Numerical simulation and analytical methods have been used to study electrophoresis of a dielectric particle having a hydrophobic surface and high surface conductivity. The results demonstrate that, in a moderate electric field and at high surface charge density, particle velocity increases and the contribution of surface conductivity considerably exceeds that of the slip length. A formula has been analytically derived for the mobility of a hydrophobic particle, which comprises three terms: (1) the linear term in the Helmholtz–Smoluchowski well-known relation, (2) a term representing the contribution of the hydrophobic surface, and (3) the surface conductivity contribution due to the high surface charge density. We present results for a small and a large slip length, corresponding to micro- and nanoparticles. Comparison of the numerical and analytical solutions we obtained demonstrates good agreement between the two approaches used.
Frants et al. (2025) studied this question.