Electrophoresis of microparticle with hydrophobic surface in strong electric field

Abstract

The study addresses the problem of electrophoresis of a dielectric particle with a hydrophobic surface. A complete dimensional formulation of the problem is presented, followed by a transition to a dimensionless formulation. The main method of investigation is the analytical solution of the problem, conducted separately for the electrical and the hydrodynamic components. The primary task was to derive a relationship for the electrophoresis velocity of the micro-particle with a hydrophobic surface based on key parameters of the problem: the intensity of the external electric field $E_{\mathrm{\infty }}$, the slip length $\beta$, the surface charge density $\sigma$, the Debye number $\nu$, and the ratio of the dielectric permittivities of the particle and the medium $\delta$. Additionally, the study includes a comparison of the analytically obtained electrophoresis velocity of the hydrophobic particle with the results of numerical modeling of electrophoresis of a dielectric particle and an assessment of the contribution of the slip length parameter to the increase in electrophoresis velocity. The influence of the parameters $\sigma$ and $\delta$ on the electrophoresis velocity is also demonstrated separately.