Modeling electrokinetic and colloid transport phenomena in Arbitrary Lagrangian Eulerian (ALE) framework

Colloidal and electrokinetic transport processes formulated as steady-state systems are often modeled as kinematic relationships. A mathematical model that renders the exact dynamics of the motion of a charged colloidal particle suspended in an electrolyte solution is presented in this study. The model consists of the governing equations for the electrokinetic particle transport as a combination of Navier-Stokes equations for fluid flow, Poisson equation for electrostatics, and Nernst-Planck equations for ion transport. A finite element analysis is employed to the governing equations in an Arbitrary Lagrangian-Eulerian (ALE) framework. Several pertinent problems of different levels of complexity and coupling between the governing equations were analyzed.;The model was employed to obtain a stand-alone method of evaluation of wall correction factors for a particle moving in a cylindrical channel. End effect on the motion of a particle in a finite channel was analyzed and a correlation was presented to calculate wall correction factors for different particle to channel radii ratios. Electrokinetic flow in a finite microchannel was also studied. The effects of exit boundary condition and channel surface waviness (through frequency and amplitude of the surface) on concentration distributions and ion rejection were analyzed. Finally, a fully coupled electrokinetic model consisting of particle motion, fluid flow, electrostatics, and ion transport was developed to analyze the electrophoresis of a charged particle. It was demonstrated that the solution of the governing equations yields different results for particle mobility depending on whether the equations were solved in a particle fixed reference frame or in a globally fixed reference frame. The difference demonstrates that non-linear governing equations do not provide an identical description of the physics of electrophoresis in alternate kinematic and actual dynamic frameworks. The present research, through a multiphysics modeling approach, provides a comprehensive understanding of the underlying principles of electrokinetic transport of a colloidal particle.