J . Ph.ys. Chem. 1990, 94, 5 180-5 183
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Determination of Ternary Diffusion Coefficients by the Taylor Dispersion Method Derek G . Leaist Department of Chemistry, D’niuersity of Western Ontario, London, Ontario, Canada N 6 A 5B7 (Received: September 6 , 1989; In Final Form: December 22, 1989)
A new procedure is described for the rapid determination of ternary mutual coefficients using Taylor dispersion. Pulses of liquid are injected into a long capillary tube containing a laminar flow of liquid of different composition. A differential refractometer at the tube outlet monitors the dispersion of the injected samples. The ternary diffusion coefficients are calculated from the temporal moments of the changes in refractive index. To test the procedure, diffusion coefficients are determined for the three-component systems sucrose + potassium chloride + water and sodium chloride + magnesium chloride water a t 25 OC. The measured diffusion coefficients are compared with accurate values obtained by optical interferometry.
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Introduction Although multicomponent diffusion is of considerable theoretical and practical importance, few systems14 have been studied, largely because the experiments tend to be intricate and time consuming. In recent years, however, the Taylor dispersion method5-I0 has emerged as a simple and rapid technique for the reliable determination of binary diffusion coefficients. The purpose of the present work is to apply the Taylor method to multicomponent systems. In a Taylor experiment, a small volume of solution is injected into a solution of different composition flowing in a long capillary tube. A detector at the tube outlet monitors the dispersion of the injected solute. The diffusion coefficient is calculated from the measured solute distribution. The method is not as accurate as the best optical or diaphragm-cell techniques, but it offers the advantages of speed and convenience. Liquid chromatography pumps and detectors that are available in many laboratories can be used without modification, and the procedure is readily automated. In addition, reliable Taylor diffusion measurements can be made on dilute solutions that would pose problems for the other techniques. Unlike diaphragm cells, calibration with materials of known diffusivity is not required. Multicomponent experiments using optical interferometry indicate that undesirable convective mixing can result from density inversions or dynamic instabilities” within free-diffusion columns. even if the lower solution is initially denser than the upper one. In Taylor diffusion experiments, unwanted convection is eliminated because the liquid is confined to narrow-bore tubing. In fact, the injection of solutions that are denser or less dense than the flowing solution yields identical measured diffusion coefficient^.^ The potential advantages prompted us to try Taylor experiments on three-component systems. Equations are developed to evaluate ternary diffusion coefficients from the shapes of the eluted solute peaks. The proposed method is tested by measuring diffusion coefficients of sucrose + potassium chloride + water and sodium chloride magnesium choride + water. Accurate optical diffusion datai2J3reported previously for these systems are used to check the Taylor results. Although the present work is concerned with ternary diffusion, suggestions are made regarding the measurement
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( 1 ) Tyrrell, H. J . V . ; Harris. K. R. Dif/usion in Liquids; Butterworths: London, 1984. (2) Cussler, E. L. Multicomponent Diffusion; Elsevier: Amsterdam, 1976. ( 3 ) Rai, G . P.; Cullinan, H. T., Jr. J. Chem. Eng. Data 1971, 18, 212. (4) Leaist, D. G. J . Chem. Soc., Faraday Trans. I 1987, 8 3 , 829. ( 5 ) Taylor. G. 1. Proc. R. Soc. London 1963, A219, 186. (6) Pratt, K . C.; Wakeham, W. A. Proc. R. Soc. London 1975, A342,401. (7) Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A . I n ? . J . Thermoohvs. 1980. I . 243 { S i Chen, S.; Davis, H. T.; Evans, D. F. J. Chem. Phys. 1982, 77, 2540. ( 9 ) Weinheimer, R . M.; Evans, D. F.; Cussler. E. L. J . Colloid Interface
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1989, 93, 2176
of diffusion in four-component and higher order systems.
Experimental Section Reagent grade sucrose, urea, and KCI were used as received. A stock solution (- 1 mol dm” (M)) of reagent grade MgC12.H20 was standardized by potentiometric titration against silver nitrate and then diluted as required. Distilled deionized water and calibrated volumetric flasks were used to prepare the solutions. The diffusion tube was a 3119-cm length of Teflon tubing wrapped in a 75-cm-diameter coil. The internal radius of the tube (0.045 15 cm) was determined by weighing the tube when empty and water filled. Solution samples (typically 0.0100 cm3,
