Journal of Fluid Mechanics

Papers

Strong-field electrophoresis

Ory Schnitzera1 and Ehud Yariva1 c1

a1 Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

Abstract

We analyse particle electrophoresis in the thin-double-layer limit for asymptotically large applied electric fields. Specifically, we consider fields scaling as ${\delta }^{\ensuremath{-} 1} $, $\delta ~(\ll \hspace *{-2pt}1)$ being the dimensionless Debye thickness. The dominant advection associated with the intense flow mandates a uniform salt concentration in the electro-neutral bulk. The $O({\delta }^{\ensuremath{-} 1} )$ large tangential fields in the diffuse part of the double layer give rise to a novel ‘surface conduction’ mechanism at moderate zeta potentials, where the Dukhin number is vanishingly small. The ensuing $O(1)$ electric current emerging from the double layer modifies the bulk electric field; the comparable $O(1)$ transverse salt flux, on the other hand, is incompatible with the nil diffusive fluxes at the homogeneous bulk. This contradiction is resolved by identifying the emergence of a diffusive boundary layer of $O({\delta }^{1/ 2} )$ thickness, resembling thermal boundary layers at large-Reynolds-number flows. The modified electric field within the bulk gives rise to an irrotational flow, resembling those in moderate-field electrophoresis. At leading order, the particle electrophoretic velocity is provided by Smoluchowski’s formula, describing linear variation with applied field.

(Received December 01 2011)

(Reviewed March 05 2012)

(Accepted March 27 2012)

(Online publication May 11 2012)

Key Words:

  • colloids;
  • low-Reynolds-number flows

Correspondence:

c1 Email address for correspondence: udi@technion.ac.il

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