Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges

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Abstract
We examine a singular electrokinetic flow around a corner or a wedge in micro-channels constructed from dielectric materials whose permittivity is small but finite compared to that of the electrolyte. When the wedge angle is less than 180°, the applied electric field, which is tangential far from the corner, develops a normal surface component that becomes singular at the corner. This normal field leakage causes opposite polarization at the two sides of the wedge and produces a converging singular tangential electrokinetic flow that ejects liquid from the tip. By expanding in cylindrical harmonics, we estimate this ejecting flow as a function of the permittivity ratio, applied electric field, angle of the wedge and the microscopic corner curvature that suppresses the singularity. The ejecting flow entrains tangential flow on the front side of the wedge and produces a vortex on the downstream side. This entrainment offers a long-range attractive hydrodynamic force that complements short-range electrostatic DLVO (Derjaguin–Landau–Verwey–Overbeek) and dielectrophoretic forces to enhance corner deposition and aggregation of colloids and proteins during electrophoresis/electro-osmosis.

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