A nonlinear study on the interfacial instabilities in electro-osmotic flows based on the Debye–Hückel approximation

Interfacial instabilities in an electro-osmotic micro-film flow are studied by deriving an evolution equation for the local film thickness and subsequent numerical integrations. The free-surface electro-osmotic flow has an inherent instability of the long-wave type, which generates corrugations on the film surface. These corrugations may critically affect the transport characteristics of the flow, and deserve a nonlinear analysis based on conservation laws. It is shown that the electro-osmotic instability can cause severe local depression of the film even in the absence of the van der Waals attraction between the film surface and the substrate. The electrical double layer (EDL) then may be penetrated by the film surface, and film rupture can occur, resulting in loss of the electro-osmotic driving force. Since the Debye–Hückel approximation used becomes inadequate as the film thins locally to a nano-scale, quantitative analysis of the incipient rupture reported would require a fully coupled system for fluid flow, ionic concentration, and electric field.