(320i) Electrokinetic Lift In Shear Flows

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, showing that these forces scale as the second power of Debye width, as opposed to earlier predictions of fourth and sixth powers.

Electro-viscous forces could explain several surprising observations involving the motion of colloidal particles at low-Reynolds-number conditions, such as the anomalous repulsion of microspheres from an adjacent wall in the presence of an imposed shear flow, as 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. These, in turn, have been ruled out in the experiments.

This particle--wall interaction is analyzed using our revised model. The undisturbed flow consists of three components: the `driving' mechanism, a stationary sphere in a shear flow, together with the `induced' components, particle translation parallel to the wall and rotation normal to it, which follow from the constraint of a force-free particle. Symmetry arguments show that the additional electro-viscous lift results from Maxwell stresses, while the additional drag results from viscous stresses.

Using a lubrication approximation we consider the case where the dimensionless particle--wall gap is small. At leading-order, both the lift and additional drag are contributed by the gap region, scaling as negative powers of its width. It is noteworthy that the streaming-potential mechanism underlying these forces arises from the `induced' flow components, rather than the driving shear component. The contributions associated with translation and rotation are comparable. For equal zeta potentials, electro-viscous drag are actually proportional to the sum of translational and rotational velocities, while electro-viscous lift is proportional to its square.