Dispersion coefficient, effective electrophoretic mobility

Determination of the effective transport coefficients, i.e., dispersion coefficient and electrophoretic mobility, as functions of the geometry of the unit cell requires an analogous averaging of the species continuity equation. Locke [215] showed that for this case the closure problem is given by the following local problems ... 

The standard Rodbard-Ogston-Morris-Killander [326,327] model of electrophoresis which assumes that u alua = D nlDa is obtained only for special circumstances. See also Locke and Trinh [219] for further discussion of this relationship. With low electric fields the effective mobility equals the volume fraction. However, the dispersion coefficient reduces to the effective diffusion coefficient, as determined by Ryan et al. [337], which reduces to the volume fraction at low gel concentration but is not, in general, equal to the porosity for high gel concentrations. If no electrophoresis occurs, i.e., and Mp equal zero, the results reduce to the analysis of Nozad [264]. If the electrophoretic mobility is assumed to be much larger than the diffusion coefficients, the results reduce to that given by Locke and Carbonell [218]. 

Kesner et al. [36] indicated a discrepancy between the theoretical retention and experimental values for some proteins in a channel with flexible membrane walls. These deviations were probably caused by the flexible membrane walls as such effects were not observed for a channel with rigid walls [256]. Nevertheless, the experimental data of Kesner et al. [36] was in reasonable agreement with the El-FFF theory [87,263] with respect to both retention and dispersion. Deviations were attributed to an electrical field gradient in the vicinity of the membrane interface [263]. Calculation of the dependence of K on 1/E from literature data on electrophoretic mobilities and diffusion coefficients confirmed the validity of the retention theory in El-FFF. 

Figure 4. Effective dispersion coefficient, K, vs. electrophoretic mobility, u. As y approaches uos, where vos ...

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