Time-varying Brinkman electrophoresis of a charged cylinder-in-cell model

Abstract

Abstract The time-evolving electrophoresis of the swarm of parallel charged circular cylinders in the transverse to their axe’s direction through an electrolyte-saturated porous medium when suddenly applying an external electric field is studied semianalytical approach using the unit cell model. The electric double layer in the porous continuum surrounding the circular cylinder in a unit cell is supposed to be thin but finite, and the effect of dynamic electroosmosis within it is included. Explicit formulas of the time-periodic electrophoresis and settling velocities of the circular cylinders in the Laplace transform as functions of the relevant physical parameters of the problem are performed for two different boundary conditions on the outer virtual surface of the cell model. The calculation results indicate that the time scale for the development of electrophoresis and sedimentation is small for a high permeability, a swarm of circular cylinders through a charged porous Brinkman medium with a higher volume fraction of the particle, and a smaller particle to porous fluid density ratio; the electrophoresis mobility increases monotonically with an increase in the electrokinetic radius of the cylinder at any instant. The time-dependent electrophoresis velocity has a monotonic decreasing function with increasing the volume fraction of the particle at a low value of the cylindrical particle-to-medium density ratio, but it may increase as the volume fraction of charged cylindrical particles increases at a high value of this density. The result of particle interaction in a suspension on the start-up of electrophoresis is much weaker than that on the time-varying sedimentation of the circular cylindrical particles. The comparison between calculations of the cell model with associated boundary conditions at the fictitious surface of the cell is derived and depicted graphically. The cell model predicts that, under otherwise specified conditions, the electrophoresis mobility in a Brinkman medium constructed by a system of parallel cylinders in the transverse direction, in general, is weaker than that of a system of spheres.