Electrophoresis of a soft particle normal to a plane

Electrophoresis of a spherical composite particle normal to a plane is investigated theoretically. The composite particle under consideration, or the "soft" particle, consists of an inner hard core coated with a concentric porous layer containing uniformly distributed fixed charges. A pseudo-spectral method based on a Chebyshev polynomial is adopted to solve the resulting electrokinetic equations. The effects of general parameters of electrokinetic interest are examined, such as the double layer thickness, the density of the fixed charges carried in the porous layer, the retarding friction coefficient of the porous layer, and so forth. In particular, the effect of the presence of the planar boundary is examined in detail, including the clearly visible deformation of the double layer due to the presence of the boundary and its electrokinetic implications. Local maximum of charge distribution within the porous layer near the north pole is observed when the double layer is thick. Moreover, the impact of the electroosmotic flow within the porous layer is explored. The appearance of a vortex flow due to electroosmosis within the porous layer is shown, which explains directly the retarding effect of mobility when the double layer becomes thinner, as the orientation of this vortex is opposite to the particle motion. Comparisons with various limiting cases available in the literature show excellent agreement, indicating the accuracy and reliability of the results presented in this study.