Two-dimensional dipolophoretic motion of a pair of ideally polarizable particles under a uniform electric field

In this paper, we have numerically studied two-dimensional dipolophoretic motion (or combined dielectrophoretic and induced-charge electrophoretic motion) of a pair of ideally polarizable (conducting) cylindrical particles carrying no net charge suspended freely in a viscous electrolyte solution confined by an electrically-neutral square cavity under an applied uniform electric field. To the study, we apply the so-called standard model based on the assumptions that the electric double layer is negligibly thin and the applied electric field is enough small. For the simulations, we develop a finite-volume based numerical approach, where a smoothed profile method is adopted for the numerical solution of the electric field and a direct-forcing based immersed-boundary method is for that of the flow field. Results show that the full dipolophoretic motion differs significantly from the pure dielectrophoretic motion due to an overwhelmingly strong induced-charge electrophoretic effect. For the pure dielectrophoresis, two particles revolve while repelling or attracting each other depending on their configuration and finally get aligned in a line with the field direction. For the full dipolophoresis, on the other hand, two particles also take attractive or repulsive motion according to their configuration, but in a fashion greatly different from the case of pure dielectrophoresis: each of two particles confined by a cavity traces a spiral trajectory around a certain point without any contact between them and asymptotically stops to remain stationary at that point.