Instabilities in free-surface electroosmotic flows

Instability of a thin electrolyte film undergoing a direct current electroosmotic flow has been investigated. The film with a compliant electrolyte-air interface is flowing over a rigid charged substrate. Unlike previous studies, inclusion of the Maxwell stresses in the formulation shows the presence of a new finite wavenumber shear-flow mode of instability, alongside the more frequently observed long-wave interfacial mode. The shear mode is found to be the dominant mode of instability when the electrolyte-solid and electrolyte-air interfaces are of opposite charge or of same charge but have very large zeta-potential at the electrolyte-air interface. The conditions for mode-switch (interfacial to shear) and the direction of the travelling waves are discussed through stability diagrams. Interestingly, the analysis shows that when the interfaces are of nearly same zeta potential, the 'free' electrolyte-air interface behaves more like a 'stationary' wall because of the ion transport in the reverse direction of the flow.