Combination of the direct-forcing fictitious domain method and the sharp interface method for the three-dimensional dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain (DF/FD) method and the sharp interface method (SI) to resolve the problem of particle dielectrophoresis in three dimensions. The flow field is solved with the DF/FD method. The electric field governed by a Laplace equation with a jump coefficient across the particle surface is solved with the sharp interface (SI) method, and the dielectrophoretic force on particles is then calculated with the Maxwell stress tensor (MST) method. The main feature of our method is that both hydrodynamic and dielectrophoretic forces on particles are calculated with the interface-resolved methods instead of the point-particle model. The accuracy of the SI/MST method for the dielectrophoretic force without the consideration of the flow is validated via two problems: the electrostatic force on the particle in a non-uniform electric field, and the electrostatic force between two particles. The capability of the proposed DF/FD–SI/MST method is demonstrated with two numerical examples: the aggregation of particles due to the conventional dielectrophoretic force, and the motion of particles due to both conventional and traveling wave dielectrophoretic forces.