Nonlinear Electrophoresis of a Charged Dielectric Particle in Polar and Nonpolar Media: The Role of the Electrohydrodynamic Coupling Parameter

Abstract Direct numerical simulation of the electrophoresis of a charged dielectric microparticle is performed using a coupled nonlinear system of Nernst–Planck–Poisson–Stokes equations within a range from weak to strong electric fields. The goal of the study is to compare the electrophoretic mobilities and the structures of the ion transport in polar and nonpolar electrolytes at a fixed particle surface charge. Two characteristic values of the Debye length, which correspond to thin and relatively thick electrical double layers, are considered to describe these two types of media. The particle surface charge is fixed at a value corresponding to the regime, in which pronounced nonequilibrium effects and the ionic cloud deformation are expected at a sufficiently high electric field strength. The main attention is focused on the dependence of the dimensionless mobility on the electric field strength and control parameter κ, which determines the intensity of the electrokinetic interaction and the influence of hydrodynamics on the ion transport. It has been shown that an increase in the field strength makes the response essentially nonlinear and is accompanied by an enhancement of the concentration polarization and changes in the spatial distributions of ion concentrations and space charges. Parametric dependences of the electrophoretic mobility have been compared for the two characteristic Debye lengths, and parameter ranges have been determined in which the difference between the polar and nonpolar media is mainly quantitative, as well as the ranges corresponding to qualitative changes in the transport regime. For the characteristic regimes, spatial distributions of the total ion concentration and charge density are presented, thus making it possible to relate the changes in the mobility with the changes in the structure of ion fluxes and the volumetric electric force. The obtained results provide criteria for the onset of a nonequilibrium regime and can be used for interpreting experiments and designing electrokinetic microsystems in polar and nonpolar electrolytes.