Abstract
A comprehensive analytical study of the electrophoresis of a suspension of charged spherical particles in an arbitrary electrolyte solution through a porous medium is analyzed using a unit cell model. The unsteady Brinkman equation with the term of the electric force governing the fluid velocity fields is solved by means of the Laplace transform. The porous medium is uniformly charged by fixed charge density Q, and the embedded spherical particle is conductive and charged with constant zeta potential. Two different accurate concepts of the boundary conditions at the outer virtual surface, are presented to solve the governing equations for the flow field. Steady-state electrophoretic velocity is obtained analytically and displayed graphically for different physical parameters. Also, a closed form of the transient electrophoretic velocity versus the dimensionless elapsed time is plotted and discussed for different values of the Debye length parameter, particle volume fraction, density ratio, permeability of the porous medium, and for highly- and non-conducting particles. The steady/ transient electrophoretic velocity is a monotonic decreasing function of the permeability parameter, the particle-to-fluid density ratio, and the particle volume fraction, but it increases with an increase in the Debye length parameter with constant zeta potential. In general, the Kuwabara cell model predicts a smaller value for the electrophoresis velocity than the Happel model, but the difference is not significant. On the other hand, when the transient velocity is normalized by its steady state, the Happel model has smaller values than the Kuwabara model. The effects of the relevant parameters on the transient starting electrokinetic flow in the porous medium are interesting and significant. The results are found to be in excellent agreement with the exact numerical results obtained by Lai and Keh.
Published Version
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