Numerical study of the influence of solid polarization on electrophoresis at finite Debye thickness

Abstract

The influence of solid polarization on the electrophoresis of a uniformly charged dielectric particle for finite values of the particle-to-fluid dielectric permittivity ratio is analyzed quantitatively without imposing the thin Debye length or weak-field assumption. Present analysis is based on the computation of the coupled Poisson-Nernst-Planck and Stokes equations in the fluid domain along with the Laplace equation within the solid. The electrophoretic velocity is determined through the balance of forces acting on the particle. The solid polarization of the charged particle produces a reduction on its electrophoretic velocity compared to a nonpolarizable particle of the same surface charge density. In accordance with the existing thin-layer analysis, our computed results for thin Debye layer shows that the solid polarization is important only when the applied electric field is strong. When the Debye length is in the order of the particle size, the electrophoretic velocity decreases with the rise of the particle permittivity and attains a saturation limit at large values of the permittivity. Our computed solution for electrophoretic velocity is in agreement with the existing asymptotic analyses based on a thin Debye layer for limiting cases.

Electrophoretic Mobility of a Dilute, Highly Charged “Soft” Spherical Particle in a Charged Hydrogel

“…This shall be referred to as the “linear continuum theory”. Recently, Bhattacharyya et al − have extended these studies to include nonlinear effects of the imposed electric or flow field which has made it possible to study electrokinetic transport under high field conditions. The objective of the present work is developing an algorithm applicable to dilute soft particles in charged gels within the framework of the linear continuum model.…”

Nonlinear electrophoresis in the presence of dielectric decrement

“…We apply the model to study two archetypal problems in electrokinetics, namely the electrophoresis of particules with fixed surface charges and the electrophoresis of ideally polarizable particles. Following numerous studies in electrokinetics [48][49][50][51][52], we rely on numerical simulations to incorporate nonlinear effects including crowding effects due to the finite size of ions, dielectric decrement in the electric double layer, surface conduction, and concentration polarization and advection in the bulk solution and in the electric double layer. To our knowledge, the present study is the first to build on the steric-dielectric decrement model of Nakayama and Andelman [42] to quantitatively describe electrophoresis in the nonlinear regime.…”

An analysis on the electrophoretic mobility of cellulose nanocrystals as thin cylinders: relaxation and end effect

“…Solid polarization was reported to signicantly affect electrophoretic mobility only when an applied electric eld was strong and a dielectric permittivity ratio of particle to solution was large. 21 In this study, however, the applied electric eld was weak and the dielectric permittivity ratio was small. Thus, the solid polarization effect is negligible.…”