Investigation of the Nonlinear Effects During the Sedimentation Process of a Charged Colloidal Particle by Direct Numerical Simulation

In this article we study the settling process of a colloidal particle under the influence of a gravitational or centrifugal field in an unbounded electrolyte solution. Since particles in aqueous solutions normally carry a non-zero surface charge, a microscopic electric field develops which alters the sedimentation process compared to an uncharged particle. This process can be mathematically modelled via the Stokes-Poisson-Nernst-Planck system, a system of coupled partial differential equations that have to be solved in an exterior domain. After a dimensional analysis we investigate the influence of the various characteristic dimensionless numbers on the sedimentation velocity. Thereby the linear-response (weak-field) approximation that underpins almost all existing theoretical work on classical electrokinetic phenomena is relaxed, such that no additional assumption on the thickness of the double layer as well as on its displacement is needed. We show that there exists a strong influence of the fluid Reynolds number and the ionic strength on the sedimentation velocity. Further we have developed an asymptotic expansion to describe the limit of small values of the surface potential of a single particle. This expansion incorporates all nonlinear effects and extends the well-known results of Booth (1954) [1] and Ohshima et al. (1984) [2] to higher fluid Reynolds numbers.