Ind. Eng. Chem. Fundam. 1980, 19, 219-221
219
EXPERIMENTAL TECHNIQUES Gaseous Diffusion Coefficients by the Stefan-Winkelmann Method Using a Polymer-Solvent Mixture as Evaporation Source JOS6
Coca," Julio L. Bueno, and Ricardo Alvarez
Department of Chemical Engineering, University of Oviedo, Oviedo, Spain
Gaseous diffusion coefficients of binary gas-vapor mixtures have been determined by the Stefan-Winkelmann evaporation tube method, using a high boiling point compound (as a polymer)-solvent mixture as evaporation source. Experimental results at 1 atm pressure have been obtained for the systems air-benzene (67 ' C ) and air-toluene (100 ' C ) and they are in good agreement with values expected when the pure solvent is used. The use of a polymer-solvent mixture as the source of vapor offers the possibility of avoiding some of the drawbacks pointed out for the Stefan-Winkelmann method.
Introduction Gas and liquid diffusion coefficients are of particular importance in considering mass transfer in gas-liquid chromatography (Szepesy, 1971) as mass transfer may affect the column efficiency considerably (Butler and Hawkes, 1972). Factors influencing mass transfer in a gas chromatographic column correspond to the different terms of the van Deemter equation (van Deemter et al., 1956) or its modified forms (Jones, 1961). In this equation the gas phase diffusion coefficient of the sample, ,BG enters in the longitudinal diffusion term and the liquid phase diffusion coefficient of the sample, ,BI,, enters in the resistance to the mass transfer process term. By using an empty tube, under appropriate conditions, Y l G can be determined (Giddings and Seager, 1962) and knowing ,BG, 2ILcan also be estimated from the dispersion of samples in columns in which the stationary phase is supported on glass beads (Butler and Hawkes, 1972). Among conventional methods for measuring gas and vapor diffusion coefficients, that of Stefan (Stefan, 1871) has been broadly used (Marrero and Mason, 1972). Some of the drawbacks pointed out for this method are the following: (a) poor precision for vapors of liquids of very high or very low pressures, (b) measurements cannot be made above the boiling temperature of the liquid, and (c) large amounts of sample and time-consuming experiments. Modifications of the Stefan-Winkelmann method (Winkelmann, 1884) have been reported in the literature (Pommersheim, 1971,1973; Mato and Bueno, 1977a), and the precision achieved is comparable with that of the chromatographic method. In this work a modified Stefan-Winkelmann technique has been used to determine gas diffusion coefficients by using a polymer or a high boiling point compound mixed with a solvent as the evaporation source. Gas-liquid chromatography stationary phases (polyphenyl ether, Carbowax 1500, and tricresyl phosphate) have been used as the second component in the mixture with a solvent (benzene or toluene). The mathematical model used in 0196-4313/80/1019-0219$01.00/0
connection with the nonsteady-state method of StefanWinkelmann has been extended for mixtures high boiling point substanc-olvent, and gas diffusion coefficients have been determined in a certain range of concentration of the evaporation liquid mixture. The use of a high boiling point compound mixed with a solvent removes several limitations of the StefanWinkelmann technique, particularly the temperature range at which the diffusion coefficient can be determined. It also allows the obtaining of some data of polymer-solvent mixtures, some of them of particular interest in mass transfer studies by gas chromatography and processes with polymers (Coca et al., 1979).
Theoretical Development The Stefan-Winkelmann method for measuring diffusivities of vapors is based on determining the rate of evaporation of a volatile liquid that can be followed by the rate of descent of the liquid surface in a glass tube or diffusion cell. The diffusion cell shown in Figure 1contains a liquid mixture of a volatile solvent A and a high boiling point compound, I, that does not diffuse into the gas phase. At the top of the cell there is a flow of gas B insoluble with the liquid at the bottom of the cell. Diffusion of A takes place through a stagnant film of A + B and for each time ti the interface depth is ti. By measuring these variables the mass flux NA*12=o can be determined and also the diffusion coefficient a)AB. By a quasi-steady-state analysis, the interface depth as a function of time can be obtained by the following equation (Pommersheim, 1971; Mato and Bueno, 1977a)
where
0 1980 American Chemical Society
220
Ind. Eng. Chern. Fundam., Vol. 19, No. 2, 1980
-
B (aas)
+B
I
/bo
I
I Figure 2. Simplified diagram of the experimental technique: A, diffusion cell; B, flow chamber; C, cathetometer; F, thermocouple probe; D, heater; T, adiabatic still.
Figure 1. Coordinates scheme and concentration profile.
Equation 1 assumes that P and pAi are independent of time, which is essentially true in most experimental conditions in an open system and for a pure solvent A. If the vapor source is a homogeneous mixture of A with a high boiling compound I as a polymer, most of the assumptions implicit in eq 1still hold, but the concentration potential in the gas phase, responsible for the diffusion process, will be a function of time as the solvent concentration in the liquid phase decreases with time. Equation 1has to be written in the following form
The right-hand side of eq 3 can be written as
where (aAB) is the average value of the diffusion coefficient determined from the concentrations in the stagnant gas film in the interval ( t 2- tl);p k is the vapor pressure at the interface, assuming saturation conditions, when the bulk concentration of the liquid phase is c A ~ . To avoid concentration gradients in the liquid phase, mixing can be provoked by using a polymer or a high boiling point substance of higher density than the solvent the homogeneity of the liquid phase was verified by holographic interferometry (SBnchez et al., 1976, 1977a,b). By graphic integration of eq 3, (arn) can be determined by performing the experiment in a small range of cAiso as to fulfill the assumptions of the quasi-steady-state regime. Experimental Equipment The experimental Stefan-Winkelmann technique was similar to that described earlier (Mato and Bueno, 1977a), but data on vapor pressures at the interface, as a function of the liquid phase composition, are required to obtain the diffusion coefficients. The evaporation tube (0.18 cm i.d. and 20 cm length) fiied with the polymersolvent mixture is immersed in an adiabatic still in which the vapors of a boiling liquid act as a thermostatic fluid. The vapors are condensed and recirculated to the still. By changing the liquid in the still different temperatures can be obtained. The temperature in the adiabatic still can be maintained to h0.05 "C. A simplified diagram of the experimental technique is shown in Figure 2. The gas, after flowing through filtering and drying stages, is preheated by passing it through a coiled stainless
Figure 3. Adiabatic still and flow chamber.
steel tube placed inside the adiabatic still. Then it flows through a small nozzle directed toward the top of the evaporation tube. This kind of arrangement allows the obtaining of good thermostatic conditions and minimizes convective effects. The liquid interface level was followed by a cathetometer to the nearest 0.001 mm. Pressure in the system was controlled to f 2 mm H20 for all runs by means of an electronic relay connected with a pump. The temperature in the diffusion chamber was measured by a mercury thermometer and could be read f O . l "C. Interface vapor pressures data are needed to determine experimental diffusivities. Values of pAi as a function of cAi were determined from mixtures of A and I by vapor pressure osmometry using a Knauer unit (Burge, 1963; Alvarez, 1977). Figure 3 shows a diagram of the adiabatic still and flow chamber.
Results and Discussion Measurements were performed using the three aforementioned liquid phases: polyphenyl ether, Carbowax 1500, and tricresyl phosphate with benzene and toluene as solvents. As shown in Figures 4 to 7, the diffusion coefficient of the solvent-air systems are constant for the range of composition shown in the gas phase. In Table I experimental results at several temperatures are compared with calculated coefficients by the Chen-
Ind. Eng. Chem. Fundam., Vol. 19, No. 2, 1980
221
Table I. Diffusivities of Benzene and Toluene (cm' s - l ) at 1 a t m Pressure
- l__ o -?
2
013
T,
0-~-0-0-0-
"C
system
67 benzene-PFE (6 rings)-air benzene-CW1500air benzene-air
aAB*
exptl
0,1199
this work
0.1193
550
-
+ polyphenyl ether (6 rings)-air
system.
I
*a 011
I
+ polyphenyl ether (6 rings)-air system.
I
h
I
2 O" I-
Figure 6. Toluene
V
01'
0.1288 0.1289 0.1284
1
Figure 5. Benzene
,.
100 toluene-PFE ( 6 rings)-air toluene-TCPair toluene-air
I + tricresyl phosphate-air
system.
I
ref this work
pAl(mmW
Figure 4. Toluene
calcd
0.1196
009 545
aAB,
Bueno (1973) 0.1101 ChenOthmer (1962) 0.1158 Slattery-Bird (1958) this work
this work Bueno (197 3) 0.1149 ChenOthmer (1962) 0.1255 Slattery-Bird (1958)
Nomenclature A = solvent B = gas cAi = concentration of A at the interface, g-mol/cm3 BG,BL = gas and liquid diffusion coefficients, cm2/s a)AB = molecular diffusion coefficient; ( BAB), mean value, cm2/s hi = total interface depth, cm I = polymer or high boiling compound K = constant defined by eq 2, dimensionless MA = molecular weight of solvent A P = pressure, atm p A i = vapor pressure at the interface, atm R = gas constant, (atrn) (cm3) (K)-l (g-mol)-' T = absolute temperature, K ti = time, s z, = interface depth, cm zo = initial interface depth, cm ~ ~ ( x ~ ~ 1 ( =,~ molar ) fraction of the liquid phase for t = 0 and t = t, dimensionless Y A ( ~ ) yA(v , = molar fraction in the gas phase for t = 0 and t = t , dimensionless Greek Letters P A = density of the solvent A, g/cmg Literature Cited
Alvarez, R.. Ph.D. Thesis, University of Oviedo, 1977. I Bueno. J. L., Ph.D. Thesis, University of Valladolid, 1973. Oo9 490 495 PA,(mm Hg 1
Figure 7. Benzene
+ Carbowax 1500-air system.
Othmer and Slattery-Bird equations. Experimental runs with the same apparatus but using pure solvents instead of polymer-solvent mixtures as the evaporation source show good agreement (Mato and Bueno, 1977a,b; Alvarez, 1977), deviations being lower than 1.5%, well within the precision limits of the technique. Therefore, the polymer or high boiling point substance does not affect the diffusivity values in the gas phase, in the operation range used in this work. This fact increases the possibilities of the StefanWinkelmann technique, particularly for measuring diffusivities in a wider range of temperatures and near the boiling point of the solvent, one of the most severe limitations of the conventional technique.
Burge, D. E., J . Phys. Chem., 87, 2590 (1963). Butler, L., Hawkes, S., J . Chromatogr. Sci., 10, 518 (1972). Chen, N. H., Othmer, D. F., J . Chem. Eng. Data, 7 , 37 (1962). Coca, J., Bueno, J. L., Alvarez, R., Polym. Bull., 1, 459 (1979). Giddings, J. C.. Seager, S. L., Ind. Eng. Chem. Fundam., 1, 277 (1962). Jones, W. L., Anal. Chem., 33, 829 (1961). Marrero, T. R., Mason, E. A., J . Phys. Chem. Ref. Data, I , 3 (1972). Mato, F.. Bueno. J. L., An. Quim., 73, 108 (1977a). Mato, F., Bueno, J. L., An. Quim., 73, 114 (1977b). Pommersheim, J. M., Ind. Eng. Chem. Fundam., 10, l(1971). Pommersheim, J. M., Ranck, B. A., I d . Eng. Chem. Fundam.. 12,246 (1973). SBnchez, V., Clifton, M. J., C. R . Acad. Sci. Ser. C . , 282, 1093 (1976). SBnchez, V., Clifton, M. J., Ind. Eng. Chem. Fundam., 18, 318 (1977). SBnchez, V., Oftadeh, H., Durou. C.. Hot, J. P., J. Chem. Eng. Data, 22, 123
(1977). Slattery, J. C., Bird, R. B., AIChE J.. 4, 137 (1958). Stefan, J., Akad. Wis. Wien., 63, 63 (1871). Szepesy, L., "Gas chromatography",p 63,Akadgmiai Kiad6, Budapest, 1971. van Deemter, J. J.. Zulderwerg. F. J., Klinkenberg, A., Chem. Eng. Sci., 5 , 271
(1956). Winkelmann, A., Ann. Phys., 22, l(1884).
Received for review March 30, 1979 Accepted December 18, 1979
