Strong-field electrophoresis

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.