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.
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