449
Znd. Eng. Chem. Res. 1992,31,449-452 MX = m-xylene PX = p-xylene TBMX = tert-butyl-m-xylene TBPX = tert-butyl-p-xylene RsgiStry NO. MX, 108383; 5-TBMX, 98-19-1; 4-TBMX,
14411-55-3; IB,115-11-7; 2-TBPX, 1985-64-4; 4-TBP, 98-54-4;
PhOH, 10895-2; diisobutylene,25167-70-8;sulfuric acid, 7664-93-9; p-xylene, 106-42-3.
Literature Cited Corson, B. B.; Heintzelman, W. J.; Odiso, R. C.; Tiefenthal, H. E.; Paulik, F. J. Separation of positional isomeric dialkylbenzenes. Znd. Eng. Chern. 1966,48,1180-2. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions: Analysis, Examples and Reactor Design; Wdey New York, 1984; Vol. 2, p 17. Kelly, J. T.; King,L. R.; Knight, H. M. Xylene separation by depolyalkylation. Znd. Eng. Chem. Prod. Res. Deu. 1962, l (4), 293-6. Levine, D. M.; Glaetonbury,J. R. Application of Kolmogoroff's theory to practicle-liquid mass transfer in agitated vessels. Chem. Erg. Sci. 1972,27,537-43.
Sankholkar, D. S.; Sharma, M. M. A new system for the measurement of effective interfacial area in agitated liquid-liquid contactors by the chemical method. Chem. Eng. Sci. 1973, 28, 2089-91. Tashiro, M.; Fukada, Y.; Nishinohara,M. Japan Patent 77,111,519, 1977; Chem. Abstr. 1978,88, 50447. Tiwari, R. K.; Sharma,M. M. Alkylation of benzene and toluene with lower olefins. Chern. Erg.Sci. 1977,32, 1253-8. Vasudevan, T. V.; Sharma, M. M. Alkylation of xylenes with sulfuric acid as a catalyst in a two phase system. Znd. Eng. Chem. Process Des. Deu. 1983,22, 161-4.
* To whom correspondence should be addressed. Swapan Kumar Ghosh, Man Mohan Sharma* Department of Chemical Technology University of Bombay, Matunga
Bombay 400 019, India Received for review April 15, 1991 Revised manuscript received September 27, 1991 Accepted October 14, 1991
A Technique for Rapid Measurement of Diffusion Coefficients A technique for rapid, simple measurement of liquid-phase mutual diffusion coefficients is presented. Dark ground optics in combination with a modified Lamm diffusion cell is used to monitor diffusion fringes in binary solutions. Data are presented for comparison to published values for the systems dimethylformamide (DMF)-H20 and acetone-H20. Agreement with literature values is within 5 % . New data for the composition dependence of the system dimethyl sulfoxide (DMSO)-H20 are also given. The method offers the advantages of speed (less than 3-min run time) and simplicity. Modifications for improved accuracy are discussed.
Introduction Optical methods base'd on free diffusion are generally preferred for determination of liquid-phase mutual diffusion coefficients due to their high accuracy. These involve monitoring the refractive index through analysis of interference patterns as a function of time and distance from the original diffusion boundary. The text by Tyrrell and Harris (1984) gives a detailed discussion of the experimental and theoretical aspects of the various techniques. Although such methods are quite reliable, the optical systems can be involved. In addition, full advantage of their potential accuracy requires long times for complete establishment of fringe patterns and relatively complicated data analyses. Steady-state techniques such as a diaphragm cell, while much simpler to analyze and operate, require much longer times and can produce erratic results (Cussler, 1984). This paper presents a modified technique based on dark ground optics which can be used for rapid and accurate anaijrsis of liquid-phase diffusion coefficients. In addition to very short run times (within 3 min), the optics upon which the spatial filtering is based leads to a very simple analysis procedure which can be readily adapted to video imaging. The technique is demonstrated by comparison with literature data for two systems along with new data for the system dimethyl sulfoxide-water. Experimental Section Materials. Diffusivity data were obtained using reagent grade NJVdimethylformamide (DMF), dimethyl sulfoxide (DMSO), acetone (as obtained from Fisher Scientific),and distilled, deionized water. Diffusion Cell. Figure 1 shows a schematic of the modified Lamm optical diffusion cell which is used. The
upper chamber (B)is made of aluminum and the lower chamber (C), in which diffusion is monitored, is made of optical-quality fused silica (Hellma Cells Inc.). Both chambers are held together by the aluminum frame (A) and Teflon pressure block (HI. The separating plate (F) is a O.OOZin.-thick, metal foil which is lubricated around the perimeter with a thin layer of vacuum grease to ensure leakageproof operation. The lower cavity (E) is filled with denser solution and the upper cavity (D)is aligned using the pressure block (G)and filled with the less dense solution. Interfacial contact is achieved by removal of the separating plate using a motor-driven device. Dark Ground Optics. Figure 2 shows a schematic of the dark ground optical system. The objective lens, pinhole aperture, and collimating lens produce an expanded, noiseless beam of uniform intensity. Changes in the solution refractive index, n(y,t), induce a retardance, 6, in the light passing through the cell given by (Klein and Furtak, 1986) NY,t) =
2 d d Y , t ) - nR1
x
(1)
where y is position in the lower solution relative to the initial interface, w is the cell thickness, X is the wavelength of light, and the reference refractive index, nR, is that of the initially uniform composition in the lower solution. The diffraction image of the phase-modulated beam emerging from the cell is filtered on the back focal plane of the transform lens with a circular stop to remove the unrefracted light image from the pinhole aperture. The stop is a 150-pm-diameter chromium disk which is evaporated onto a glass plate using a photolithographic technique (Gaides, 1992). The resultant filtered image is focused through the camera for recording of the fringe
QSSS-5SS5/92/2631-Q449$Q3.QQ/Q0 1992 American Chemical Society
450 Ind. Eng. Chem. Res., Vol. 31, No. 1,1992
Figure 1. Diffusion cell consisting of aluminum chamber (B), o p tical glaen chamber (C), aluminum frame (A), Teflon pressure hloek (H), and aeparating plate (F). Cavity E is fded with denser solution and block G aligns chamber cavities (Dand E) prior to removal of the separating plate. dinusion cell
circular
pinhole
0 Ho-Ne laser
A ' VI
SmP
A
obje~+~e mllimating lens lens
A transform lens
video camera
Figure 2. Dark ground optical system.
pattern superimposed on the cell. Proper adjustment of the stop position relative to the pinhole image is generally neeescary in order to ensure that all of the refracted beam is included in the fdtered diffraction Dattern. Under such conditions, the relationship betweed the phase shift and fringe pattern intensity will be given by (Born and Wolf, 1989) I(y,t) = 4 C sin2 (6(y,t)/2) (2) where Cis a constant associated with the optical elements.
Data Analysis For small composition differences in the upper and lower solutions, the refractive index will be a linear function of concentration. Under conditions of free diffusion, the one-dimensional,time-dependent profile of component 1 in a binary, 1-2 system, will be given by
Figure 3. Dark ground fringe pattern during DMF-H,O diffusion.
*
(2) at 25 0.3 "C. The lower dark region corresponds to the uniform, initial concentration in the lower solution, and the top is the interface between the two solutions. Positions of the three outermost minima are also noted. Precise location of the position of minimum intensity within a given fringe is determined using video imaging software based on the methodology described elsewhere (McHugh and Spevacek, 1987). The accuracy of location of a minimum is *0.01 mm with this method, and the time accuracy is f0.05 s. The slightdunevennessin the horizontal image of a given fringe line results from the method of initial boundary formation; however, this distortion tends to he exaggerated in the photographs. Variations along a given line are actually within the flimita of the fringe minimum location noted above and therefore do not limit the accuracy of the measurement. Knowing n.and n,, D can he evaluated from ( 5 ) for a given fringe and averaged for several fringes. Since measurement of the quantity n, - nl has an uncertainty (+0.0004 refractive index units in our case), greater accuracy can he obtained by minimizing the following objective function N
where D is the mutual diffusion coefficient. Subscripts 1 and u represent initial compositions in the lower and upper solutions, respectively. According to (3),positions of a given refractive index vary with the square root of time. From (1)and ( 2 ) ,the condition for minimum intensity is 6 = 2m71, thus mX n, - nl =, ; m = integer (4)
Q = (X(D - D j ) 2 ) 1 / 2
(6)
j=1
where DJ refers to the value for the jth fringe, N is the number of fringes measured, and D is the average value. In our case, maximum precision is obtained using the.fmt three fringes.
Results As an example, we consider the run with the binary system DMF (l)-HzO(2) shown in Figure 3. The average Equation 3 can he rearranged to the following form: volume fraction of DMF is 0.635, and the difference hetween the two solutions is 0.05. The refractive index difference, measured with a Bausch & Lomb ABBE-3L refractometer, is 0.0051. The motions of the three minimum-intensity positions are shown in Figure 4. Correwhere subscript m refers to the intensity minimum and sponding slopes are 6.766 X S , is the slope of the ym2versus t plot. Depending on the 4.498 X and 3.384 X1 Pcm2/s, respectively, from which the mutual diffusion sign of nu - nl, m can he positive or negative. For our system, X = 632.8 nm and w = 4 mm. coefficient has the value 0.963 X cm2/s. Figure 3 shows an example of a typical expanding fringe Table I shows a comparison of diffusivities from this pattern for a run with the binary system DMF (l)-H20 work and values from the literature for the binary systems
0.0081
o m=l m=2 A
,-/
m=3
1
Ind. Eng. Chem. Res., Vol. 31, No. 1,1992 451
0.0 0.0
t(sec) Figure 4. Fringe minimum, ym,squared versus time for the diffusion process shown in Figure 3. Table I. Mutual Diffusion Coefficients of Component (l)-H1O (2) Systems compoDtbia work, Dliteraturs, nent (1) ai, bI n.. - nl cm2/s cmz/s dev. % 1.16 DMF 0.66 0.61 0.0051 0.963 X 10" 0.952 X DMF 0.98 0.92 0.0027 1.438 X 1.461 X lod 1.57 acetone 0.08 0.00 0.0039 1.279 X 1.220 X 4.84
DMF-H20 obtained by Volpe et al(1986) using the Gouy technique, and acetoneHzO obtained by Anderson et al (1958) using Mach-Zehnder diffusiometer. Agreement in all cases is within 5 % . Figure 5 shows a complete set of new measurements for the system DMSO-HzO at 25 f 0.3 "C. The two end points are estimated from data for the self-diffusion coefficients of DMSO (Johnston et al., 1979) and water (Packer and Tomlinson, 1971) in the dilute ends where the self-diffusion and mutual-diffusion coefficients are equal (Bearman, 1961).
Discussion The two optical methods which compare with that presented here are the Mach-Zehnder and shearing interferometry techniques (Tyrrell and Harris, 1984). Both produce fringe patterns superimposed on the cell image; however, their additional optical complexity introduces the possibility of inherent aberrations, as well as a considerable increase in cost and operational difficulty. Since, in the present method, only the lower chamber of the diffusion cell is illuminated, the resulting fringe pattern of the filtered image arises solely from diffraction effects as given by (2). This leads to a considerable simplification in the analysis since interference effects associated with the superposed symmetric diffusion pattern are avoided. As a consequence, as indicated in (51, one does not need to know the precise zero time since only the slope of the fringe motion plot (Figure 4) is used. For highly nonideal systems, the steep composition dependence of the diffusivity would require small initial composition differences (i.e., values of nu - n,)in order to justify the assumption of constant D and to avoid complications due to bulk flow. In such a case, increasing the diffusion cell optical path length, w ,would lower the initial concentration difference needed to produce the necessary fringes (see (1)).Additionally, one could make the cell fully transparent to enable analysis of the full fringe pattern in both chambers, effectively lowering the error in determining nu - nl. However, such a modification would ne-
this work Packer and Tornlinson(l971) A Johnston et aL(1979)
0 1.6
0.6 0.8 1.o H20 Figure 5. Mutual diffusion coefficients of DMSO-H20 system.
0.2
0.4
cessitate a more complicated analysis to account for the interference effects on the diffraction image (Tyrell and Harris, 1984). The principal object of this paper has been to show the type of precision and rapidity possible with a relatively simple cell design and very simple analysis algorithm. Improved accuracy can be achieved with better temperature control; however, for most transport modeling applications, the precision obtained with the current system is quite sufficient and the cell design and method are therefore well suited for routine measurements.
Acknowledgment This work has been carried out under a grant from the National Science Foundation (CTS 90 13289). We also acknowledge the important contributions made by our colleague, Mr. Gary Gaides, in the development of the optical technique used in this study.
Nomenclature C = constant associated with the optical elements D = mutual diffusion coefficient (cm2/s) D = average mutual diffusion coefficient (cm2/s) Dj = mutual diffusion coefficient for the jth fringe (cm2/s) I = fringe pattern intensity n = refractive index N = number of fringes used to calculate D Q = objective function (cm2/s) S = slope of the y 2 versus t plot (cm2/s) t = time ( 8 ) w = diffusion cell thickness (cm) X = mole fraction y = position coordinate in the lower solution relative to the initial interface (cm) Subscripts 1 = lower solution region m = position with minimum intensity R = reference solution u = upper solution region Greek Symbols 6 = phase change with respect to the reference solution X = wavelength of light q5 = volume fraction
Literature Cited Anderson, D. K.; Hall,J. R.; Babb, A. L. Mutual Diffusion in Nonideal Binary Liquid Mixtures. J. Phys. Chem. 1958,62,404-409.
452 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 Bearman, R.J. On the Molecular Basis of Some Current Theories of Diffusion. J. Phys. Chem. 1961,65,1961-1968. Born, M.; Wolf, E. Principles of Optics; Pergamon: New York, 1989; pp 424-428. Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems; Cambridge: New York, 1984;pp 133-137. Gaides, G. E. Measurement and Analysis of Bath-Side Interfacial Concentration Gradienta During Membrane Quenching by Phase Inversion. Ph.D. Dissertation, University of Illinois at Urbana, 1992. Johnston, R. C.; Lobdell, C. 0.;Janauer, G. E. Cation Exchange in Mixed Solvent Media. 2. Alkali Ion and Solvent Self-Diffusion in Dowex 50W-Dimethyl Sulfoxide-Water. J. Phys. Chem. 1979, 83,1816-1820. Klein, M. V.; Furtak, T. E. Optics; Wiley: New York, 1986;p 485. McHugh, A. J.; Spevacek, A. J. A Technique for Monitoring the Kinetics of Flow-Induced Crystallization. J. Polym. Sci., Polym. Lett. Ed. 1987,2.5,105-110.
Packer, K. J.; Tomlinson, D. J. Nuclear Spin Relaxation and SelfDiffusion in the Binary System, Dimethylsulphoxide (DMSO) + Water. Trans. Faraday SOC.1971,67,1302-1314. Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworth London, 1984,pp 126-176. Volpe, C. D.; Guarino, G.; Sartorio, €2.; Vitagliano, V. Diffusion, Viscosity, and Refractivity Data on the System Dimethylformamide-Water at 20 and 40 OC. J. Chem. Eng. Data 1986, 31, 37-40.
Chorng-Shyuan Teay, Anthony J. McHugh* Department of Chemical Engineering University of Illinois Urbana, Illinois 61801 Received for review July 23, 1991 Revised manuscript received October 30, 1991 Accepted November 12, 1991
ADDITIONS AND CORRECTIONS Boiling Incipience in a Reboiler Tube [Volume 30, Number 3, Page 5621. Hamid Mi* and S. S. Alam Page 567. In eq 9, the value of the constant should be 0.0405 and not 0.405 as printed. The correct equation is therefore
9)
0.216
X 100 = 0 . 0 4 0 5 ( ~ ~ B ~ 0 . 3 0 8 ~ ~ " ~ 0 . 3 6 6 ~ .(9) 6g2( L zOB
