Electrophoretic Transport in Porous Media:  A Volume-Averaging Approach

Abstract

Volume-averaging methods are applied to develop expressions for the effective electrophoretic mobility and dispersion coefficients in porous media as functions of media structure and electrical field. Case 1 accounts for electrophoretic transport in a two-phase system where both phases may be electrically conductive and the medium is uncharged, and case 2 adds hydrodynamic pressure-driven flow to one of the two phases. The results for case 1 suggest that the electrical field induces dispersion and that the ratio of the dispersion coefficient in the porous medium to free solution diffusivity is not in general equal to the corresponding ratio of electrophoretic mobilities. Calculations for a square unit cell where the fluid is conductive and the obstacles are not conductive show that as the electrical field increases the effective dispersion coefficients increase; however, the effective mobilities are independent of the electrical field. This finding supports recent Monte Carlo studies that suggest the basic assumption of the classical theory of gel electrophoresis is incorrect. The results for case 2 indicate that the electrical field will affect the mean retention time in the column and induce additional dispersion through coupling with the hydrodynamic flow field.

When can the Ogston-Morris-Rodbard-Chrambach model be applied to gel electrophoresis?

“…Additional criticism of these challenges to the basic assumptions of the OMRC model is given in the rebuttal by Tietz [15]. Using the method of volume averaging [16], Locke [17] has shown that when variations of the local electrical field due to the presence of the obstacles are properly accounted for, the left-hand side of Eq. (1) is valid for any spatially periodic and isotropic media containing non-conducting obstacles that do not have percolation limits.…”

“…This result would also be valid, therefore, for ordered media. Locke [17] found that the electrophoretic mobility in this type of porous media is given by where S 1 is a function of the local electrical field and geometry (see Eq. 53 and 55 of Locke [17]).…”

“…Locke [17] found that the electrophoretic mobility in this type of porous media is given by where S 1 is a function of the local electrical field and geometry (see Eq. 53 and 55 of Locke [17]). Determination of this function involves the solution of two closure problems; one for the propagation of the electrical field in the unit cell with a specified local geometry and one for the electrophoretic mobility itself.…”

“…Determination of this function involves the solution of two closure problems; one for the propagation of the electrical field in the unit cell with a specified local geometry and one for the electrophoretic mobility itself. The solution of the electrical field will depend upon the electrical conductivity of both the fluid phase and the obstacle phase (details are given in [17]), and the solution for the electrophoretic mobility will in turn depend upon the electrical field. The closure problem, arising in the volume averaging method, represents the effects of point-wise deviations from the volume-averaged quantities.…”

“…Note that a solution to the closure problem requires the solution of partial differential equations in a given geometry and in general no closed-form or analytical formula is available. Locke [17] showed that the function S 1 is identically zero for the case where the electrical field propagates around nonconducting obstacles that make up the nonpercolating media. In general, if the obstacles are conducting then this term is not zero and it will depend upon the magnitude of the electrical field as well as on the geometry (Eq.…”