In the thin-double-layer limit $\kappa a\gg 1$, electrokinetic flows about free surfaces are driven by a combination of an electro-osmotic slip and effective shear-stress jump. An intriguing case is that of a highly conducting liquid drop of radius $a$, where the inability to balance the viscous shear by Maxwell stresses results in an $O\left(\kappa a\right)$ velocity amplification relative to the familiar electro-osmotic scale. To illuminate the inherent nonlinearity we consider uncharged drops, where the induced surface-charge distribution results in a fore-aft symmetric electrokinetic flow profile with no attendant drop translation. This problem is analyzed using a macroscale model, where the double layer is represented by effective boundary conditions. Because of the intense flow, ionic convection within the $O(1/\kappa )$-wide diffuse-charge layer is manifested by a moderate-zeta-potential surface-conduction effect. The drop deforms to a prolate shape in response to the combination of hydrodynamic forces and the effective electrocapillary reduction of the surface-tension coefficient, both mechanisms being asymptotically comparable. The flow field and the concomitant drop deformation are calculated using both a weak-field approximation and numerical simulations of the nonlinear macroscale model.

• Received 4 March 2013

DOI:https://doi.org/10.1103/PhysRevE.87.041002