Electrokinetic lift

Electrolyte flow relative to a charged surface induces a bulk electric field (the ``streaming potential'' phenomena). This field, and the flow perturbation it animates, generate both electrical and hydrodynamic ``electro-viscous'' forces whose magnitude has been a matter of ongoing controversy. Recently we have revisited this problem, predicting $O(\delta^2)$ scaling (as opposed to earlier prediction of $\delta^4$ and $\delta^6$), $\delta \ll 1$ being the dimensionless Debye width. These electro-viscous forces can explain the anomalous repulsion of polystyrene microspheres from an adjacent wall in the presence of an imposed shear flow, observed by Prieve and co-workers. Owing to the symmetry properties of the linear Stokes equations, such repulsion is inadmissible in the absence of inertial effects. This particle--wall interaction is analyzed using our revised scheme. The undisturbed flow consists of three components: the `driving' shear mechanism and the `induced' particle translation and rotation. We consider a small dimensionless particle--wall gap $\epsilon$. At leading-order, both the lift and additional drag are contributed by the inner gap region. The lift force is $O(\delta^2\epsilon^{-3})$ while the additional drag is $O(\delta^2\epsilon^{-2})$. The streaming-potential mechanism underlying these forces arises from the `induced' rather than the driving component.