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Nonlinear electrophoresis at arbitrary field strengths

Ory Schnitzer (Technion), Ehud Yariv ()

Electrohydrodynamics and electrokinetics of fluid systems

Mon 9:00 - 10:30

Barus-Holley 161

It is well known that Smoluchowski's thin-double-layer electrophoresis formula breaks down at mildly large zeta potentials because of `surface' conduction. In the linear weak-field regime – extensively analyzed by Dukhin, O'Brien, and Hunter – surface conduction acts as negative feedback, resulting in mobility curves which are non-monotonic in zeta. In this talk, we analyze particle electrophoresis beyond this regime. We start by deriving a generic macroscale model in the thin-double-layer limit, valid for arbitrary electric field magnitude. In this coarse-grained description, transport processes occurring on the Debye scale are embodied in a set of effective boundary conditions. The removal of scale disparity associated with the double layer facilitates numerical simulations and sets the stage for systematic perturbation schemes. For weak fields, a weakly nonlinear analysis of our model furnishes a velocity correction to Dukhin's formula which favorably agrees with numerical simulations. A superior approximation path entails perturbing the macroscale model for small but non-zero Dukhin numbers (Du), allowing for the analysis of particle electrophoresis at arbitrary field strengths; this limit actually encompasses the entire range of practical zeta-potential values. The calculation of the O(Du) correction to Smoluchowski's formula is reduced to solving an advection-diffusion problem governing the bulk concentration perturbation. In the limit of strong electric fields, salt polarization is confined to a thin diffusive boundary layer; the velocity correction scales with the 3/2 power of the electric field.