Dielectrophoretic sphere–wall repulsion due to a uniform electric field

Abstract

When a zero-net-charge particle is placed under a uniform electric field, the decay of the Maxwell stress with the third power of distance ensures a nil electric force. A nonzero force may nonetheless be generated in the presence of a planar wall due to a mechanism which resembles conventional dielectrophoresis under nonuniform fields. In the prototypical case of a spherical particle this force acts perpendicular to the wall; its magnitude depends upon the pertinent boundary conditions governing the electric potential. When a particle is suspended in an electrolyte solution, where the double-layer structure ensures zero net charge, these conditions are electrokinetic in nature; they involve a balance between bulk conduction and diffusion, represented by normal derivatives, and an effective surface-conduction mechanism, represented by surface-Laplacian terms whose magnitude is quantified by appropriate Dukhin numbers. The dimensionless force depends upon the particle and wall Dukhin numbers as well as the ratio λ of the size of the particle to its distance from the wall. The remote-particle limit λ ≪ 1 is addressed using successive reflections. Calculation of the first few terms in the asymptotic expansion of the force only requires the evaluation of a single reflection from the wall. The leading-order term, scaling as λ⁴, is repulsive, with a magnitude that varies non-monotonically with the particle Dukhin number and is independent of the wall Dukhin number. Surface conditions on the wall enter only at the O(λ⁵) leading-order correction.