Direct Simulations on the Electrophoretic Motion of Multiple Charged Particles using an Immersed Boundary Method

In the present study, we perform the so-called direct simulations on the electrophoretic motion of multiple inertialess charged dielectric particles freely suspended in an electrolyte solution by proposing a direct-charging (direct-forcing) based immersed-boundary method to tackle the complex geometry involved in the particulate flows. The proposed method has an excellent advantage of being able to readily treat the Neumann- as well as the Dirichlet-type interface condition required to solve the Laplacian, the Poisson and the Nernst-Planck equations for the electric field (Poisson-Nernst-Planck model) and the Navier-Stokes equation for the flow field. The method is validated by performing numerical simulations on two different electrokinetic flows (one or two charged particles under no external electric field and one charged particle interacting with a charged planar wall under a uniform external electric field) and then showing that the present results exactly agree with those obtained in different ways. After the validation, the same simulation is successfully applied to the electrophoretic motion of multiple charged particles and the resultant electrokinetic flow. Note that the proposed method can be easily extended as it is to other electrokinetic flows whose governing equations are identical or similar to those of the present electrophoresis.