We have developed the smoothed profile method to study dynamical properties of colloidal dispersions. This method is applicable to several complex problems including electrophoresis, where hydrodynamic and electrostatic problems are coupled. We compute the fluid velocity and the electrostatics potential by solving both Navier-Stokes and Poisson equations directly. The time evolutions of the colloidal particles and the density of counter ions are then determined by solving Newton's equation of motion and advection-diffusion equation, respectively, in a consistent manner so that the electrohydrodynamic coupling can be fully taken into account. The electrophoretic mobilities of spherical colloidal particles are calculated in several situations including those in concentrated dispersions. The comparisons with theories show quantitative agreements.
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