Direct Numerical Simulation of the Settling of a Charged Colloidal Particle

Abstract

In many industrial processes it is necessary to control the interactions between particles and the ambient electrolyte in which they are dispersed. In this paper we consider the sedimentation of a single charged colloidal particle in a Newtonian electrolyte to study the basic physical effects of this process. We investigate the settling of the particle by direct numerical simulation. This approach finally leads to the Stokes‐Poisson‐Nernst‐Planck system, a system of coupled partial differential equations. For the numerical approximation of the solution we use the finite element method. We show that the settling velocity does not solely depend on the ion concentration of the electrolyte, but also has a significant dependence on the particle Reynolds number. In the case of small particle Reynolds numbers our results are in good agreement with the existing literature. We have further developed a new zeta potential expansion that is capable of describing the whole range of particle Reynolds numbers in the Stokes limit.