Free-surface instability in electro-osmotic flows of ultrathin liquid films

The stability of a free surface under electro-osmotic flow in thin liquid films is investigated where the film thickness can be varied over the scale of a thick to thin electrical double layer while considering the relative contribution from the van der Waals forces. The role of interfacial Maxwell stress on thin film stability is highlighted. This configuration gives some interesting insights into the physics of free surface stability at a scale where various competing forces such as the Coulombic force, van der Waals force, and surface tension come into play. The effects of the mentioned forces are incorporated in the Navier-Stokes equations and a linear stability analysis of the resulting governing equations is performed to obtain the Orr-Sommerfeld equations. The characteristic stability curve of the system is obtained through an asymptotic analysis of the Orr-Sommerfeld equations in the long wave limit. In this study, special focus is given to the effect of the interfacial zeta potential on the free surface stability. It is found that when the free surface and the substrate zeta potential have the same polarity the system is unstable. Since the strength of the free surface potential depends upon the nature of the fluid substrate interaction, this study can help in choosing a proper combination of fluid and substrate to design microfluidic and nanofluidic channels with a desired flow rate without triggering the interfacial instability.