work and that of Tambo (25), Jacob (13), and Patel (21). Tambo attempted to determine the amount of extracted acid from optical density measurements taken around the edge of the photographic image of the drop profile. This method was unsuccessful since the ex- tracted material was very close to the drop surface and it was difficult to distinguish the boundary between the extracted material and the drop. Jacob obtained optical density measurements through the center of a drop at various heights from which the average concentration of the extracted picric acid at each point was determined. The concentration 10 was assumed symmetrical around the horizontal periphery of the drop surface at any height. This method was checked by drawing a drop back into the capillary from which it was formed. The amount of picric acid which was left behind in the water phase was determined from optical density measurements. A value of 1. 48 was obtained for the ratio of the amount of picric acid left behind after withdrawing the drop to that extracted during the formation of the drop. This compares with a value of l. 927 which was calculated as an estimate of the upper limit for this ratio. The calculations are given in Appendix A. The value for the lower limit is 1. 0 and corresponds to no extraction during with- drawal of the drop. The value of the ratio obtained by Jacob seems reasonable since it falls approximately half way between the limits. However, the data were lower than predicted by theoretical models which were based on the assumption that mass transfer was controlled by diffusion in the continuous phase. Patel (21) showed that Jacob's data could not be explained even by considering diffusion as the mechanism of transfer in both phases and proposed that the low values of Jacob's data were due to the presence of surface active impurities in the system. Data were taken by Patel on a purified system and greater amounts of extraction were obtained. The results were in closer agreement with theoretical equations based on transport by molecular diffusion in both 11 phases, but since less acid was extracted than predicted theoretically, the interfacial resistance was not completely eliminated. One prOposed explanation for the low values obtained by Jacob and Patel was that ionization of the picric acid at the surface of the drops would affect the rate of extraction. Zeleny (31) showed theoret- ically that the ionization of picric acid as it is being extracted from the toluene phase to the water phase did not affect the rate of diffusion. As a result of the work done by Jacob and Patel, it was felt that additional data should be taken with more highly purified chemicals. THEORETICAL MODELS ON MASS TRANSFER FROM FORMING DROPS The present investigation is concerned with the mechanism of mass transfer from forming drops. The experimentally measured mass transfer from a forming drop was compared with that predicted by several theoretical equations. The equations were derived from various models, the final form of each equation depending on the as- sumptions made. Mass Transfer by Diffusion In the first three models mass transfer from a sphere growing at a constant volume flow rate was approximated by mass transfer from a plane surface to a semi—infinite medium. The effect of convection on the concentration distribution was considered negligible. Since the partition coefficient favored the drop phase, the mass transfer was con- sidered to be controlled by diffusion in the continuous phase. The un- steady state diffusion equation and boundary conditions are: 2 D Era—.3. : 8_c (3) C 3x at c (x, 0) = 0 c (0, t) — Hcd lim c(x, t) = finite x——»oo 12 where where 13 diffusion coefficient of the solute in the continuous phase time concentration of the solute in the continuous phase distance measured from the interface concentration of the solute in the drop phase, a constant concentration of solute in the concentration of solute in the partition coeffient ( continuous phase disper sed phase The solution to Equation (3) is c = Hc erfc[ x ] (4) d D 2 Ct x 2 \/Dct 2 erfc —X—-— : 1- _2_ e42 da. (5) 2‘\/Dct V? The rate of mass transfer across the interfacial area A is given Q9 (6) 09 8x fl:_D fdAici C x=0 14 where N is the amount of solute extracted. Substituting (4) into (6) /D dN = H cd -—C[dA t'l/Zdt. (7) 11' J Licht and Pansing (16) proposed that the rate of mass transfer across succeeding surface elements was equal to the rate of mass transfer across the first element formed. Therfore, jdA was equal to the surface area present at any time. 2/3 3 dA = 411' (£1- (8) 41r where Q = volumetric formation rate. Substituting (8) into (7) and integrating, l N 2 7/6 _ : . 34 . Coulson and Skinner (4) assumed that during the time of formation of the drOp, the extraction took place over the average area of the drop. Therefore, (10) where tf = final formation time 15 Substituting (10) into (7) and integrating, =3.27Hc 1/2 7/6 02/3 d DC t (In Haritatos and Liberman (11) assumed that the extraction from each new element depended on the time of exposure, te , of that ele- ment. The rate of mass transfer across each new element was independ- ent of the exposure time of the proceeding elements. Therefore, Equa- tion (7) become 5 tf D tri/z N=Hc —£ ft- dt dA d 17 0e e 0 / D tf W 1 2 N =Zlicd\- C (q-t)’/ dA (12) 0 2/3_1/ 2 3 3 Substituting dA = 3 (4n )(4—(3-T dt into (12), t 1/2 2/3 _]f f 1/2 __l6w 30 1/2 0 -0 N "—7§_"(4n Dc 0 1773' dt (13) With a suitable change in variable, the integral in Equation (13) becomes the 8 function (22). The evaluation of the integral can be found in Appen- dix B. Substituting the numerical value for the integral, Equation (13) 16 becomes N D:/2 t7/6 (14) Mass Transfer by Diffusion and Convection Ilkovic (14) derived an equation to predict the instantaneous diffusion current through a dropping mercury electrode. The equation was derived from a model which assumed that the convective diffusion took place in a boundary layer of thickness 0 on the surface of the drop. The drop was assumed spherical and the volume increased with time at a constant volumetric rate producing radial motion in the continuous phase. The drop growth was not accompanied by tangential motion of its surface. The equation of convective diffusion from a sphere in spherical coordinates and boundary conditions are: 2 BC BC _ 3 c 2 3c E+Vr8—r—Dc 2+r3r (15) 3r c(r,0) = 0 c[R(t), t] = Hcd t> 0 lim c(r,t) = finite r—voo where R — radius of the drop radial distance, spherical coordinate ’1 ll 17 The concentration of the diffusing solute was assumed to be sym— metrical with respect to the angular coordinates. For the radial velocity, the continuity equation gives v .r =constant Considering the drop surface, r = R and v = vR r v=v .R (16) Since the mass transfer was assumed to occur in a boundary layer r'R—TR + y (17) where y < < R and y is the distance over the boundary layer. The following approximations were made: 2 2 8 8 °:——9 (18) 2 2 3r 3y __ 23.21.. 9.9 -1 2.9. r BrNR r R 3y 82 1 8 l Cszs- >> ——Es::—g (19) 2 2 R By R 0" 8y 0' 2 . 2 8c . . 8 c From Equat1on (19), the term — 8—; was small 1n compar1son to 2 Br and was omitted from Equation (15). am (at _ac 8R) - _ : _ __ — A (at) l t) 8y(3t (0) r y h 33-1(19)1/3 1 w ere 8t ‘ 41r t173 The velocity vr was given by , 1/3 R 1 X 1 5Q -2/3 2X . z ._ AV, _ . 2.. ._ -— 21 Vr VR 2”“). 21 VR ZVR R 3) n) t 3)t ( ) r (1+ R) 8 By omitting the term E —C- and substituting Equations (20) and (21), r 8r Equation (15) becomes 8 2 8 82 _£ _ _ X _C = D C (22) 8 t 3 t By C 2 3y Introducing the variable, 2/3 2 = t ‘ y, Equation (22) becomes 2 8c 4/3 a c — = D A 23 3 t c t 2 ( ) 19 Substituting a new variable, Equation (23) become 5 8c 8 c (24) T=0;c=0 T>0;c=Hcd;Z‘0 T>O; c=finite;z———.oo The solution to (24) is Z c = H c erfc d 2'\/T =Hcderfc EY "\F.Z. Dt 7 \/ c By replacing the variable x by y and subtituting Equations (8) and (25) (25) into (6), the equation for the amount extracted becomes N Dc1/2 t7/6 (26) —2—7—3:3.57Hcd Q Another approximate solution to Equation (15) was derived by Michels (18). The boundary conditions for mass transfer were the same and angular symmetry was assumed. The final equation for the 20 amount extracted was N D1/2 t7/6 (27) —-27—3= 3.02HCd Q Michels also proposed another model. A description of the theoretical calculations follow 3. radial coordinate H II angular coordinate E II Figure 2. Cordinate system for a forming drop according to Michels' model. A mass balance for the transport of a single component in a fluid with constant liquid diffusivity was given by 8c 8c 8c 1 8 8c . 1 8 28c 8t+Ur8r +Uw 80.) DC 2 , 3... 800 1n”) 23:11' 8r ‘28) r Slnw r Spherical symmetry was assumed in the other angular direction. The angular direction (.0 is shown in Figure 2. The first term in the brackets 21 on the right side of the equation was omitted since the diffusion in the direction tangent to the drop surface was considered negligible. The radial velocity, Ur , and the tangential velocity, Um, were determined from an appropriate combination of velocity potentials for an inviscid fluid. Substituting Ur and U00 into Equation (28), 82c 2 8c 8c Q l 1 8c D 2+—-é- :7" 2 1-—3 cosw-—-2- 5— C 8r r r 41TR X X r -——93—- 1+ )sinw _8_E (29) 4TI'R X 2X 80.) where f 1 1. U = - QZ El-rrrélcosw --1-2- I 41rR ) 2X ’ X Q I 1 ~. Uw—- 211+ 3(sinw 41TR L 2x} r = radial distance, spherical coordinate r X = — R and Q = volumetric flow rate The boundary conditions for mass transfer were lim c(r, (.0, t) = finite r —*oo c(r,w,0) ‘ 0 c[R(t),w,t) = Hc ' t > 0 d) 22 Neglecting tangential mass transfer by convection and considering diffusion of the solute close to the interface, the solution to Equation (29) was 3 (27; +-2- cos w)l/2 c=Hcd erfc U 1/2 (30) 0 where r - R : - 1 : U X R 411DC 8 = R Q The equation for the rate of extraction is 8N _ 8c 8t--Dcf8r r=RdA (31) Substituting (30) into (31) 1T H c aN _ d 1/2 1/2 1/2 8t-—7—3 2 D Q j (7+6 cos w) dA (32) 217R 0 Integrating over each element of surface by substituting dA = 21rstinw dd) 3 and R = (-—Q-}) , Equation (32) becomes 411' N D172 t7/6 (33) 7—3 = 3.45Hcd Q 23 Determination of N by Considering a Volume Element in Space In this work the equation for the total amount extracted was also derived by considering a volume element in space. dN=ch =c 211 r2 sinwdwdr (34) 11 oo = 211 H c erfc (r-R) a r2 dr sinw dw (35) d R 0 r 1/2 Q 4 (11 Dc R)1/2 whe re 1/2 ___ (7+6 cos (.1) Equation (35) can be integrated with respect to r holding wconstant if a change in variable is made. Let r-R a=x ( R 1 R 2 2 2 2 dr=— dx andr :R —X +_X+1 a a2 a Substituting the new variable into (35) and integrating, 1 N: 211 H cd R/ 1T/OOO: — + -:2£+; erfc (x) dx sinwdw 11 =211Hc R3 —1————+——2—+ d 0 3%: a3 4a2 V11a sin to doc (36) 24 . . . . 3Qt 1/3 . Integrating w1th respect to to and substituting R = ( a?) , Equatlon (36) becomes N‘ 3/2 3/2 1/3 4/3 1/2 2/3 1/6 =11.79D t +9.95DQ t +4.1D Q t (37) H cd c c c The first and second terms are much smaller than the last term on the right side. Therefore, a good approximation to Equation (37) is Hc 273“ ' d N — 4 1 Di/Zt7/6 Q (38) Obviously, there is a difference between the two methods of determining the total amount of solute extracted. The results of both methods are given in Equations (33) and(38). The only explanation given at the present time is that the assumptions used in deriving Equa- tion (3) somehow cause this difference. All of the equations derived from the proposed models were of the general form N Di/2t7/6 —7—2 3 =KHcd (39) where K is a constant depending on the model. The values of K for the models are summarized below: 25 Investigator Value of K Licht (16) 2. 34 Coulson (4) 3. 27 Haritatos (11) 4.03 Ilkovic (14) 3. 57 Michels (18) a. Equation (27) 3. 02 b. Equation (33) 3. 45 c. Equation (38) 4. 1 APPARATUS A photographic technique was used to study the extraction of picric acid from a toluene drop forming in a stagnant water phase. Motion pictures of the forming drop were analyzed to determine the total amount of acid which was extracted and the distribution of the ex- tracted acid over the drop surface. The apparatus consisted of a vertical extraction column, a light source, standard cells, a drop forming device, a light filter, and a camera mounted on an adjustable platform (Figures 3 and 4). The extraction column was fabricated from four brass bars 30 inches long and 3/8 inches thick which were soldered tOgether form- ing a square internal cross section of one inch on a side. Two open slots were machined in the front and back faces of the column so that there was an inside distance of 1. 25 inches between two 1/4 inch plate glass windows eighteen inches long and one inch wide which were sealed in the Openings with epoxy resin (insoluble in water and toluene). A brass measuring scale with several holes one centimeter apart was fixed at the center of one side of the column so that the holes were vis— ible beside the capillary and could be photographed with the forming drop. The light source consisted of three 20-watt blue fluorescent tubes each 1. 5 inches in diameter and 23 inches long which produced a high light 26 27 intensity in the desired 3800 to 5500 X wavelength range (30). The tubes were placed vertically side by side parallel to the back face of the column and operated by a 1000 cycle alternating current power source. For a lower frequency current, say 60 cycle, it was observed that the light output per frame of motion picture film varied sinusoidally with time. A piece of window glass ground on one side was placed be- tween the bulbs and the extractor to diffuse the light. Optical density measurements taken from pictures of the forming drops were compared to optical densities of solutions of known con— centrations. The latter solutions were photographed in brass standard cells which were three inches high with windows two inches in length and all other dimensions the same as those of the extraction column. Pictures of the forming drops and standard solutions were taken at 35 frames per second at f2. 8 with a Bolex Paillard movie camera using 16 millimeter Kodak, Plus X, reversal safety film. A number 34 Kodak Wratten Filter was placed between the camera and the front face of the column. The drop forming device consisted of the plunger drive shown in Figure 4, a variable speed transmission, and the syringe shown in Figure 3. The drops were formed at the tip of a 0. 037 inch inside diameter glass capillary which was joined to a 20-gage hypodermic needle with epoxy resin. The end of the needle was bent at a right angle 28 [ CONTINUOUS PHASE EXTRAOTOR aoov MEASURING if? FLUORESCENT smp .1 / LIGHT ' LIGHT GLASS \' DIFFUSER 11111100111 1 / \ E J LIGHT FILTER \ - / ' DROP W/ F svamee 0/ CAMERA— 1 j \ k j SPINDLE CAPILLARY TO 011111111 Figure 3. Apparatus used to photograph the forming drops. 29 63.6 Homes?“ .v unswmh A 22mm imzo< unozam \ 85 .232; mmqunum $.38 unozEm 30 and was held in place in the side of the extractor by a rubber stOpper which was coated with epoxy resin. The level of the drop phase in the capillary was adjusted to a point below the tip by screwing the manual advancer against the syringe plunger so that a pocket of air separated the continuous and discon- tinuous phases in the end of the capillary. The column of air prevented mass transfer between the phases until the drop began to form. The volume of the drop phase which was forced into the capillary in order to form an air bubble plus a toluene drop was controlled by the distance between the collar and the collar stop and was the same distance which the spindle moved the plunger. The motion of the spindle was produced by engaging the arm on the spindle with the screw that was driven by the transmission. The arm on the spindle was lowered on the threads of the screw by depressing the spindle release. The spindle release was locked in the depressed position by the collar stop. As the spindle moved forward, the collar pushed against the collar stop which allowed the spring to return the spindle release to its initial position and simultaneously the arm of the spindle was disengaged from the screw. Formation times ranging from 0. 15 to 20. 0 seconds could be obtained by adjusting the output speed of the transmission. EXPERIMENTAL PROCEDURE Preparation of Chemicals and Solutions Two different purities of toluene were used as the drop phase. The first source of toluene was prepared by triple distilling a C.P. grade toluene in an 18 inch, all glass distillation apparatus packed with 1/4 inch Raschig rings. The first 50 milliliters of the top product and the last 50 milliliters were discarded each time. The boiling and product flasks were rinsed each time with acetone, dis- tilled water, cleaned with a solution consisting of 5 percent hydro- fluoric acid, 30 percent nitric acid, and 65 percent water by volume, rinsed again with distilled water, and dried by heating with a gas flame. The product was collected over the boiling range of 111 if 0. 50C. The second source of toluene was a spectroquality reagent purchased from the Matheson Coleman 8. Bell Company. The water used in all rinsing operations and as the continuous phase was distilled in a glass apparatus. The water for the con- tinuous phase was saturated with toluene and the toluene for the drop phase was saturated with distilled water. A Baker Analyzed reagent grade picric acid was recrystallized three times from the same toluene that was used in the runs. The cleaning procedure described above, neglecting the acetone rinse, was used to clean all the glass apparatus each time the acid was 31 32 recrystallized. The recrystallized picric acid had a melting point of 122. 3 i 0. 10C. This compares with a value of 122°C obtained by Moore and Peck (19) in recrystallizing picric acid from benzene and a value of 122. 50C obtained by Brownlie and Cumming (3). The concentrations of all picric acid-toluene solutions were determined by titration with sodium hydroxide solutions to the end point of bromothymol blue indicator. An appropriate amount of pure ethanol was added to each titration sample to form a single phase; otherwise the titrations would be diffusion controlled since toluene and water do not mix. The conentrations of the sodium hydroxide solutions were determined by titration with potassium acid pthalate (primary standard) to the end point of phenolphthalein indicator. The picric acid-water standard solutions were prepared by dilu- tion. A solution of approximately two grams per liter of acid in water was prepared from which portions were taken and diluted with water to the desired concentration. The optical density of a picric acid-toluene solutionchanged when exposed to the light source for a period of two weeks. Measure- ments were taken with a Coleman Universal Spectrophotometer at a wavelength of 4600 X. The optical density remained constant for eight hours and increased linearly with time over the remaining period. This change was not observed with a sample of the toluene solution which was placed in a dark area or with samples of picric acid-water 33 solutions tested under the same conditions. As a result, all solu- tions were stored in the dark. Procedure for Taking Data Prior to making a run, the extractor was rinsed with acetone, water, cleaned with a detergent and rinsed for at least three hours with tap water followed by rinsing with a dilute sulphuric acid solution and finally with distilled water. The lights and transmission were allowed to warm up for a half hour. Between dr0ps, the column was drained and rinsed with the continuous phase. The capillary was rinsed after each drop with dis- tilled water and blown dry with filtered air. The solutions of known concentrations were photographed in the standard cells at the same position in front of the fluorescent tubes at which the drOps were formed so that both would be exposed to the same light conditions. Solutions of picric acid in toluene saturated with water and in water saturated with toluene were photographed. The Speed of the camera was determined by photographing the movement of the hands of a stOp watch and counting the number of frames of film exposed during a one second interval of time. The experiments . 0 were carried out at a temperature of 25 '1 2 C. Film Processing and Optical Density Measurements The 16 millimeter Plus X reversal movie film was deveIOped as a negative. Each roll of film contained the standard solutions and the 34 drops, so that both were processed under the same conditions. One frame of each standard solution and selected frames of each forming drop were cut from the film and enlarged on 4" by 10H Kodak No. 1 photographic plates. The images on the film were enlarged approximately 5 times by a Wollensak 135-millimeter enlarger. The photographic plates were exposed for approximately 2 seconds at f 32, developed in D-19 Kodak developer for 8. 5 minutes, rinsed in 5 percent acetic acid solution for 40 seconds, fixed in Kodak acid fixer for 15 minutes, washed in running water for 20 minutes, and dried. Two photographic plates were exposed for different times to the light source of the enlarger as a check on the uniformity of the emul- sion and the light of the enlarger light source. Seventy-eight readings of percent transmission were taken from the first plate with a densi- tometer (recording microphotometer, Jarrell-Ash Model 203) and 108 from the second plate. An average value of 42. 5 percent transmission with a standard deviation of 2. 02 was obtained for the first plate. An average value of 26. 7 percent transmission with a standard deviation of l. 35 was obtained for the second plate. The deviations from the average values were attributed in part to the granularity of the plates and in part to non-uniform dispersion of the light sensitive particles in the emulsion. The uniformity of the film was determined by taking pictures of a standard solution at the beginning of a roll of film, half way between 35 the beginning and the end, and at the end. Percent transmission readings taken with the densitometer using an unexposed portion of the film as the 100 percent transmission reference showed no significant difference between the three readings. After the plates were processed, optical density measurements were taken from the drop images and the standard solutions. Readings were taken at 0. 02 millimeter intervals on the plates. The densito- meter was turned on a half hour before being used and occasionally the references for zero and one hundred percent transmission were checked. The variation of the drop diameter over the drop height was determined from images of the drops on photographic plates which also contained the images of the one centimeter spaced holes of the brass measuring scale discussed in the section on Apparatus. The images were enlarged approximately 50 times the size of the images on the film. The measured diameters were compared with the distance between two consecutive holes in order to obtain the actual diameter. ANALYSIS OF DATA Relationships were developed to relate the "darkness, " i. e. optical density, of a photographic image of the drop to the total amount of extracted acid and to the distribution of the extracted acid over the drop surface at any instant during drop formation. One advantage of using the picric acid-water-toluene system was that at equivalent con- centrations, solutions of picric acid in toluene transmitted one hundred times as much light as solutions of picric acid in water for the wave- 0 length range of 3800 to 5500 A. Determination of the Total Amount of Extracted Acid from Optical Density Measurements Through the Drop Image Jacob (13) experimentally showed that Beer's and Lambert's laws of light absorption were valid for a narrow wavelength range of light being absorbed by consecutive solutions of picric acid in toluene and water. A standard cell was constructed with three compartments which were separated by thin glass partitions fixed parallel to the windows of the cell. In each experimental run the center compartment was filled with a picric acid-toluene solution or a picric acid-water solution. The two side compartments were filled with solutions identical to one another. An optical density measurement (photographic plate optical density) was taken for each combination of solutions. 36 37 Two calibration curves of optical density versus concentration were prepared; one for aqueous solutions and the other for picric acid-toluene solutions. For each point of data , the solutions in all three compartments were identical. With the aid of the calibration curves and assuming that the concentrations of two of the compartment solutions were known, the concentration of the solution in the third compartment was determined and compared to the actual value. There was an average error of 2. 7 percent in six of the seven runs carried out and 21. 7 percent error in the seventh run. The highest concentration of picric acid-water solution that was used in Jacob's experiments was 0. 0325 grams per liter. Assuming that equilibrium was established, the concentration of the picric acid in the water phase at the interface of a growing drop would be approx- imately 13. 0 grams per liter or less depending on the concentration of the acid in the drop phase. Consequently, additional experiments have been performed using a three compartment standard cell and higher concentrations of picric acid in water. The results are given in Table 1. Only one calibration curve, Figure 5, was needed since only water solutions of picric acid were used in the experiments. True average concentrations were cal- culated and compared with values determined experimentally. The true average concentration, Cav , was calculated from the relationship 38 2.3 l 2.0 1.5 l]!]F[lll|l[TTlTT[T| Optical Density 0 'ITI'I'T'I'T'T'T'I'I 7 I .01 .02 .03 .04 .05 .06 Concentration (g/l) Figure 5. Three compartment standard cell calibration curve of picric acid in water. 39 N (1/3) uotienuaouog .m can v 93% CH hmvo .o oomo .0 004.0 .0 mmoo .o vmmo .o mmoo .o mmmo .0 come .o 989.13sz pauiunaieq An'eiueuxtxadxa 133cm ofimcwm m mm meadooaofi paw meow mo GOSMSCooGoo owmno>m .:mooo.o +1. :oo~o.o n A one **% 1H a: :mooo .o+ mo Houno wcwudmmmfi m wasooom 02: mmxmu paw maom oumuoa mo Gowumaucoocoo mwmuoefim ecu. meow 3983 Ho coflmficwocoo owmnoiw * A can .:wm\..m .O n .:mooo.o fl :mvoo.o n m owvo.o wao.o cho.o ommo.o Hw~0.o memo.o ommo.o Ammo.o memo.o Empo.o wmmo.o mnmo.o Ammod vowed mnvod Hmoo.o onmo.o Nmmo.o ammo .o Ohvo .o mmvo .o Hmvo.o onmo.o mmmo.o ***U **U *0 :\wv con—whacoocoO ommno>< odnH. H N .:Hmhm.O H A .w 98 .e .e .m .N .2 28m 5 0:. .H Mom .0 omv A hwfi .N ammo; 5: .N owm 4 3% .H Aiisuaq 19311d0 paxnseew HA : Ho .0 : No .0 H06 : No .0 : Ho .0 mth .: a NO 0 3 \mV GowumHuCoocoO com :oO “CoauummEoO 66.25. .m 5 364 owuownm mo mcoflgom mooosw< mo mcoflmbcmocoO ommuoaq. Hmucoefluomxm pad 33H. 2% mo GOmwummgoO A 3an 40 L=CL+CL+CL 4o Cavg 1122 33 () where L1 = thickness of solution C1 in the first compartment L2 = thickness of solution C2 in the second compartment L3 = thickness of solution C3 in the third compartment 2 + + L L1 L2 L3 Since C1 = C3 and L1 = L3, Equation (40) becomes : 4 CanL 2C1Ll + C2L2 ( l) The experimental average concentrations were determined by com- paring the optical density measurements of column 4 in Table l with the calibration curve. The experiments were carried out at a temperature of 26. 70C. Since picric acid ionizes in solution, both molecules and picrate ions are present. There is a problem as to whether the absorption of the molecules is the same as that of the picrate ions. The experimentally determined average concentration is actually a measure of the concentration of the light absorbing particles in solu- tion. Therefore, the concentration calculated by Equation (41) should be the true average concentration of the light absorbing particles. Hantzsch (9, 10) and Halban (8) proposed that the undissociated acid exists in two isomeric forms in equilibrium with one another. The 41 first, the normal form, should show practically equal light absorption as that of the picrate ion, while the other, the pseudo form, could have different light absorption. Halban and Ebert (8) defined the monomolecular equilibrium concentration of normal form constant as . and spectrophotometrically concentrat1on of pseudo form found its value to be 4. 0 x 10"4 at a wavelength of 4500 R. They as- sumed that the normal form of the acid absorbed the same as that of the picrate ion and that the pseudo form did not absorb the light. The degree of light absorption by an aqueous solution was taken as a meas- ure of the concentration of the picrate ion since very little of the normal form extisted at equilibrium. As a result, two different average concentrations were calculated by Equation (41) and compared to the experimental values. Column 5 of Table 1 gives the average concentration of picrate ions and column 7 gives the average concentration of both ions and molecules as a single entity. The degree of ionization for the higher concentrations, 11. 5729 and 5. 0060 grams per liter, by calculations given in Appendix C, was 77 and 87 percent respectively. The lower concentrations were es- sentially one hundred percent ionized. Referring to Figure 1, the results can not be explained by as- suming that only the picrate ions absorb the light. Column 6 takes into account the effect of a positive measuring error on the actual average 42 concentration of the ions in the cell. There is still a difference of l. 25 to 11.70 percent or an average of 6. 88 percent between the values in column 6 and the experimental values in column 8. The values given in column 7 were calculated assuming that the acid is completely ionized for the concentrations that were used or that the molecules absorbed as much light as the ions. The values in this column agree with the experimental values within the measuring error. Applying Beer's and Lambert's laws of light absorption to a series of phases L. 1 n 1 D : 10g — = 2: f K, C. dX (42) o t . 1 1 1:1 L. 1-1 where D0 - optical density t = Ii 2 fraction of light transmitted o I ‘-‘ intensity of light exiting from a series of solutions 10 = intensity of light entering a series of solutions Ki = a constant for phase i at a particular wavelength ci = concentration in phase i L - L i. i—l = thickness of phase i dx = differential thickness n = number of phases 43 For the case of light passing through a liquid drop of toluene in water, Equation (42) becomes L1 L2 I"3 D = K C dx+ chx+ K c dx (43) o w wl t t w w2 : L L I40 0 1 2 where L1 = distance in front of the drop L3 = column thickness L2 - L1 = drop diameter at the position of optical density measurement L3 - L2 = distance behind the drop Subscripts w and t refer to the water phase and the toluene phase respectively. Since less than 1 percent of the acid initially present in the drop was extracted, the concentration in the drop was approximately constant. Therefore, L2 Kt ctdx = KtCtO (L2 — L1) L1 where cto is the initial concentration of the picric acid in the drop. Assuming symmetry about a vertical axis through the drop, 44 Therefore Equation (43) becomes D =2L + L-L 44 c K Kct0(2 ) i) o lw'avg w t 1 The second term on the right side of Equation (44) can be replaced with a picric acid-water solution optical density by applying Equation (42) to standard solutions of water and toluene. D ' ' = K L - L : K ' L = K ' L 4 rop optical den51ty tct0( 2 l) t Cst 3 wcsw 3, ( 5) where cs't = concentration of a standard toluene cell that absorbs as much light as the toluene drop _ C (L2- L1) ‘ o t L3 cgw = concentration of a standard water solution that ab- sorbs as much light as the standard toluene solution of concentration c'st c'SW was found from the value of c'st and standard cell calibration curves of optical density versus concentration for water and toluene solutions of picric acid. Substituting (45) into (44) D=2Lc +Kc' L. (46) o 1w,avgw wsw3 Since D =K c L3, (47) o w sw where c is the concentration corresponding to each density measure- sw ment along the vertical axis of the drOp, Equation (46) becomes 45 (Csw - CSW) : 4 C:w, avg L3 2L ( 8) Csw is obtained from a standard cell calibration curve of Optical density versus concentration of picric acid in water. It should be emphasized again that all Optical density measurements correspond to photographic emulsion optical densities and not to solution Optical densities. However, solutions with equal optical densities will have equal photographic emulsion Optical densities. Assuming that the extracted material is close to the drOp surface, the total amount of extracted acid can be determined by integrating Cw, avg over the surface of the drOp. Referring to Figure 6, db repre- sents the height over which the density measurements were made and dx represents a small element of the drOp circumference. The total amount of extracted acid is HI Csw' Cew :j 11D L dh (49) 0 46 h=H' Extracted material | Capillary Figure 6. Coordinate system for determining the total amount of extracted picric acid. Equation (49) was numerically integrated using a digital computer. A summary of the procedure for determining the values of the terms in Equation (49) is given below. Referring to Figure 6, Optical densities are measured along the h axis at equal intervals. For each point on the h axis the diameter, D, of the drop is determined. Two calibration curves of optical density versus concentration are prepared; one for solutions of picric acid in water and the other for solutions of picric acid in toluene. The solutions are photographed in the standard cells. 47 The values of Csw are Obtained from the picric acid-water curve. The concentrations corresponding to the drop Optical densities are the required values. For each point along the h axis, ctO(D/L3) is calculated and the Optical density corresponding to this concentration is obtained from the picric acid-toluene calibration curve. The concentration corresponding to this optical density on the picric acid-water curve is the value of Cl sw' Experimental Determination of Solute Distribution Over the Drop Surface Consider Figure 7 in which: h = height measured from the capillary tip dh = differential height T = tangent at point 0 P - line perpendicular to T at height h 0 - angle between the line P and the diameter at height h dS arc length along the surface of the drop for differential height dh Figure 7. Coordinate system for determining the distribution of the 48 extracted picric acid over a drop surface. The surface area dA of the drop along height dh is given by Since d5 = dh/cos 8, From Equation (49), Dividing (51) by (50), dA = 11D dS dA 11Ddh cose dN= w W 2 (c -C' ) dN _ sw sw — - L cos 8 dA 2 3 (50) (51) (52) N A plot of -d— 'versus h represents the distribution of the solute over the dA drop surface. 49 Theoretical Determination of Solute Distribution over the Drop Surface Considering the washer shaped volume element in Figure 8 and Equation (30), -:—E- was evaluated as follows: (1 51$ _211cxdxdh dAp ’ 211x'dh .. by) .. _./ x' = radius of the drop at height h Ad = element of surface area Ap = projection of Ad in the x direction Figure 8. Coordinate system for determing the theoretical distribution of the extracted acid over a drop surface. The concentration of the extracted material declines very rapidly as the distance from the drop surface increases. Therefore, x was equal to x' and 50 dN (1(3r «ICdX P (D (X) 1/2 r-R 7/4+6/4cosw 1/2 j—NNIR:: 2:] Hcderfc ( R )( r11DCR ) Q dx (53) cIAP RZ-h2 2 Lettingz=x/r, r= x2+h2, andcosw=h/ Vx2+h , h/R 1/2 0° 7/4+6/4 2 2 —dN a: Hc erfc (1/z2+(h/r)2- H z +(h/R) ) dA d 4 P 2 11 (ll-(hm 2 Q 1/ Rdz (54) DcR , in the x In Equation (54), Ap is the projection of the drOp area, Ad dN dA , the amount of d solute in the continuous phase per unit area of drop surface at a given direction. Multiplying (54) by ([1- (h/R)2 gives height on the vertical axis of the drOp. The multiplication factor does not apply when |h| > R. Equations (52) and (54) were solved using a digital computer. Calculation of the Overall Mass Transfer Coefficient The overall mass transfer coefficient was defined by the following equation: 51 ‘21.— = w avg“ ‘55) where Ac = Hcd, since c = 0 in the water phase KW = overall mass transfer coefficient based on continuous phase resistance Aavg = 3/5 Af= average area exposed during drop formation Af = area formed in time tf dN 71? was obtained by measuring slopes at time t from a plot of N versus t. Theoretical mass transfer coefficients were determined as follows: From Equation (39), N = K H c D:/2t7/6 Q2/3 d Differentiating, 93-1 = 7/6KH Dl/Ztl/éQz/3 dt c and dN _ : K dt w (3/5 Af) H cd where A :4“ g 2/3 f 411 Equations (56a) and (56b) were solved for Kw. 1/2 0. 400 K Dc Kw : V2 tf (56a) (56b) (57) 52 Effect of Dispersed Phase Resistance on Mass Transfer Assuming that the transport of the picric acid was short range and controlled by diffusion in the continuous phase, H VD Ct0 c 2 F (58) VI? 1 Patel (21) derived a relationship for the flux of picric acid through a Flux through the interface I plane surface in which diffusion was considered as the mechanism of mass transfer in both phases. _ IthO V Dc Vat/H _ (59) F 2 WE Vin/Em Dividing (60) by (59), F2 j/Dt/ H F1 VDC + VI):/H (60) The diffusivity of picric acid in water at a temperature of 25.05 '1’ 0.050C was measured using a Mach-Zhender interferometer. Details of the measuring technique are given elsewhere (2). The error using this method was not greater than 1 percent. The results are given in Table 2. For calculation purposes, an average diffusivity was used. The average diffusivity was defined by 53 '13 D dc 0 - -5 2 D = -————————-—— =1.250x10 cm /sec (61) 13 dc Table 2. Diffusivity of Picric Acid in Water Concentration of Picric . . . 5 2 Acid in Water (g/l) D1ffu81v1ty x 10 (cm /sec) 1. 006 ‘ l. 262 2. 506 1. 311 6. 500 1. 332 10. 714 1.146 The concentration of the picric acid in the toluene phase was 114. 9 grams per liter and from the distribution data of picric acid between water and toluene given in Appendix D, the concentration of picric acid in equili- brium with the drop phase was 13. 0 grams per liter. Patel calculated a value of 1. 31 x 10_5 cmZ/sec for the diffusivity of picric acid in toluene using the Wilke (29) correlation. Substituting the above data into Equation (61), F __?. F1 = 0.90 (62) 54 Consequently, if complete mixing is not attained in the forming drops, the dispersed phase resistance can not be neglected. Theoretical Calculations Based on the Assumption that only the Picrate Ions Absorb Light If it was true that the picrate ions absorbed light and the molecules did not, the experimental data would only be a measure of the amount of ions in the aqueous phase. For comparison, the theoretical models would have to be based on the same assumption. Coulson and Skinner (4) assumed that the extraction from a growing drop could be approximated by extraction from a plane surface of area equal to the average area of the sphere defined by Equation (10). As- suming that only the picrate ions absorb light, dN' = fCAavg dx (63) where f = fraction of picric acid ionized at concentration, C x 2 distance from the plane surface of area, Aavg Aavg = average area of the drop defined by Equation (10) N' = amount of ions in the water phase f was calculated from 2 Keq : lcff (64) where Keq = equilibrium constant. Substituting Equation (4) for c and Equation (10) for A into (63) avg 55 (I) N'= f(-:-)(3611 oz t2)1/3 Hcderfc —— dx (65) 2 VDCt 0 At 25°C, Keq = o. 133 and Hcd : 0.013 grams per milliliter. Equation (65) was solved using a digital computer. Equations (11) and (65) are compared in Figure 9, a logarithmic , 2/3 . . plot of (N or N )/Q versus t1me. The upper line corresponds to Equation (11) and the lower line to Equation (65). 56 300 Ill 200 I 100 ' I 'l'l'l‘l'W'l p—o O 'l‘l'l'l‘l‘lrl'l (N or N')/QZ/3 (10)5 l ' 131'1'1'11'1'1 l .1 1 1 1111111111111111 1 14111111111111111 L 1 1111111111111111 .01 .l l 10 Time (sec) Figure 9. Comparison of the total amount of picric acid extracted to the amount of the acid ionized according to Coulson and Skinner's model. SUMMARY OF RESULTS The data in Table 3 are a summary of the results Obtained for both the distilled and spectroquality toluene. Each drOp was analyzed at various times during the formation period. Each analysis is labeled as the drOp number and a collection of drOp numbers of a particular forming drOp is called a drop set. DrOp sets 8, 10, and 12 were ob- tained using the spectroquality toluene as the drOp phase. The data for drOp sets 1 through 6 were taken from the same photographic plate and roll of film. The data for drOp sets 8, 10, and 12 were taken from a different plate and roll of film except for the drop numbers with primes. The images of the drop numbers with primes were taken from the same roll of film on which drOp sets 8, 10, and 12 were photographed, but were analyzed on a separate plate. For comparison, the data are given in Figures 10 and 11 as /3 logarithmic plots of N/Q2 versus time along with plots of the upper and lower limits of Equation (39). The overall mass transfer coefficients are compared with the upper and lower limits of Equation (57) in Fig- ures 12 and 13, logarithmic plots of KW versus time. The distributions of the extracted acid over the drOp surfaces are represented in Figures 14 through 17 as plots of dN/dAd, the amount of acid in the water phase per unit area of drOp surface, versus height from the tOp of the drOps. For comparison, Equation (54) was solved for drOps 57 58 which closely approximated the shape of a sphere with the results shown in Figure 18 as plots of dN/dA versus height from the tops of d the drOps. The initial concentration of the picric acid in the drOp phase for drOp sets 1 through 6 was 116. 3 grams per liter and 114. 9 grams per liter for the remaining drOps. In drOp sets 1, 2, 3, 4, 8, and 10 there is an estimated time error of L1 0. 014 seconds, '1 0. 028 seconds in drOp set 12, and 31‘ 0. 006 seconds in drOp sets 5 and 6. 59 me .0 Ne .mN om O o A: com .m w co .H ow .NH hm .w v .Ho oom .N m cm; mm.NH HmN 041v oomé N Nm xv ma .m Nw .H NH .H WMN com .o HtN mwN .0 pm .om 5N .o N .moH Amp .0H m hmm .o 00 .MN oo .w o .ow meow .w m «11m .0 or .NN pm .0 M .0m mow .w o mmw .0 mm .mL NH .m m do mow. .m m “:0 .0 MN .MH NN .m o .mv mow .m w mo .H mm .oH mN .N N .wm meow .N m 00 .N Ho .m wN A m .mN meow .H N mood mo.N ammod mmvd m.NH oovd and OH x Aoom\gov OH x va OH x Aoom\AmEov .02 m a ewfinbxm N Sam 3on m2 x $83 NS x ANEUV 3ch e85. nee M “5593‘. OTSOHESHO> mEdHo> don/w Goflmauoh QMMmQ damn mo Fumacndm .m 338B 60 MNN mm.m~ Odd NUMN. omwd w H06 No.: 34‘ wdm MNOO m mm .m mm O Ow .N w .onv com .o N Hm.: omim hoO Named \1.ON oodd Htv ma 4 mO.¢N hmd v.2: MNNN m cm A on OH mo O m .wh mom 4 w mo; wodfi >m.¢ mdm woNA N do .N 3‘ 41 NN. .N H.m¢ mom .0 N NO .w om .m Ow .m ON .H o .wN “ION .o Him OOOO wth Nwé mm .0 oNoH OOm .m th OH x AOOO\EOV O0H x Amy NoH X Aoom\maov OH x A 9.8V OH x A gov Aoowv @838 “MM m 3% pmuomuuxm 3mm BOTH N Oggnm> N 803W Gowumghoflm “Om Ocsoefiw OTSOSBHO> QOHQ 625388 .m @333. 61 : .nm SUN mw.m How .0 odd hmod Him Ev .m no .m ow .N o .3. mNN .o m AHA: Nimrm Np; adm 3; .o N ANNA MN .N mm .2 Sec .o a.: wmod H1O «.0 .m ON .N mm .m N .w» wmm .o m Nth .w Ma .0 ow .w N 4O ONv .o v mm .m O0 .N. 5N .m n .3... com .o m MN .w Om .v mm .H m .mm «.3 .o N OMAH mmN ¢>.o~ vNé N..mN O0“ .0 Hum ow. .N NO .wN >0 O mo .q H .00 owN .H mtv x E x w x o m 80 .oZ MOM AU®m\ UV QOH A v NOH A 0 \m v OH Uh A EUV OH x ANHHHUV AUQWV UEflyHL fig“ 3 Ovuomflxm 3mm 2,lo N m N M m530> «1.6.14 son—manoh uom 3.90814 OMSOFSHO> gong AOODGSGOOV .m e33. 62 mew .o NO .vN Nw .A. N .mw vAN .N m ow; mOOA Nw.m ANN. :OA 4. mm .N wwél wwfi oém oNA .A m N04» mmd ooé 96m me .o N m: .Nm mOo .o we. .m N: .o Om .O mvo .o AtoA voOA NA .m NA .A m.¢N OONO L ON; omON mwd wéo Ann; m ow .N AN .ON A; .O Adm. ooo .A 2v ON .m OO .3 mm .w N .mm OwO .o m Oc .oA Om .: mm .m 0N .N m .5»). Hum .o Nam x own 80 x w on own EU .02 m3 A \ V O3 A v NoH A \m v A: x A Boy OH x A gov Aommv 0&5. van 3 UOOOOHHXH 8.8m 30AM N m. N N M o830> mon< Goflmfizom pom B5084 OTSOEOAOAV QOHQ Aeneanceoov .m 283. 63 HA.~ OO.>N mm.w O.N© ooo.m .® Am.® mw.N >O¢.o ®.NH owN.O .m AO.mH Nw.A wom.o ®©.© MvH.O .N NO.H mm.hm h¢.© v.00H 00¢.m h NH.A No.0N NM.N m.¢m Hhm.¢ O NH.H Om.MN vb.m O.Ah wmm.m m MN.A No.wH Nm.¢ w.wm hmO.N v Nh.A Aw.¢a NN.N h.m¢ OO®.~ m Oh.m ¢O.w N¢.H 0.5N m¢©.O N no.b~ wO.~ OO.~ PNN.O ww.h owo.o H1NH mm.® m>.m mmw.o m.®~ HNN.O .N mw.ON ®¢.~ w¢.m wNm.o 0.0A OO~.O .A1OH x w x m 5 .02 m2 x Anemflfii neemwnnmxw mezeeemcflnmm 3 m2 x AME”: m2 x £83 153 care can M “c.9084 330853.? OEDAO> dofiq. Comumauoh QMMwQ ApodcficoOv .m 2an 64 200'— _ Drop Set 100:: o 1 E . 2 K = 4.1. O :_ 0° :- [J 3 0 :- c? .. I 4 _, db _. A 5 D O A A10 .— 6 D m .- o L— . ' :1 E Slope = 1.167 7 on" :- _ O E -— .,. O '- IA \ .— z _ A )— I A _ A I; A L K = 2. 34 ,1 11111J1111111|11 1 I 1111111111111111 1 1 1111111111111111 1 1 .02 .1 1 10 Time (sec) Figure 10. Comparison of the experimental data with that predicted theoretically using the distilled toluene as the drOp phase. 20 65 200 1 Drop Set 100 ' I ' I'l'l'l'l'l'l T 1 10 Slope = 1.167 O l I rrlTUlllllllll (N/QZ/3) 1105) r K=2.34 T 1 r1'T'l'l'l'l'l'l _1 1 11111111111111111 1 11 111111111111111 1 1 1111111111111111 .01 .1 l 10 Time (sec) Figure 11. Comparison of the experimental data with that predicted theoretically using the spectroquality toluene as the drop phase. 100 10 ’6‘ CD in \ E 3. M 2 X 3 M 1 .1 66 ; Drop 5 Set 5' o 1 F- ” Slope = -0 5 D 3 -— A _ . 4 '7 K 2 34 A. A A 5 — Z . A. E A 6 1: r a ‘ _ A _ . K = 4 1 1:1 ' I 1.. no. 2 :1 :- CF ES. 0 :— ° ' -— o I“ o O — O 1 1 1 1111111111111 1 1 1 1 11111111111111 1 1 111 11111111111111 1 1 .02 .1 l 10 20 Time (sec) Figure 12. Comparison of theoretical and experimental overall mass transfer coefficients using the distilled toluene as the drop phase. 3 67 100 E: 1: Drop 1‘ Set : . O o 8 " 10 t- - ' D O _ K=2.34 c) 12 D 10 :- ‘J o 1; E q.) :— \m :— Slope = -0.5 b _ o E _. o 3 ': - K241 ‘0 +— 9.. c 0. >1 A 1:1 :43 F 00 1:1 1::- 0 DR: E O 1-— .1 1 1 1l1|11111|1|1|1l 1 l 111111111l111111 1 l 1|1|1l1|11111l1| .01 .1 l 10 Time (sec) Figure 13. Comparison of theoretical and experimental overall mass transfer coefficients using the spectroquality toluene as the drop phase. (haunt of Picric Acid in the Inter Pheee per Unit. Area of Map Surfeee);105(u/cn2) 68 OL_111 0 .2 L 1 l 1 .11 11.l__1 .6 11.15111. {m the Tap of the Dmp (on) Figure 14. Experimentally determined distribution of the extracted solute over the drOp surface for drop nets 1, 2, and 3. (Amount of Picric Acid in the Water Phase per Unit Area of [rap Surface) x 105 ( 91/131112) 69 L1 1 l_1 .11 .6 Height from the Tap of the Drop (cm) Figure 15. Experimentally determined distribution of the extracted solute over the drop surface for drop sets 4 and 5. (Amount of Picric Acid in the Water Phase per Unit Area of Drop Surface) 1 105(5111/cu2 ) 70 - DropSetB 11 1t 3 3 2 2 1 1— 011111L111mji1011114111L111 O .2 .1; .6 0 .2 .11 .6 hr— DropSeté h 3 3 2 2 1 1 L. 01111111111110111L1L41_1111 O .2 .11 .6 0 .2 oh .6 Heigit from the Top of the Drop (cm) Figure 16. Experimentally determined distribution of the extracted solute over the drop surface for drop sets 6, 8, and 10. (Amount of Picric Acid in the Water Phase per Unit Area of Drop Surface) 1 105(911/132) Height from the Tap of the Drop (cm) Figure 17. Experimentally determined distribution of the extracted solute over the drOp surface for drop set 12. DISCUSSION OF RESU LTS Referring to Figure 19, the data from Figures 10 and 11 are compared with Jacob's data. The solid lines are the experimental data and the broken lines represent the upper and lower limits of Equation (39). The low values obtained by Jacob were attributed to the presence of impurities in the system which inhibited mass transfer. Assuming that the system was contaminated, additional data were taken by this investigator using bulk toluene which was triple distilled. In- spection of Figure 19 shows that data of the correct order of magnitude were obtained, but the slope of a line through the data was lower than the theoretical slope. Consequently, a purer toluene, spectroquality reagent, was used as the drop phase to collect more data. More ex- traction was obtained, but the slope was still lower than the theoretical slope as revealed on Figure 19. Differentiation of Equation (39) with respect to time gives the rate of extraction as a function of time and volumetric flow rate. The rate of extraction is then found to be proportional to the product, 02/3 tl/é. Starting at zero formation time the rate of extraction con- tinually increases. From plots of experimental values of N versus t it was found that the rate of extraction, dN/dt, was either constant or decreased starting from zero time for a fixed volumetric flow rate. 73 DISCUSSION OF RESU LTS Referring to Figure 19, the data from Figures 10 and 11 are compared with Jacob's data. The solid lines are the experimental data and the broken lines represent the upper and lower limits of Equation (39). The low values obtained by Jacob were attributed to the presence of impurities in the system which inhibited mass transfer. Assuming that the system was contaminated, additional data were taken by this investigator using bulk toluene which was triple distilled. In- spection of Figure 19 shows that data of the correct order of magnitude were obtained, but the slope of a line through the data was lower than the theoretical slope. Consequently, a purer toluene, spectroquality reagent, was used as the drop phase to collect more data. More ex- traction was obtained, but the slope was still lower than the theoretical slope as revealed on Figure 19. Differentiation of Equation (39) with respect to time gives the rate of extraction as a function of time and volumetric flow rate. The rate of extraction is then found to be proportional to the product, QZ/3 t1/6. Starting at zero formation time the rate of extraction con- tinually increases. From plots of experimental values of N versus t it was found that the rate of extraction, dN/dt, was either constant or decreased starting from zero time for a fixed volumetric flow rate. 73 74 Present work, distilled toluene Present work, Jacob's work spe ctr oquality toluene 1 1111111111111111 1 1 1111111111111111 1 1 1111111111111111 100 E: C" P. 10 :_:_ m2 1; MA :— \ N 1—— G \ E I— 1 a .1 .01 Figure 19. .1 l 10 Time (sec) Comparison of the data of the present work with Jacob's data and with that predicted theoretically. ————— theoretical experimental 75 Referring to Figure 19, it is noted that early in the lifetime of a drop the rate of extraction was greater than theoretically predicted and later in the lifetime of the drop the rate of extraction was lower. Examination of the motion pictures of a forming drop showed that there was a stagnant area on the drop surface near the capillary tip. Tangential convection currents were observed over the remaining portion of the drop surface as shown schematically on Figure 20. The velocity of the fluid was too great to be entirely the result of gravity. The major force contributing to the velocity of the fluid was attributed to the viscous drag of the circulating fluid within the drop. The tan- gential convection currents originated at the top of the drop and were dampened out in the stagnant part. It was apparent from the motion pictures that the convection currents transported the extracted acid from the top part of the drop and deposited it at the stagnant portion near the capillary tip. Also, it is believed that adsorbed surface active impurities were simultaneously swept down toward the capillary where they accumulated at the interface. The concentrated impurities formed a coherent film which retarded the circulation at this part of the drop. Early in the lifetime of a forming drop only a small fraction of the drOp surface was stagnant. As the drop increased in size, a greater fraction of the area became stagnant even to the point where the entire surface of the drop became motionless. Therefore, early in the lifetime of a forming drop most of the drop surface was exposed to the cleaning 76 Tangential convection currents Stagnant area Movement of extracted acid by gravity Capillary Figure 20. Schematic diagram of a forming drop. effect of the tangential convection currents resulting in greater rates of extraction than predicted theoretically. This explains the data lying above the theoretical curves on Figure 19. With increasing time more of the surface became stagnant resulting in lower extraction rates since the surface was no longer swept clean of the extracted acid. In addition the adsorbed surface active impurities could reduce the rate of extraction. It is proposed that the film of adsorbed surface active impurities presented a resistance to the transfer of solute from the drop phase to the water phase in the 77 form of a physical barrier. Consequently, in the later part of the drop life the rate of extraction was lower than predicted theoretically. As the drop grows, the resistance due to the film plus its effect on the convection currents explains the deviation between the experimental and theoretical rate of extraction resulting in the low slope of the data. Garner and Skelland (6) similarly observed the gradual reduction of circulation in nitrobenzene drops contaminated with surface active impurities. Drops of nitrobenzene containing aluminum particles were formed at the top of a column of water and the circulation pattern inside of the drops was observed as the drops fell through the continuous phase. It was observed that the circulation inside a drop first began to cease at the rear pole of the drop and gradually the circulation throughout the drop was stopped. After purifying the nitrobenzene no decrease in the circulation within the drops was observed even after the drops fell a distance of 143 centimeters. They proposed that at low concentrations of surface active material the circulating motion of the interface may cause the adsorbed molecules to accumulate at the rear of the drop surface, giving a coherent film which progressively extends over the interface until circulation is stopped. The investigation conducted by Garner and Skelland lends credence to the present work. Figure 18 gives the theoretical distribution of the extracted acid over the surfaces for the indicated drops. For a fixed height from the top Of a forming drop, dN/dAd, the amount of solute extracted per unit 78 area of drop surface, increases as the time increases. Except for drop sets 1, 2, and 12 in Figures 14 through 17, dN/dA in general d decreases for a fixed height from the top of the drop, since the rate of extraction decreased or stayed constant while the area increased. The motion pictures also revealed that the extracted acid in the stagnant area moved slowly down toward the capillary tip as shown on Figure 20. The velocity of the motion was much lower than the velocity of the con— vection currents and was attributed to gravity. As a result of this motion, dN/dAd dropped off abruptly near the capillary tip. All of the theoretical equations with the exception of one (Michels) were derived from models based on the assumption that the tangential flow around a sphere had a negligible effect on mass transfer. Michels derived equations for both the tangential and radial velocities about a growing sphere from a combination of velocity potentials, but in solv- ing the mass balance equation he considered the term representing the tangential flow of material around the sphere to be negligible. The results of the present work showed the opposite to be true. If the surface active impurities were eliminated, the dominating factor affecting mass transfer would be the cleaning effect of the tangential motion. The amount of solute extracted as a function of time would be higher than predicted by any of the models. One of the assumptions used in deriving the theoretical equations was that the drops were spheres and consequently the area of a forming 79 drOp at any instant should have been the area of a sphere. For each drOp listed in Table 3 the actual area was calculated and compared to the area obtained by considering the drOp to be a sphere. The results showed that there was a difference of less than 2 percent between the two calculations for forty drOps with the actual area being larger than the spherical area. DISCUSSION OF EXPERIMENTAL ERROR At the beginning of the section on Analysis of Data is a dis- cussion concerning experiments which were carried out by Jacob (13) with a three compartment cell. The compartments were filled with picric acid-toluene or picric acid-water solutions with the side com- partments having solutions identical to one another. Assuming that the concentrations of two of the solutions were known, the concentra- tion of the third was determined experimentally and compared to the actual value. The error ranged from 0. 3 to 4. 7 percent in six out of the seven runs made and there was an error of 21.7 percent in the seventh. Noting that the highest concentration of picric acid-water solu- tion used by Jacob was 0. 0325 grams per liter and that the concentra- tion of the acid at the interface of a growing drop would be much higher, additional experiments were carried out by this investigator using higher concentrations of picric acid-water solutions in a three com- partment standard cell. Only water solutions of picric acid were used in the experiments. The true average concentration of the picric acid over all three compartments was calculated and compared to the experimentally determined average concentration. The results agreed within the measuring error. Both investigations were a measure of the experimental error 80 81 in applying Beer's and Lambert's laws of light absorption to a series of solutions using the photographic method of measurement. The influence of light reflection and refraction due to the shape of the drop on film optical density measurements was determined experimentally by Jacob. Density measurements were taken from drOps in equilibrium with the continuous phase and compared to calculated values. A series of measurements were taken horizontally through the drop from the top of the drop to the capillary tip. There was a significant difference between the calculated and experimental Optical densities in one drop of the three that were formed. The average error for this drop was 8. 1 percent with the greatest deviation from this value being near the top of the drop. The average errors for the other two drops were 4. 9 and 4. 0 percent. The experiments could be considered a duplication of the experi- ments carried out with the three compartment cells, but performed under more realistic conditions. For a given height, the light passed through three solutions in series; through the aqueous solution of picric acid in front of the drop, through the drOp itself, and through the aqueous solution of picric acid in back of the drop. Assuming that the concen- tration in the drop and the concentration of the solution behind the drop were known, the concentration in front of the drop was determined from Jacob's data and compared to the actual value. The average errors for the three drOps were 2. 54, 2. 34 and 8. 0 percent. 82 An additional error was noted in this work. In drop sets 8, 10, and 12 the data for the drops with the primed numbers were taken from one plate and the remaining majority from a second plate. There was an estimated error of 10 percent between the results calculated for each plate. An overall estimate of the experimental error is between 12 and 18 percent. CONCLUSIONS It was possible to study the extraction of picric acid from a toluene drop forming in a stagnant water phase using a photographic technique. Motion pictures of the forming drop were analyzed to determine the total amount of acid which was extracted and the distri- bution of the extracted acid over the drop surface. The data were compared with values calculated from several theoretical equations. All of the equations with the exception of one (Michels) were derived from models based on the assumption that the tangential flow around a sphere had a negligible effect on mass trans- fer. Michels derived equations for both the tangential and radial velocities about a growing sphere from a combination of velocity potentials, but in solving the mass balance equation he considered the term representing the tangential flow of material around the sphere to be negligible. The results of the present work showed the Opposite to be true. The dominating factor affecting mass transfer was the tangential flow. Surface active impurities interfere with mass transfer in two ways: by direct resistance to penetration of the surface by solute molecules and by hindering the tangential motion around a drop. The viscous drag of the circulating fluid within a forming drop caused tangential convection currents in the water phase at the drop 83 84 surface. The tangential convection currents originated at the top of the drop and moved down over the drop surface carrying the extracted acid toward the capillary tip. Simultaneously, adsorbed surface active impurities were swept down toward the capillary tip where they accumulated at the interface in the form of a film and retarded the motion at this part of the drop. As the drop grew, the film of impuri- ties progressively extended over the drop area until the entire surface became motionless. Consequently, early in the lifetime of a drop most of the surface was exposed to the cleaning effect of the tangential convection currents resulting in rates of extraction greater than pre- dicted by any of the models. Later in the lifetime of a drop the resistance to mass transfer due to the film of adsorbed surface active impurities plus the retarding effect of the film on the tangential convection cur- rents resulted in extraction rates lower than predicted theoretically. More extraction was obtained by careful purification of the system. Mass transfer coefficients decreased with formation time. NOMENCLATURE 2 area, cm . . . 3 concentration 1n phase 1, gm/cm equilibrium concentration, gm/cm initial concentration, gm/cm 3 concentration of solution in compartment j, gm/cm concentration of a standard toluene cell that absorbs as much light as the toluene drop, gm/cm3 concentration in the water phase corresponding to the transmission at each point, gm/cm concentration in the water phase which gives the same transmission as a concentration Gist in the toluene phase (c'st :CtO. D/L3), gm/cm3 diameter, cm . . . . . 2 diffuswity of solute in phase 1, cm /sec optical density fraction of solute ionized in the water phase flux, gm/cm -sec variable height, cm grams of solute in the continuous phase grams of solute in the discontinuous phase partition coefficient, height of drop, cm heat of ionization, cal/mol constant constant light absorption constant for phase i 85 NI 86 overall mass transfer coefficient, cm/sec thickness of compartment j, cm distance in front of the drop, cm effective column thickness, cm distance behind the drop, cm amount of gas absorbed, gm amount of solute extracted, gm amount of extracted solute ionized, gm volumetric flow rate, cm3/sec radial distance, cm constant radius of the drop, cm; gas constant, cal/0K - mol fraction of light transmitted; time, sec percent transmission; temperature, 0K radial velocity, cm/sec angular velocity, cm/sec radial velocity, cm/sec volume, cm variable distance, cm variable distance over boundary layer of thickness 0', cm beta function gamma function thickness of boundary layer, cm 87 Subscripts d discontinuous phase c continuous phase 0 initial 0 optical, initial r radial S standard t toluene w water to angular 10. 11. 12. 13. 14. 15. 16. BIB LIOG RAPHY Baird, M. H. 1., Chem. Eng. Sci., 9, 267 (1959). Bidlack, D. L. and D. K. Anderson, Mutual Diffusion in the Liquid System Hexane-Hexadecane, Unpublished Notes, Dept. of Chem. Eng., Mich. State Univ. (1963). Brownlie, I. A. and W. M. Cumming, Biochemical Journal, (London), 40, 20 (1946). Coulson, J. M. and S. J. Skinner, Chem. Eng. Sci., 1, 197 (1952). Garner, F. H. and A. H. P. Skelland, Ind. Eng. Chem., 46, 1255 (1954). Garner, F. H. and A. H. P. Skelland, Chem. Eng. Sci., 4, 149 (1955). Groothuis, H. and H. Kramers, Chem. Eng. Sci., 4, 17 (1955). Halban, H. von, and I. Ebert, Z. Physik. Chem., 112, 359 (1924), Hantzsch, V. A., Zeitschr. f. Electrochemie, 29, 221 (1923). Hantzsch, V. A., Zeitschr. f. Electrochemie, 30, 194 (1924). Haritatos, N. J. and M. Liberman, M. S. Thesis, M. 1. T. (1953L International Critical Tables, McGraw-Hill Book Co. , Inc. New York (1930). Jacob, P. Y., M. S- Thesis, Mich. State Univ. (1961). Levich, L. G., Physicochemical Hydrodynamics, Prentice- Hall, Inc. , New Jersey (1962). Licht, W., Jr., and J. B. Conway, Ind. Eng. Chem., 42, 1151 (1950). Licht, W., Jr., and W. F. Pansing, Ind. Eng. Chem., 45 1885 (1953). 88 17. 18. 19° 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 89 MacGillavry, D. and E. K. Rideal, Rec. trav. chim., 56, 1013 (1937). Michels, H. H., Ph. D. Thesis, Univ. of Delaware (1960). Moore, C. E. and R. Peck, Journal of Organic Chemistry, 20, 673 (1955). Neale, S. M., Trans. Faraday Soc., 17, 505 (1922). Patel, P. N., M. S. Thesis, Mich. State Univ. (1962). Reddick, H. W. and F. H. Miller, Advanced Mathematics for Engineers, 3rd ed. , John Wiley 8: Sons, Inc. , New York (1955). Seidell, A. , Solubilities of Organic Compounds, 3rd ed. , 2, D. Van Nostrand Co. , New York (1941). Sherwood, T. K., J. E. Evans, and J. V. A. Longcor, Ind. Eng. Chem., 31, 1144(1939). Tambo, W., M. S. Thesis, Mich. State Univ. (1960). West, F. B. et a1., Ind. Eng. Chem., 43, 234 (1951). West, F. B. et a1., Ind. Eng. Chem., 44, 625 (1952). Whitman, W. G. et a1., Ind. Eg. Chem., 18, 363 (1926). Wilke, C. R. and P. Chang, Am. Inst. Chem. Engrs. J., l, 264 (1955). Zeleny, R. A., M. S. Thesis, Worcester Polytechnic Institute (1954). Zeleny, R. A., Extraction from Forming Drops, Unpublished Notes, Dept. of Chem. Eng., Mich. State Univ. (1962). APPENDICES 90 APPENDIX A An Estimate of the Upper Limit for the Ratio of the Amount of Picric Acid Extracted Durirg the Formation and Withdrawal of a Drop to the Amount of Acid Extracted During Formation According to Jacob's Data From Jacob‘s data (13), N 6/7 (66) yar-kt where k is a constant. Letting N1 = amount of picric acid extracted during formation and N2 = amount extracted during withdrawal assuming no acid present when withdrawing starts, then 2 N Q /3 t 6/7 N1 Q1 t1 Substituting Q = V/t into (67), N t 2/3 t 6/7 t 0.1905 2 l 2 2 N— = .— .— = .— “’8’ 1 2 1 1 The values for t2 and t1 are 2. 26 and 3. 36 seconds respectively. Therefore, 2 fi— = 0.927 91 92 The estimate of the upper limit for Jacob's experiment is N1+N2 N 1 =1. 927 APPENDIX B ti (t f- t)1/‘2 Evaluation of the Integral] dt 17 3 o t From Equation (13) the integral, t 1/2 f (tf- t) ‘73— d“ t is to be evaluated. Letting x = t/tf, t 1/2 1 f (tf t) dt = t 7/7 -1/3 (1 )1/2 d —7_t1 3 f X - X X 0 0 Comparing (69) to the 8 function (22), 1 (3(m.n) =fxm-1(1-X)n-ldx = “—1? n . 0 (69) shows that the values for m and n are 2/3 and l. 5 respectively. I" is defined as the gamma function (22). Substituting in the values for l2/3, l 1. 5, and (2.167 from a table of gamma functions, t 1/2 If “f” 7/6 T dt - 1.1088 tf 0 93 APPENDIX C Calculation of the Fraction of Picric Acid Ionized in Water at 26.70C Given that the equilibrium constant at 180 C was 0. 16 (12), the value at 26. 70C was calculated using K A Inif=-'§(%;-%) (7., where K2 = value of the equilibrium constant at temperature T2, 299.7°K Kl = O. 16 value of the equilibrium constant at temperature T1, 2910K AH = heat of ionization, -4,570 cal/mol at 300C (20), assumed constant from 18-300C R = gas constant, 1.9872 cal/ OK-mol Solving Equation (70), K2 = 0.128. The fraction of picric acid ionized was calculated from 2 cf K2 ’ l-f where c = initial concentration of picric acid in water (moles/l) f = fraction ionized 11. 5729 5. 0060 : —— = 0, = —— = . . Forc 229.114, f 77 andforc 229.114 f 0 87 The molecular weight of picric acid is 229. 114. 94 APPENDIX D Distribution of Picric Acid Between Water and Toluene at 25°C (23) gm per 100 m1 Aqueous Layer Toluene Layer 0. 172 0. 289 0. 250 0. 572 0. 374 l. 104 0. 559 2. 351 0. 891 5. 380 1. 137 8. 586 1. 336 11. 770 95 APPENDIX E Data The following is a tabulation of the data obtained from measure- ments taken from the drop images. h = distance measured from the top of the drop along the vertical axis of the drop T 2 percent transmission at position, h r = radius of the drop at height, h Csw: concentration in the water phase corresponding to the transmission, T c' = concentration in the water phase which absorbed as much light as the toluene drop of concentration, CtO' at height, h AC 2 Csw ‘ Cl... Drop 1-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0. 0149 8. 0 0. 0514 0. 877 0. 0447 13. 0 0. 0835 1.10 0. 0745 16. 0 0. 0964 0. 970 0.104 15. 0 0.104 1. 02 0.134 14. 0 0. 0964 1. 07 0. 164 17. O 0. 0843 0. 893 0.194 23. 5 0. 0514 0. 633 0. 209 ---- 0. 0470 ..... 96 97 Drop 1-2 r. Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0149 5.5 0.0637 1.17 0.0447 6.0 0.0984 1.92 0.0745 10.0 0.122 1.46 0.104 10.0 0.135 1.47 0.134 7.0 0.141 2.00 0.164 6.0 0.142 2.23 0.194 5.5 0.139 2.32 0.224 5.5 0.127 2.24 0.253 5.5 0.106 2.08 0.283 5.0 0.0581 1.64 0.298 --- 0.0470 ---- Drop 1- 3 r. Auc h (cm) %T r (cm) (gm-cm/l) x 103 0.0148 4.1 0.0686 1.43 0.0444 2.8 0.117 2.85 0.0740 3.8 0.137 2.92 0.104 3.5 0.153 3.26 0.133 2.7 0.169 3.79 0.163 2.4 0.177 4.03 0.222 4.0 0.170 3.19 98 Drop 1- 3 (continued) 0.252 2.7 0.160 3.64 0.281 4.0 0.146 2.87 0.311 3.0 0.115 2.91 0.340 4.0 0.0710 1.91 0.355 --- 0.0470 ---_ jDrop 1-4 r. Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0147 4.5 0.0766 1.50 0.0441 2.6 0.129 3.08 0.0735 2.4 0.157 3.77 0.103 3.0 0.172 3.74 0.132 4.0 0.181 3.35 0.162 4.0 0.191 3.39 0.191 3.4 0.194 3.70 0.221 2.8 0.201 4.02 0.250 3.0 0.190 3.82 0.279 2.5 0.179 4.02 0.309 2.9 0.161 3.59 0.338 3.3 0.144 3.14 0.368 2.7 0.115 2.97 0.397 7.0 0.0565 1.39 0.411 --- 0.0470 ---- 99 Drop 1- 5 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0146 5.5 0.0823 1.42 0.0438 2.3 0.133 3.32 0.0730 2.4 0.165 3.96 0.102 2.1 0.190 4.67 0.131 2.1 0.210 4.92 0.161 2.1 0.221 5.03 0.190 2.0 0.231 5.19 0.219 2.1 0.231 5.08 0.248 2.5 0.229 4.67 0.277 2.5 0.222 4.63 0.307 2.0 0.215 5.04 0.336 2.2 0.206 4.70 0.365 2.1 0.186 4.56 0.394 2.5 0.165 3.87 0.423 2.4 0.135 3.40 0. 453 2. 9 0. 0887 2. 35 0. 468 --- 0. 0470 -_-.. Drop 1- 6 h (cm) %T r (cm) (ng13.- Ainc/1) x 10 0.0147 5.0 0.0816 1.49 0.0440 2.9 0.134 3.05 100 DrOp 1- 6 (continued) 0.0733 2.9 0.172 3.72 0.103 2.9 0.201 4.15 0.132 3.2 0.231 4.15 0.161 3.2 0.240 4.23 0.190 2.5 0.246 4.86 0.220 2.3 0.248 5.09 0.249 2.0 0.248 5.43 0.278 2.0 0.253 5.40 0.308 1.9 0.242 5.48 0.337 2.0 0.240 5.27 0.366 2.0 0.232 5.15 0.396 2.1 0.212 4.85 0.425 2.0 0.186 4.64 0.454 2.0 0.156 4.17 0.483 2.2 0.121 3.41 0.513 2.4 0.0880 2.39 0.528 --- 0.0470 ---- Drop 1- 7 r . Ac h (cm) %T r (cm) (gm-cm!” x 10 0.0148 5.0 0.0843 1.56 0.0444 3.0 0.145 3.01 0.0740 2.9 0.178 3.70 0.104 2.9 0.206 4.15 101 .Drop 1#7(confinued) 0.133 2.8 0.209 4.46 0.163 2.5 0.239 4.83 0.192 2.4 0.251 5.00 0.222 2.5 0.263 4.92 0.252 2.7 0.267 4.73 0.281 2.8 0.269 4.64 0.311 2.8 0.268 4.63 0.340 2.9 0.258 4.52 0.370 2.7 0.249 4.66 0.400 2.1 0.233 5.16 0.429 2.0 0.214 5.10 0.459 2.0 0.186 4.79 0 488 2.0 0.173 4.30 0.518 2.0 0.139 3.63 0.548 2.1 0.0899 2.60 0.562 --- 0.0470 ---- Drop 1-8 r .IAc h (cm) %T r (cm) (gm-cm/l) x 103 0.0147 3.4 0.0926 1.92 0.0440 2.6 0.146 3.27 0.0733 2.5 0.187 4.05 0.103 2.0 0.219 5.02 0.132 2.0 0.237 5.32 0.161 2.0 0.247 5.47 102 .Drop 1-8(confinued) 0.190 2.0 0.260 5.54 0.220 2.0 0.266 5.57 0.249 2.0 0.272 5.58 0.278 2.0 0.274 5.58 0.308 2.0 0.274 5.57 0.337 2.0 0.275 5.55 0.366 1.9 0.270 5.67 0.396 1.9 0.261 5.63 0.425 1.9 0.258 5.57 0.454 1.9 0.256 5.49 0.483 1.9 0.237 5.35 0.513 1.9 0.209 5.14 0.542 2.0 0.183 4.69 0.571 2.0 0.148 4.19 0.601 2.1 0.125 3.46 0.630 4.0 0.0966 1.99 0.644 --- 0.0470 --_- Drop 2-1 r .Afic (cm) %T r (cm) (gm-cm/l) x103 0.0145 9.5 0.0589 0.739 0.0435 8.5 0.0686 1.43 0.0725 10.0 0.118 1.44 0.102 10.0 0.130 1.46 0.131 7.0 0.139 1.99 103 .Drop 2-1(confinued) 0.160 6.5 0.142 2.11 0.189 4.5 0.131 2.58 0.218 4.0 0.123 2.60 0.247 3.5 0.101 2.44 0.276 7.9 0.0565 1.25 0.290 --- 0.0470 ---- .Drop 2-2 r .ASC h (cm) %T r (cm) (gm-cm/l) x 103 0.0149 5.3 0.0726 1.34 0.0447 3.5 0.119 2.68 0.0745 3.4 0.146 3.16 0.104 3.3 0.165 3.46 0.134 3.0 0.176 3.74 0.164 3.0 0.182 3.79 0.194 3.0 0.186 3.78 0.224 2.9 0.184 3.81 0.253 3.0 0.177 3.68 0.283 2.8 0.166 3.67 0.313 3.0 0.145 3.33 0.343 2.7 0.123 3.07 0.373 2.5 0.0694 2.25 0.387 --- 0.0470 ---- 104 Drop 2-3 r. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0148 4.5 0.0835 1.58 0.0444 2.1 0.133 3.44 0.0740 2.3 0.169 4.01 0.104 2.7 0.191 4.13 0.133 2.6 0.203 4.40 0.163 2.6 0.209 4.48 0.192 2.5 0.215 4.57 0.222 2.5 0.214 4.55 0. 252 2. 9 0. 213 4.19 0. 281 3. 0 0. 209 4. 05 0.311 3.3 0.198 3.80 0. 340 3. 5 0. 186 3. 52 0. 370 3. 3 0. 169 3. 45 0.400 2.75 0.141 3.38 0.430 2.4 0.107 3.04 0. 459 2. 6 0. 0530 l. 99 0.474 --- 0.0470 ---- Drop 2-4 r .ASC h (cm) %T r (cm) (gm-cm/l) x 103 0.0149 3.5 0.0807 1.65 0.0446 2.4 0.121 3.13 105 Dr 0p 2- 4 (continued) 0.0743 2.5 0.169 3.75 0.104 2.1 0.189 4.56 0.134 2.1 0.206 4.88 0.163 2.1 0.219 5.06 0.193 2.1 0.228 5.15 0.223 2.1 0.235 5.18 0.252 2.7 0.237 4.59 0.282 2.9 0.235 4.41 0.312 2.7 0.235 4.54 0.342 2.3 0.230 4.82 0.371 2.0 0.218 5.01 0.401 1.9 0.203 4.95 0.431 1.9 0.185 4.69 0.460 1.9 0.160 4.33 0.490 2.0 0.143 3.78 0.520 2.0 0.106 3.18 0.549 6.0 0.0573 1.44 0.565 --- 0.0470 ---- Drop 2-5 r . Ac (cm) %T r (cm) (gm-cm/l) x 103 0.0148 5.0 0.0952 1.65 0.0443 2.3 0.150 3.32 0.0738 2.1 0.173 4.17 0.103 2.0 0.197 4.83 106 Drop 2- 5 (continued) 0.133 2.0 0.218 5.18 0.162 2.0 0.240 5.37 0.192 2.0 0.252 5.47 0.221 2.0 0.260 5.52 0. 251 2. 0 0. 265 5. 54 0. 280 2. -5 0. 271 4. 95 0.310 3.0 0. 272 4. 48 0.339 3.0 0.269 4.47 0. 369 2. 5 0. 258 4. 91 0.398 2.5 0.253 4.88 0. 428 2. 5 0. 246 4. 83 0.457 2.0 0.242 5.29 0.487 2.0 0.229 5.15 0.516 2.0 0.210 4.94 0.546 2.0 0.189 4.65 0.575 2.0 0.165 4.24 0.605 2.0 0.137 3.73 0.634 2.7 0.0903 2.76 0.664 10.0 0.0532 1.01 0.677 ---- 0.0470 ---- Drop 3-1 r .AAC h (cm) %T r (cm) (gm-cm/l) x103 0.0147 27.5 0.0488 0.465 0. 0440 23. 5 0. 0992 0. 732 0.0733 19.0 0.122 0.774 107 .Drop 3-1(confinued) 0.103 13.0 0.137 1.13 0.132 10.0 0.142 1.48 0.161 9.0 0.139 1.62 0.190 8.0 0.135 1.77 0.220 7.2 0.119 1.85 0.249 8.0 0.0976 1.59 0.278 20.0 0.0504 0.706 0.293 ---- 0.0470 ----- .Drop 3-2 r .Afic h (cm) %T r (cm) (gm-cm/l) ){103 0.0147 17.0 0.0634 0.659 0.0441 14.5 0.114 1.05 0.0735 17.0 0.138 0.811 0.103 11.5 0.161 1.28 0.132 9.5 0.172 1.62 0.162 8.0 0.179 1.96 0.191 6.2 0.185 2.46 0.221 5.0 0.192 2.87 0.250 4.0 0.180 3.22 0.279 4.2 0.171 3.02 0.309 5.0 0.146 2.57 0.338 6.0 0.111 2.09 0.368 7.0 0.0764 1.48 0.382 - - 0.0470 ---- 108 Drop 3-3 r .Afic h (cm) %T r (cm) (gm-cm/l) x 103 0.0148 17.5 0.0781 0.722 0.0443 16.0 0.125 0.953 0.0738 14.5 0.156 0.959 0.103 14.0 0.176 0.962 0.133 11.5 0.195 1.27 0.163 8.4 0.205 1.91 0.192 8.8 0.210 1.81 0.221 7.0 0.211 2.32 0.251 5.3 0.212 2.94 0.280 4.0 0.211 3.50 0.310 3.3 0.202 3.79 0. 339 2. 9 0.191 3. 88 0.369 2.6 0.163 3.81 0. 398 2. 8 0. 146 3. 34 0. 428 3. 2 0. 0992 2. 70 0.457 3.7 0.0488 1.68 0.472 --- 0.0470 ---- Drop 3-4 r .ISC h (cm) %T r (cm) (gm-cm/l) x 103 0.0149 14.5 0.0781 0.820 0.0447 10.5 0.130 1.39 109 Dr0p 3- 4 (continued) 0.0745 9.0 0.167 1.68 0.104 7.5 0.189 2.12 0.134 6.0 0.208 2.67 0.163 5.5 0.221 2.91 0.193 4. 6 0. 228 3. 34 0.223 4.3 0.232 3.51 0.253 3.7 0.235 3.85 0.283 3.4 0.235 4.03 0.312 3.0 0.228 4.27 0. 342 2. 9 0. 224 4. 29 0.372 2.6 0.211 4.41 0. 402 2. 2 0. 195 4. 56 0. 432 2. 2 0. 179 4. 27 0.461 2.2 0.150 3.84 0.491 3.5 0.113 2.73 0. 521 5. 0 0. 0675 1. 68 0.537 — - 0. 0470 ---- Drop 3-5 1' . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0147 3.3 0.0821 0.918 0.0440 9.0 0.137 1.58 0. 0733 9. 0 0.179 1. 69 0.103 6. 0 0. 207 2. 63 0.132 5.2 0.226 3.04 110 Drop 3- 5 (continued) 0.161 5.0 0.241 3.16 0.190 4.6 0.250 3.36 0.220 4.3 0.260 3.53 0.249 3.5 0.266 4.08 0.278 3.0 0.270 4.48 0.308 2.7 0.272 4.76 0.337 2.2 0.270 5.27 0 366 2.1 0.265 5.36 0.396 2.1 0.257 5.30 0.425 2.0 0.244 5.33 0.454 2.0 0.236 5.20 0.483 2.0 0.211 5.01 0.513 2.0 0.197 4.76 0.542 2.0 0.179 4.42 0.571 2.0 0.146 4.00 0.601 2.0 0.129 3.52 0.630 3.0 0.0764 2.51 0.659 15.0 0.0480 0.751 0.675 -—-- 0.0470 ..... Drop 4-1 r . Ac h(mn) %T r(mn) (gmhcm/U x 103 O. 0147 37. 0 0. 0403 0. 350 0.0440 31.5 0.0807 0.621 0.0732 26.5 0.100 0.656 111 Drop 4-1 (continued) 0.103 24.0 0.115 0.651 0.132 17.7 0.121 0.846 0.161 12.0 0.124 1.24 0.190 7.0 0.119 1.89 0. 220 6.2 0.113 1.97 0.249 4.0 0.0887 2.21 0.278 5.8 0.0548 1.41 0.293 - - 0.0470 ---- Drop 4-2 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0149 26.0 0.0548 0.505 0.0447 22.0 0.110 0.757 0.0745 20.4 0.132 0.671 0.104 18.5 0.151 0.674 0.134 16.4 0.162 0.777 0.164 16.0 0.172 0.795 0.194 10.4 0.173 1.45 0.224 5.9 0.174 2.47 0.253 3.8 0.169 3.19 0.283 3.7 0.161 3.13 0.313 3.0 0.145 3.24 0.343 2.8 0.109 2.93 0.373 3.9 0.0629 1.84 0.387 - - 0.0470 ---- .Drop 4-3 r. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0149 22.4 0.0642 0.568 0.0446 25.0 0.111 0.679 0.0743 23.0 0.145 0.533 0.104 20.4 0.165 0.514 0.134 17.5 0.184 0.626 0.163 15.4 0.194 0.773 0.193 11.4 0.200 1.29 0.223 8.0 0.204 2.01 0.252 5.2 0.205 2.93 0.282 3.5 0.200 3.70 0.312 3.0 0.195 3.93 0.342 2.9 0.185 3.90 0.371 2.4 0.176 4.08 0.401 2.0 0.162 4.12 0.431 2.0 0.146 3.73 0.460 2.4 0.0984 2.96 0.490 10.4 0.0520 1.04 0.504 ---- 0.0470 ---- Drop 4-4 r. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0149 21.4 0.0726 0.644 0.0446 21.4 0.129 0.730 113 DrOp 4-4 (continued) 0.0743 17.4 0.161 0.735 0.104 17.4 0.185 1.15 0.134 14.4 0.200 0.843 0.163 11.4 0.210 1.24 0.193 8.5 0.218 1.87 0.223 6.3 0.224 2.58 0.252 4.5 0.227 3.37 0.282 3.7 0.226 3.79 0.312 3.0 0.224 4.20 0.342 2.5 0.216 4.52 0.371 2.4 0.210 4.51 0.401 2.0 0.195 4.73 0.431 2.0 0.181 4.51 0.460 2.0 0.160 4.20 0.490 2.0 0.137 3.79 0. 520 2. 0 0.113 3. 23 0.549 3.2 0.0645 1.94 0.565 --- 0.0470 ---- Drop 4-5 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0147 26.8 0.0725 0.594 0.0440 23.0 0.127 0.697 0. 0733 21.5 0.169 0. 532 0.103 18.0 0.200 0.580 0.132 14.7 0.211 0.752 114 Drop 4- 5 (continued) 0.161 11.5 0.229 1.12 0.190 7.8 0.243 2.18 0.220 4.5 0.251 3.42 0.249 3.5 0.255 4.07 0.278 3.5 0.259 4.07 0.308 3.0 0.262 4.46 0.337 2.5 0.257 4.90 0.366 2.0 0.255 5.42 0.396 1.9 0.248 5.48 0.425 1.9 0.240 5.37 0.454 1.8 0.227 5.42 0.483 1.5 0.213 5.58 0.513 1.5 0.195 5.30 0.542 1.5 0.172 4.97 0.571 1.5 0.160 4.60 0.601 1.6 0.135 4.07 0.630 1.8 0.112 3.50 0.659 2.0 0.0725 2.81 0.689 2.0 0.0601 2.02 0.703 --- 0.0470 ---- Drop 5-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0148 44.4 0.0370 0.303 0.0444 43.4 0.0770 0.515 0.0740 42.4 0.0997 0.462 115 Drop 5-1 (continued) 0.104 37.4 0.117 0.423 0.133 36.9 0.125 0.371 0.163 34.0 0.130 0.390 0.192 30.4 0.130 0.451 0. 222 25. 4 0. 125 0. 572 0.252 15.5 0.121 0.975 0.281 7.3 0.105 1.77 0. 311 4. 4 0. 0906 2.10 0.340 5.4 0.0582 1.47 0.355 --- 0.0470 ---- Drop 5-2 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0. 0145 34. 4 0. 0405 0. 359 0. 0435 37. 9 0. 0810 0. 564 0. 0725 35. 4 0.114 0. 493 0.102 30.4 0.129 0.438 0. 131 30. 0 0. 140 0. 368 0.160 28.9 0.146 0.352 0.189 25.0 0.151 0.437 0.218 21.4 0.150 0.563 0.247 16.9 0.149 0.803 0.276 10.4 0.145 1.42 0. 305 5. 7 0.131 2. 26 0. 334 4. 2 0.126 2. 56 116 Drop 5- 2 (continued) 0.363 3.0 0.101 2.72 0.392 2.9 0.0810 2.31 0.421 --- 0.0470 ---- Drop 5-3 r .Akc h (cm) %T r (cm) (gm-cm/l) x 103 0.0149 31.4 0.0496 0 409 0.0446 19.4 0.0902 0 830 0.0743 26.4 0.121 0 577 0. 104 27.4 0. 142 0 402 0.134 25.9 0.163 0.341 0.163 23.4 0.172 0 366 0.193 21.4 0.179 0 422 0.223 18.4 07180 0 583 0.252 15.4 0.180 0 823 0.282 11.9 0.178 1.23 0.312 8.0 0.173 1.91 0.342 4.6 0.164 2.81 0.371 3.4 0.150 3 15 0.401 2.4 0.134 3.41 0.431 2.4 0.114 3.09 0.460 2.4 0.0854 2.62 0.490 6.9 0.0488 1.21 0.504 --- 0.0470 ---- 117 Drop 5-4 I. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0145 28.4 0.0548 0.456 0.0435 25.4 0.0952 0.703 0.0725 24.4 0.129 0.603 0.102 22.0 0.149 0.532 0.131 20.2 0.168 0.523 0.160 18.4 0.180 0.574 0.189 17.8 0.192 0.580 0.218 17.4 0.195 0.591 0.247 15.9 0.196 0.718 0.276 14.4 0.195 0.881 0.305 10.4 0.193 1.47 0.334 13.4 0.188 1.02 0.363 4.4 0.185 3.07 0.392 3.0 0.177 3.62 0.421 2.4 0.161 3.80 0.450 2.0 0.144 3.85 0.479 2.0 0.126 3.56 0.508 2.0 0.105 3.20 0.537 2.0 0.0831 2.68 0.566 15.4 0.0484 0.755 0. 581 ---- 0. 0470 ----- 118 Drop 5-5 r. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0147 28.9 0.0524 0.468 0.0440 28.0 0.102 0.659 0.0733 27.9 0.141 0.481 0.103 28.5 0.162 0.283 0.132 20.9 0.179 0.430 0.161 19.4 0.195 0.434 0.190 17.4 0.206 0.520 0.220 13.4 0.210 0.928 0.249 13.4 0.212 0.914 0.278 13.9 0.216 0.848 0.308 11.9 0.215 1.16 0.337 9.9 0.212 1.56 0.366 5.4 0.210 2.86 0.396 3.4 0.200 3.71 0.425 2.7 0.188 4.01 0.454 2.4 0.177 4.05 0.483 2.0 0.161 4.14 0.513 1.9 0.142 3.97 0.542 1.9 0.130 3.67 0.571 2.0 0.110 3.25 0.601 2.4 0.0798 2.61 0.630 8.4 0.0677 1.16 0.645 - - 0.0470 ---- 119 Drop 6-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0. 0146 59. 3 0. 0265 0.176 0. 0438 60. 0 0. 0546 0. 318 0. 0730 56. 0 0. 0682 0. 392 0. 102 51. 0 0. 0834 0. 434 0. 131 46. 0 0. 0909 0. 471 0.161 39. 0 0. 0902 0. 537 0. 190 37. 0 0. 0909 0. 560 0. 219 43. 0 0. 0909 0. 509 0. 248 33. 0 0. 0826 0. 609 0. 277 23. 5 0. 0758 0. 716 0. 307 8. 0 0. 0682 1. 29 0. 336 14. 0 0. 0546 0. 818 0. 365 43. 0 0. 0470 0. 393 0. 379 ---- 0. 0470 ----- Drop 6-2 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0. 0147 63. 0 0. 0379 0.192 O. 0441 56. 0 0. 0614 0. 386 0. 0735 49. 5 0. 0863 0. 435 0.103 46. 0 0.112 0. 384 0.132 39. 0 0.117 0. 389 120 Drop 6- 2 (continued) 0.162 32.5 0.128 0.427 0.191 27.0 0.129 0.500 0.220 30.0 0.134 0.435 0.250 33.0 0.132 0.392 0.279 28.0 0.130 0.497 0.309 19.0 0.125 0.779 0.338 9.5 0.115 1.51 0.367 6.5 0.110 1.92 0. 397 4. 0 O. 0985 2. 32 0.426 4.0 0.0839 2.09 0.455 24.0 0.0644 0.658 0.470 ---- 0.0470 ..... Drop 6-3 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0148 51.0 0.0318 0.290 0. 0442 47. 0 0. 0834 0. 560 0.0736 33.0 0.114 0.577 0.103 31.0 0.128 0.440 0.133 31.0 0.139 0.264 0.162 35.0 0.152 0.291 0. 191 30. 0 0. 154 0. 335 0.221 27.0 0.155 0.423 0.250 24.0 0.154 0.768 0.280 17.0 0.152 1.02 121 Drop 6 - 3 (continued) 0. 309 14.0 0.148 1.71 0. 339 8. 5 0.133 2. 28 0. 368 5. 5 0.121 2. 58 0. 397 4. 0 0. 107 2. 73 0. 427 3. 0 0. 0959 2. 45 0. 456 3. 2 0. 0757 1. 98 0. 486 4. 3 0. 0644 0. 908 0. 515 14. 0 0. 0488 0. 493 0. 530 ---- 0. 0470 ..... Drop 8-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0133 93.0 0.0331 0.198 0. 0398 88. 0 0. 0710 0. 721 0. 0664 85. 5 0. 0952 1. 08 0.0929 75.5 0.101 1.72 0.119 69. 0 0.109 1. 95 0.146 67. 0 0. 0966 1. 86 0.173 76. 5 0. 0786 1. 30 0.199 76. 0 0. 0483 0. 971 0. 212 ---- 0. 0470 ----- 122 Drop 8-2 r. Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0133 84.0 0.0497 0.557 0.0399 80.5 0.0966 1.31 0.0665 73.5 0.114 1.97 0.0931 57.5 0.141 2.77 0.120 42.0 0.159 3.40 0.146 26.5 0.163 4.04 0.173 19.0 0.168 4.38 0.200 20.0 0.172 4.34 0.226 24.5 0.164 4.14 0.253 26.0 0.157 4.04 0.279 24.0 0.147 4.03 0.306 24.0 0.136 3.80 0.333 20.0 0.116 3.39 0.359 20.0 0.0724 2.34 0.372 -—-- 0.0470 ---- Drop 8-3 r. Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0132 72.0 0.0724 1.01 0.0397 68.0 0.114 1.97 0.0661 59.0 0.143 2.70 0.0925 46.0 0.164 3.29 123 Drop 8- 3 (continued) 0.119 23.0 0.178 4.26 0.145 27.5 0 191 3.99 0.172 9.5 0.201 5.15 0 198 12.0 0 208 4.88 0.225 13.5 0.208 4.74 0.251 10.0 0.208 5.09 0.278 7.0 0.205 5.49 0.304 6.5 0.197 5.57 0.331 7.5 0.188 5.41 0.357 8.0 0.177 5.28 0.383 7.0 0.159 5.23 0.410 7.0 0.141 4.80 0.436 7.0 0.110 3.93 0.463 10.0 0.0538 2.34 0.476 ---- 0.0470 ---- Drop 8-4 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0131 70.5 0.0572 0.921 0.0394 64.0 0.109 2.04 0.0656 57.0 0.147 2.78 0.0919 40.0 0.172 3.52 0 118 27.5 0 191 3.99 0.144 15.5 0.210 4.60 0.171 10.5 0.218 5.11 124 Drop 8- 4 (continued) 0.197 8.5 0.228 5.40 0.223 9.0 0.232 5.34 0.250 10.0 0.236 5.21 0.276 9.0 0.237 5.33 0.302 6.0 0.233 5.83 0.328 4.5 0.228 6.15 0.355 4.0 0.216 6.24 0.381 4.0 0.212 6.15 0.407 3.5 0.192 6.25 0. 433 3. 8 0.185 6.11 0.460 3.5 0.167 5.97 0.486 3.8 0.149 5.43 0.512 4.5 0.120 4.45 0. 539 6. 0 0. 0828 2. 96 0.552 - - 0.0470 ---- Drop 8-5 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0132 67.0 0.0855 1.31 0.0395 66.0 0.138 2.22 0.0658 59.0 0.168 2.77 0.0922 44.0 0.191 3.25 0.118 30.0 0.212 3.75 0.145 21.0 0.223 4.26 0.171 15.0 0.234 4.70 125 Drop 8- 5 (continued) 0.197 12.0 0.250 5.01 0.224 9.0 0.259 5.42 0.250 6.0 0.263 6.01 0. 276 5. 5 0. 266 6. 14 0.303 5.5 0.263 6.13 0.329 5.5 0.262 6.12 0.355 5.5 0.257 6.10 0.382 4.0 0.252 6.51 0.408 3.4 0.241 6.66 0. 434 3. 8 0. 230 6. 42 0.461 4.0 0.212 6.21 0.487 4.5 0.191 5.96 0.513 3.5 0.164 5.93 0.540 4.0 0.130 4.94 0. 566 10. 0 0. 0897 2. 87 0.579 ---- 0.0470 ---- Drop 8-1' 1' . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0122 95.5 0.0541 0.395 0.0365 94.5 0.0917 0.697 0.0608 86.5 0.100 1.31 0.0851 74.0 0.119 1.89 0.109 66.0 0.131 2.06 0.134 68.5 0.135 2.07 126 Drop 8-1' (continued) 0. 158 56. 0 0. 139 2. 22 0.182 61.0 0.136 2.12 0. 207 60. 0 0. 129 2. 07 0.231 61.0 0.121 1.95 0. 255 72. 0 0. 0996 1. 66 0. 279 32. 0 0. 0646 1. 71 0. 303 ---- 0. 0470 ---- Drop 10-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x 10 0.0132 92.0 0.0367 0. 372 0. 0396 91. 0 0. 0646 0. 702 0. 0660 90. 5 0. 0748 0. 804 0. 0924 90. 0 0. 0755 0. 858 0.119 89. 5 0. 0646 0. 797 0.132 ---- 0. 0470 ----- Drop 10-2 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0131 73.0 0.0612 0.971 0.0393 71.0 0.105 1.87 0. 0655 64. 0 0. 128 2. 42 127 DrOp 10- 2 (continued) 0.0917 55.0 0.140 2.78 0.118 47.5 0.156 2.96 0.144 35.0 0.167 3.24 0.170 31.5 0.168 3.34 0.197 25.5 0.165 3.55 0.223 22.0 0.163 3.70 0.249 18.0 0.150 3.86 0.275 17.0 0.138 3.76 0.301 20.0 0.109 3.18 0.328 21.0 0.0544 2.05 0.340 ---- 0.0470 ---- Drop 10-3 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0132 66.5 0.0612 1.11 0.0396 68.0 0.116 2.04 0.0660 57.0 0.146 2.71 0.0924 47.0 0.168 2.89 0.119 42.0 0.184 2.80 0.145 33.5 0.193 2.90 0.172 26.0 0.203 3.12 0.198 21.5 0.204 3.33 0.224 19.0 0.205 3.50 0.251 14.0 0.204 3.92 0.277 13.0 0.201 4.07 128 DrOp 10- 3 (continued) 0.304 10.0 0.186 4.44 0.330 8.5 0.179 4.65 0.356 7.5 0.161 4.72 0.383 7.5 0.128 4.42 0. 409 10. 0 0.102 3. 52 0.436 13.0 0.0551 2.15 0. 449 ---- 0. 0470 ---- Drop 10-4 r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0133 69.0 0.0680 1.15 0.0398 70.0 0.119 2.01 0.0663 56.0 0.156 2.75 0.0973 46.5 0.177 2.77 0.119 37. 0 0.197 2. 75 0.146 29.0 0.211 2.91 0.172 21.5 0.222 3.28 0.199 18.5 0.228 3.49 0.225 15.0 0.234 3.78 0.252 14.0 0.236 3.88 0.278 11.0 0.231 4.20 0.305 11.0 0.227 4.19 0.331 8.5 0.222 4.51 0.358 8.5 0.213 4.47 0.384 7.5 0.201 4.69 129 Drop 10-4 (continued) 0.411 6.5 0.185 4.93 0.437 6.5 0 166 4.89 0.464 7.0 0.129 4.53 0.490 9.0 0.0980 3.63 0.517 14.0 0.0680 2.21 0.531 ---- 0.0470 --__ Drop 10-5 r . Ac (cm) %T r (cm) (gm-cm/l) x 103 0 0133 57.0 0.0748 1.43 0.0399 55.0 0.127 2.48 0 0665 43.0 0.159 3.07 0.0931 34.0 0.189 3.10 0.120 27.0 0.207 3.02 0.146 22.0 0 222 3.25 0.173 19.0 0.233 3.46 0.200 14.5 0.245 3.90 0 226 12.0 0.248 4.22 0.253 10.5 0.252 4.44 0.279 9.5 0.255 4.59 0.306 8.5 0.252 4.72 0.333 7.0 0.250 4.96 0.359 6.5 0.246 5.00 0.386 6.5 0.238 4.94 0.412 5.0 0 228 5.22 130 Drop 10- 5 (continued) 0.439 5.0 0.213 5.14 0.466 5.0 0.191 5.19 0.492 5.0 0.177 5.22 0. 519 5. 5 0.152 4. 99 0.545 6.0 0.126 4.49 0.572 6.5 0.0878 3.61 0.599 10.0 0.0653 2.19 0. 612 ---- 0. 0470 ---- Drop 10-1' r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0128 80.0 0.0345 0.351 0.0384 79.5 0.0690 0.555 0.0640 75.5 0.0848 0.675 0.0896 70.0 0.0966 0.852 0.115 61.0 0.0876 1.08 0.141 62.0 0.0828 1.04 0.166 61.5 0.0635 0.940 0.179 ---- 0. 0470 ..... 131 Drop 10-2' r . Ac h (cm) %T r (cm) (gm-cm/l) x 103 0. 0122 94. 0 0. 0470 0. 433 0. 0366 92. 5 0. 0814 0. 756 0.0610 91.0 0.0991 0.777 0. 0854 87. 5 0.113 1. 28 0.110 78.5 0.123 1.81 0.134 74. 5 0.125 1. 88 0. 159 58. 0 0. 125 2. 04 0.183 56. 5 0.117 1. 99 0. 207 58. 0 0.101 1. 83 0. 232 57. 0 0. 0787 1. 55 0. 256 ---- 0. 0470 ---- Drop 12-1 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0. 0131 79. 0 0. 0426 0. 644 0.0393 79.5 0.0721 1.15 0. 0655 77. 0 0. 0793 1. 35 0. 0917 80.0 0.0793 1.18 0.118 79.0 0.0727 1.13 0. 144 76. 5 0. 0524 0. 992 0.157 ---- 0. 0470 ..... 132 .Drop 12-2 r .AAc h (cm) %T r (cm) (gm-cm/l) x 103 0.0126 37.0 0.0459 1.16 0. 0377 40. 0 0.101 2. 46 0. 0628 43. 0 0. 123 3. 00 0. 0879 43. 0 0. 136 3. 22 0.113 40.5 0.144 3.38 0. 138 39. 0 0. 149 3. 45 0.163 37.5 0.151 3.48 0. 188 39. 0 0. 145 3. 38 0. 214 39. 0 0.136 3. 29 0.239 40.0 0.126 3.06 0. 264 34. 5 0. 0970 2. 77 0. 289 36. 0 0. 0596 1. 85 0.301 ---- 0.0470 ---- Drop 12-3 r .13c h (cm) %T r (cm) (gm-cm/l) x103 0. 0131 26. 0 0. 0655 1. 54 0.0393 24.0 0.111 3.02 0.0655 23.0 0.138 3.85 0. 0917 24. 0 0.158 4.14 0.118 22.0 0.172 4.30 0.144 21.5 0.180 4.33 133 Drop 12- 3 (continued) 0.170 19.0 0.187 4.45 0.197 19.0 0.189 4.45 0.223 19.0 0.185 4.45 0.249 18.0 0.182 4.48 0.275 19.5 0.170 4.32 0.301 21.0 0.157 4.06 0.328 21.0 0.128 3.67 0.354 21.5 0.0996 3.00 0.380 21.0 0.0623 2.00 0.393 ---- 0.0470 --_- Drop 12-4 r . AC h (cm) %T r (cm) (gm-cm/l) x103 0.0127 29.0 0.0741 1.65 0. 0382 25. 0 0. 119 3. 22 0.0637 22.5 0.152 4.06 0.0892 21.0 0.174 4.34 0.115 19. 0 0.191 4. 43 0.140 18.5 0.199 4.39 0.166 18.0 0.207 4.42 0.191 17.5 0.213 4.46 0.217 17.5 0.215 4.46 0.242 18.5 0.215 4.38 0.268 19.0 0.211 4.37 0.293 19.0 0.197 4.41 134 Drop 12-4 (continued) 0.319 21.0 0.194 4.34 0.344 22.0 0.176 4.30 0.369 21.0 0.161 4.26 0.395 20.0 0.132 4.00 0.420 20.0 0.111 3.36 0.446 28.0 0.0688 2.08 0.459 ---- 0.0470 ---- Drop 12-5 r . Ac h (cm) %T r (cm) (gm-cm/l) x10 0.0131 15.5 0.0721 1.84 0.0393 13.5 0.117 3.58 0.0655 11.0 0.159 4.67 0.0917 10.0 0.183 5. 09 0.118 9. 0 0. 202 5. 20 0.144 8.5 0.213 5.35 0.170 7.0 0.224 5.64 0.197 9.0 0.232 5.35 0.223 9.0 0.233 5.35 0.249 9.5 0.235 5.28 0.275 12.0 0.233 4.97 0.301 11.5 0.229 5.00 0.328 11.5 0.221 4.97 0.354 12.0 0.209 4.87 0.380 12.5 0.196 4.88 135 Drop 12- 5 (continued) 0.406 13.0 0.178 4.81 0.432 13.5 0.156 4.58 0.459 15.0 0.126 4.04 0.485 17.0 0.0904 3.15 0.511 30.0 0.0492 1.71 0. 524 ---- 0. 0470 ---- Drop 12-6 r . Ac h (cm) %T r (cm) (gm-cm/l) x103 0.0131 11.5 0.0734 2.04 0.0393 10.0 0.128 3.87 0.0655 10.0 0.164 4.83 0. 0917 8. 5 0.190 5. 28 0.118 5.5 0.208 5.80 0.144 5.5 0.223 5.94 0.170 5.5 0.234 6.02 0.197 7.0 0.242 5.73 0.223 7.0 0.248 5.75 0.249 6.5 0.250 5.85 0.275 7.0 0.251 5.74 0.301 7.0 0.249 5.73 0.328 7.0 0.246 5.70 0.354 7.5 0.240 5.58 0.380 7.0 0.231 5.63 0.406 8.0 0.220 5.40 1361 Drop 12-6 (continued) 0.432 7.5 0.206 5.41 0. 459 7. 0 0. 187 5. 48 0.485 7.5 0.164 5.24 0.511 9.0 0.134 4. 64 0.537 11.0 0.105 3.65 0.563 17.0 0.0623 2.14 0. 577 ---- 0. 0470 ---.. Drop 12-7 r. Ac h (cm) %T r (cm) (gm-cm/l) x 103 0.0131 9.0 0.0688 2.13 0.0393 7.5 0.129 4.01 0.0655 6.5 0.167 5.19 0.0917 5.5 0.197 5.73 0.118 5.5 0.216 5.84 0.144 5.5 0.235 6.00 0.170 4.5 0.245 6.36 0.197 6.0 0.254 5.97 0.223 6.0 0.256 6.00 0.249 6.0 0.268 6.00 0. 275 6. 0 0. 269 6. 00 0.301 4.0 0.271 6.60 9 0.328 3.5 0.269 6.77 0.354 3.0 0.265 6.96 0.380 3.0 0.262 6.95 lil’l ‘ 137 .Drop 12#7(confinued) 0.406 3.0 0.254 6.88 0.432 3.0 0.244 6.79 0.459 2.8 0.232 6.78 0.485 2.7 0.214 6.62 0.511 2.8 0.197 6.50 0.537 2.8 0.174 6.34 0.563 3.5 0.151 5.76 0.589 3.8 0.125 5.04 0.615 5.5 0.0970 3.79 0.642 12.0 0.0636 2.16 0.655 ---- 0.0470 -___ .Drop 12-2' r .l3c (cm) %T r (cm) (gm-cm/l) x 103 0.0123 82.5 0.0394 0.647 0.0368 89.0 0.0715 0.872 0.0612 87.5 0.0840 1.09 0.0858 88.5 0.0879 1.02 0.110 87.5 0.0847 1.06 0.135 85.0 0.0787 1.13 0.159 85.0 0.0623 1.01 0.184 ---- 0.0470 ---- 138 Drop 12-3‘ r . Ac (cm) %T r (cm) (gm-cm/l) 3:103 0.0124 82.0 0.0466 0.709 0.0371 82.0 0.0781 1.27 0.0618 82.0 0.0919 1.45 0.0865 82.0 0.0997 1.50 0.111 82.3 0.102 1.47 0.136 82.0 0.0958 1.44 0.161 81.5 0.0886 1.38 0.185 78. 5 0. 0696 1. 27 0.210 ---- 0.0470 ---- Drop 12-9' r . Ac (cm) %T r (cm) (gm-cm/l) x 103 0.0121 7.0 0.0669 1.81 0. 0363 5. 5 0.127 3. 26 0.0605 5.1 0.159 4.12 0. 0847 4. 7 0. 185 4. 30 0.109 3.7 0.203 4.91 0.133 3.4 0.222 4.93 0. 157 3. 5 0. 236 4. 85 0.182 3.5 0.243 4.87 0.206 3.5 0.252 4.90 0.230 3.5 0.257 4.93 It‘lll‘III' .OOOOOOOOOOOOOOOOO . 254 . 278 . 303 . 327 . 351 . 375 . 399 . 424 . 448 . 472 . 496 . 520 . 545 . 569 . 593 . 617 630 139 Dr0p 12-9' (continued) OOOUTUJOO Nu)" U10000‘ 6.1 :9 OOOOOOOOOOPOOOOOO . 259 . 262 . 261 . 259 . 251 247 236 . 227 . 215 . 202 .180 .161 .140 .114 . 0840 . 0525 . 0470 .63 .62 .05 .88 .22 .19 .19 .14 .08 .71 .05 .55 .43 Nwfiubmmmmmmmaxmfiub .70 .29 p—a 13.-liail-Illlllllllll.lll 1 ll APPENDIX F Calibration Curves Figures 21 through 25 are calibration curves of optical density versus concentration for solutions of picric acid in water and in toluene. 140 141 2.2 - 2.0 — 1— t 1.5 - 3 T '8 1— g .. Q 1.0— 8 1— .5 _ Q. _ O b .5 — 0 1 J 1 l 1 l 1 I L l 1 J 0 .01 .02 .03 .04 .05 .06 .07 Concentration (g/l) Figure 21. Standard cell calibration curve of picric acid in water for drop sets 1 through 6. Ill l.11l|3lllllllllllllllllllr.lllliil ‘1'. 142 2.5 2.0 1.5 lT'lleTlllellllTTI[Tlllllllllr] Optical Density 0 U1 lllj‘r—ITIIII 1'1 0 .01 .02 .03 .04 .05 .06 .07 Concentration (g/l) Figure 22. Standard cell calibration curve of picric acid in water for drop sets 8 and 12 excepting the primed numbered drops. 143 2. 5: . .1 o 7 o 2.0— : 0 I. 6 1.5 —- r _ '8 __ s: _. Q) Q _ H 1— ‘“ +— E.” _. to CL .— 0 - 1.0 — 1 o .5 — " I) : O : . . ’ o L‘ 3 e 1 1 1 l 1 I 1 l 1 l l l 0 .01 02 .03 .04 .05 .06 .07 Concentration (g/l) Figure 23. Standard cell calibration curve of picric acid in water for drop set 10 excepting the primed numbered drOps. ’1 1 144 2.5 l '1'] 2.0 'I'JTI'I 1.5 f'lrl'III'Ill Optical Density 1.0 U"! IIIITTrlllj11lll1|fl1II O .01 .02 .03 .04 .05 .06 .07 Concentration (g/l) Figure 24. Standard cell calibration curve of picric acid in water for the drops with primed numbers. fillil‘l'llllllnlll:illiliii .11! 145 7 .7 _ 6 .6 I. .4 _. .4; 7 * (a .2 I. .2 L o — . 1 I 1 o 7 1 J 1 J 0 10 20 30 35 0 10 20 30 >. (a) (b) .t‘.‘ 1.2 - 1.2 _ m I- c _ a "" 1—- 7; 10 — 10 L .3 ” r- 0CL : _ .8 - .8 _ I— L— .6 _ .6 L — +— L_ L. 4 — 4 _. - )— .2 .. .2 5. 0 - 4 l 1 l 1 l 1 0 5 1 l 4 J 0 10 20 30 35 0 10 20 30 (C) (d) Concentration (g/l) Figure 25. Standard cell calibration curves of picric acid in toluene: (a) drop sets 8 and 12 excepting the primed numbered drops; (b) drops with primed numbers; (c) drop sets 1 through 6; (d) drop set 10 ex- cepting the primed numbered drops.