Discrete solution of the electrokinetic equations

Details Discrete solution of the electrokinetic equations Discrete solution of the electrokinetic equations

2004-04-13

arxiv.org/abs/cond-mat/0404289v1

Physics

Condensed Matter

Statistical Mechanics

24 pages, 7 figures

Scientific paper

10.1063/1.1760739

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number.

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