Dielectrophoretic motions of multiple particles and their analogy with the magnetophoretic counterparts

To investigate the dielectrophoretic motions of multiple particles, we have performed the so-called direct numerical simulations on two-dimensional flows involving inertialess dielectric particles of two to five suspended in a viscous fluid under a uniform external electric field and then compared the results with those of the corresponding magnetophoretic counterparts. For the simulations, the electric field (or the force acting on each particle) is described by the numerical solution of the Maxwell equation (or Gauss's law), where the smoothed representation technique is employed to tackle the jump of electric conductivity across the particle-fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where one-stage smoothed profile method is employed to satisfy the no-slip condition at the interface. In all the simulations, the particles are initially equi-spaced on a circle with an origin at the center while a uniform electric field is externally imposed. Results show that all particles move with repelling or attracting one another depending on the locally nonuniform electric field formed due to the presence of multiple particles. Consequently, they become clustered largely into two groups, then revolve in the clockwise or counterclockwise direction, and finally get aligned in a line with the field direction. One exception is their initial configuration which is symmetric with respect to the axis perpendicular to the electric-field direction, where all the particles move eternally far away from one another with keeping the symmetry. In addition, it is found that the two-dimensional relative motions of dielectric particles under a uniform external electric field are qualitatively in fairly exact agreement with those of paramagnetic particles suspended in a nonmagnetic fluid under a uniform external magnetic field.