Electrophoresis of a single charged porous sphere in an infinite medium of electrolyte solution

Electrophoresis of a single charged porous sphere in an infinite medium of electrolyte solution is investigated theoretically. The porous sphere is treated as a Brinkman medium with uniformly distributed electric charges. General electrokinetic equations including the full nonlinear Poisson equation are employed as the governing equations, which are then solved with a pseudo-spectral method based on Chebyshev polynomials. Key parameters of electrokinetic interest are examined for their effects on particle motion. Motion-deterring nonlinear effects, the condensation effect and the double layer polarization effect, are separated from each other and examined in detail for their respective impact on the particle motion. The Debye-Hückel approximation is found to overestimate the particle mobility severely: Up to ten times for a porous sphere both highly charged and highly permeable in some situations, which is attributed to the polarization effect. Convenient charts of correction factors for this overestimation are provided to facilitate the usage by interested experimental researchers in the field of the study of polyelectrolytes, such as DNA and proteins, which are well modeled as charged porous spheres.