Fast and Convenient Implementation of the Taylor Dispersion Method

Abstract

A highly labor-efficient implementation of the Taylor dispersion method for measuring mutual diffusion coefficients in binary liquid systems is described. The experimental setup has been fully automated; it is possible to measure the diffusion coefficients over the whole concentration range in a single experiment using standard HPLC equipment. Software has been developed for processing the data; diffusion coefficients can be calculated from the measured concentration against time curve in various ways (e.g. from the first and second moments and by fitting procedures) within a few seconds. Experiments on the methanol + water system (25 and 35 "C) and the ethanol + water system (25 and 40 "C) have an accuracy of 0.5-1.5%. IntroductionLiquid diffusion plays an important role in chemical engineering, and the design of process equipment requires a knowledge of mutual diffusion coefficients. The purpose of this work is to develop an apparatus for measuring diffusion coefficients in liquid systems over a wide range of temperature and pressure in a fast, accurate, and laborefficient way. The instrument developed here should not need any repeated calibration, and the calculation of the diffusion coefficient from the measured variables is simple and easy to computerize.Experimental techniques used widely for measuring diffusion coefficients are the diaphragm cell technique, interferometric methods, and the Taylor dispersion method (1 -5). Interferometric methods permit the most accurate measurements near room temperature, but it is not (yet) possible to employ these instruments over a wide range of temperature and pressure. The disadvantages of the diaphragm cell are the necessity for calibration of the cell with a system of known diffusivity. Another disadvantage is the long measuring time. The Taylor dispersion technique provides a good alternative. The method is fast, the setup consists of standard HPLC components, and the measurements can be readily automated (6). Therefore, we have chosen the Taylor dispersion method.The Taylor dispersion method is based on the following principle (7, 8): a slow, laminar flow of a liquid mixture is pumped through a long capillary and a narrow pulse of a mixture of a slightly different composition is injected into this capillary. Due to the combined effects of convective flow and molecular diffusion, the pulse ultimately assumes a Gaussian distribution, whose temporal variance is dependent on both the average flow velocity and the molecular diffusivity.At the end of the diffusion capillary the concentration is measured as a function of time; the diffusion coefficient is calculated from the first and second temporal moments or by fitting the dispersion equation to the experimental curve.

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“…Further conditions for the diffusion coefficients are D 11 D 22 ~ D 12 D 21 > 0 and (D 11 -D 22 ) 2 + 4D 12 D 21 > 0. (16,17,18) The assumptions made in the derivation of the working equations are similar to those of the binary dispersion technique (6) with an effective diffusion coefficient D eff . (15) By comparing Toor's method, (17) used in the derivation with of Price's equations, with Taylor's derivation of the binary equation, (23) D eff can be described with the eigenvalues of the D ij matrix…”

“…The effective diffusion coefficient is of the same order of magnitude as the main diffusion coefficients and is used in the equations that provide the criteria for the operating conditions (e.g., calculation of the flow rate). (6,15) The calculation of the Fick diffusion coefficients may be complicated due to their mutual dependence. In a solvent-fixed situation, in which diffusion causes no bulk motion of the liquid, the following relation can be derived (19) where u ij = (du i /dC j ) T,p,Ck=0j is the molar chemical potential and (D ij ) s is the solvent-fixed diffusion coefficient.…”

“…Furthermore, all these procedures are able to fit • D 11 , D 22 . D 21 (4-parameter fit); residence time T calculated, (6) detector sensitivities calculated from the peak areas. • D 11 , D 22 , D 12 (3-parameter fit); D 21 is calculated during the iterative process using Eq.…”

Thermodynamics and transport properties of citral

“…The radially-averaged concentration of component i at time t at the end of the tube relative to the background (carrier) concentration can be expressed as 27 c…”

A técnica de dispersão de taylor para estudos de difusão em líquidos e suas aplicações

“…Utilizando-se de sua semelhança com métodos cromatográ-ficos, van de Ven-Leucassen e colaboradores 26 propuseram a total automação da técnica de Taylor, permitindo sua utilização contínua e sem a participação direta de um operador. Outra modificação foi proposta a fim de diminuir o tempo necessário para obtenção das curvas de dispersão: Bello e colaboradores 27 relataram a obtenção de coeficientes de difusão para solutos de interesse biológico e proteínas em alguns poucos minutos, em contraste com os períodos usuais próximos a uma hora.…”