Electrophoresis of a charged colloidal particle in porous media: boundary effect of a solid plane

Electrokinetic treatments such as the electrophoretic technique have been applied successfully to various soil remediation and contaminant removal situations. To understand further the fundamental features involved, the electrophoretic motion of a charged particle in porous media is investigated theoretically in this study, focusing on the boundary effect of a nearby solid plane toward which the particle moves perpendicularly. The porous medium is modeled as a Brinkman fluid with a characteristic screening length (λ(-1)) that can be obtained directly from the experimental data. General electrokinetic equations are used to describe the system and are solved with a pseudospectral method based on Chebyshev polynomials. We found that the particle motion is deterred by the boundary effect in general. The closer the particle is to the boundary, the more severe this effect is. Up to a 90% reduction in particle mobility is observed in some situations. This indicates that a drastic overestimation (10-fold!) of the overall transport rate of particles may occur for large-scale in situ operations in porous media, such as soil remediation utilizing large planar electrodes, should a portable analytical formula valid for bulk systems only be used. Correction factors for various situations in porous media are presented as convenient charts with which to aid engineers and researchers in the field of environmental engineering, for instance, as a realistic estimation of the actual transport rate obtainable. In addition, the results of present study can be applied to biomedical engineering and drug delivery as well because polymer gels and skin barriers both have a porous essence.