An immersed boundary method for simulating the electric potential in flows with active colloids*

This study is motivated by fluid flows with Janus particles actuated by an electric field. A Janus particle is a microparticle composed of two dielectric materials with different electric permittivities. This difference in permittivity generates an asymmetry in the electric field, which can be leveraged to control the particle’s motion. CFD simulations of Janus particles face the challenge of computing the electric potential in both the fluid and particle. This electric potential is coupled by a set of Dirichlet and Neumann conditions at both the fluid-particle interface and the interface between the two dielectrics in the particle. Applying these interface conditions using a conventional body-fitted grid is computationally expensive when the particle geometry is complex, particularly if the particle moves. We consequently develop a novel Immersed Boundary Method (IBM) for computing the electric potential to second-order spatial accuracy. The method places no constraints on the particle geometry, and permits general discontinuous Robin interface conditions if desired. To demonstrate our method, we solve for the electric potential and resulting force on a Janus particle adjacent to an electrode.