Fully resolved immersed electrohydrodynamics for particle motion, electrolocation, and self-propulsion

Simulating the electric field-driven motion of rigid or deformable bodies in fluid media requires the solution of coupled equations of electrodynamics and hydrodynamics. In this work, we present a numerical method for treating such equations of electrohydrodynamics in an immersed body framework. In our approach, the electric field and fluid equations are solved on an Eulerian grid, and the immersed structures are modeled by meshless collections of Lagrangian nodes that move freely through the background Eulerian grid. Fluid-structure interaction is handled by an efficient distributed Lagrange multiplier approach, whereas the body force induced by the electric field is calculated using the Maxwell stress tensor. In addition, we adopt an adaptive mesh refinement (AMR) approach to discretizing the equations that permits us to resolve localized electric field gradients and fluid boundary layers with relatively low computational cost. Using this framework, we address a broad range of problems, including the dielectrophoretic motion of particles in microfluidic channels, three-dimensional nanowire assembly, and the effects of rotating electric fields to orient particles and to separate cells using their dielectric properties in a lab-on-a-chip device. We also simulate the phenomenon of electrolocation, whereby an animal uses distortions of a self-generated electric field to locate objects. Specifically, we perform simulations of a black ghost knifefish that tracks and captures prey using electrolocation. Although the proposed tracking algorithm is not intended to correspond to the physiological tracking mechanisms used by the real knifefish, extensions of this algorithm could be used to develop artificial "electrosense" for underwater vehicles. To our knowledge, these dynamic simulations of electrolocation are the first of their kind.