Nonlinear alternating electric field dipolophoresis of spherical nanoparticles

We consider the nonlinear electrokinetic problem of a freely suspended conducting (infinitely polarized) spherical micro- or nanosize particle surrounded by an unbounded electrolyte solution. The uncharged particle is exposed to an alternating (ac), nonuniform, and axisymmetric ambient electric field. As a result, the particle acquires a dipolophoretic (DIP) mobility of magnitude, which is quadratic in the amplitude of the applied electric field. The resulting phoretic velocity is driven by two independent nonlinear mechanisms. One is the common dielectrophoretic effect, whereby the nonuniform field exerts an electrostatic force on the image multipole singularity system within the particle. The other is the so-called "induced-charge electrophoresis" resulting from the action of the electric field on the excess charge around the particle induced in the diffused layer by the field itself. Both effects are quadratic in the amplitudes of the electric field and depend on the forcing frequency and on the dimensionless Debye screening length scale. It is demonstrated in the sequel that the two generally act in opposite directions which may result in mutual cancellation. Under the assumptions of a "weak" electric field and the neglect of surface conductance, we present a concise analysis of the resulting nonlinear streaming (dc) velocity (averaged over a period) for a spherical metalic particle that is exposed to a time-harmonic oscillating (ac) electric field. The analysis of this fundamental nonlinear DIP problem is provided for arbitrary forcing frequencies and for any Debye thickness. Numerical simulations are given for the case of a "two-mode" interaction consisting of a uniform-gradient electric field combined with a uniform field, where the two modes are either "in" or "out" of phase.