Determination of the Dynamic Electrophoretic Mobility of a Spherical Colloidal Particle through a Novel Numerical Solution of the Electrokinetic Equations

Abstract

The standard equations developed to describe the electrophoretic motion of a charged particle immersed in an electrolyte subjected to an oscillating electric field are solved numerically with a new technique suitable for stiff systems. The focus of this work is to use this solution to determine the dynamic particle mobility, one of several quantities that can be extracted from these equations. This solution is valid from low frequencies to indefinitely high frequencies and has no restriction on zeta potential, double-layer thickness, or electrolyte composition. The solution has been used to calculate the dynamic electrophoretic mobility of a particle for a wide range of double-layer thicknesses and zeta potentials. The solution agrees with analytic approximations obtained previously by other authors under the conditions of a thin double layer and low zeta potential. The results are also consistent with calculations valid at frequencies where the ion diffusion length extends a significant distance beyond the double layer as obtained by another numerical technique.

Dynamic electrophoresis of concentrated droplet dispersions at arbitrary surface potentials

“…As a increases further, however, the double layer thickness gets so thin that eventually the distortion of the ionic cloud becomes negligible again, and the dynamic electrophoretic mobility restores to its previous behavior, i.e., to increase accordingly with increasing surface potential. Similar behaviors are also observed in the case of an isolated spherical particle (Preston et al, 2005) and concentrated dispersion of spherical particles (Hsu et al, 2002), both at high surface potential.…”

The dielectric response of a colloidal spheroid

“…The most widely used numerical code is due to DeLacey and White [1], whose code was later extended by Mangelsdorf and White [2]. In certain cases (for thick double layers or/and for high frequencies), the numerical analysis can be time consuming or sometimes impossible, but some recent studies are making progress on this topic [3].…”

Dynamic Electrophoretic Mobility of Concentrated Dispersions of Spherical Colloidal Particles. On the Consistent Use of the Cell Model

“…As one means of ensuring correct results, two independent programs were used to perform the calculations. One was written in the Fortran 90 language and uses the COLSYS collocation package 43 to solve the above system of odes, in the same manner described in ref to handle boundary value problems for stiff differential equations (which these equations become at sufficiently high frequencies 39,44 ). A second program was written in the Matlab language, and utilizes the internal BVP4C routine, which is also a collocation algorithm.…”