Instabilities in free-surface electroosmotic flows

Abstract

With the recent development of novel microfluidic devices electroosmotic flows with fluid/fluid interfaces have emerged as very important subjects of investigation. Two immiscible fluids may need to be transported in a microchannel, or one side of a channel may be open to air for various purposes, including adsorption of airborne molecules to liquid for high-sensitivity substance detection. The liquid/liquid or liquid/gas interface in these cases can deform, resulting in significant corrugations followed sometimes by incipient rupture of liquid layers. For electroosmotic flow the rupture, leading to shortcircuit, can cause overall failure of the device. It is thus imperative to know the conditions for the rupture as well as the initial interfacial instability. Studies based on the Debye-Huckle approximation reveal that all free-surface electroosmotic flows of thickness larger than the Debye screening length are unstable and selectively lead to rupture. Layers of the order of Debye screening length, however, are not properly described by the Debye-Huckle approximation. Even for micro-scale layers, the rupture phenomenon can make local layer thickness to be nanoscale. A fully coupled system of hydrodynamics, electric field, and ionic distribution need to be analyzed. In this paper linear instability and subsequent nonlinear developments of a nanoscale free-surface electroosmotic flow are reported.