Surface instability of a thin electrolyte film undergoing coupled electroosmotic and electrophoretic flows in a microfluidic channel

We consider the stability of a thin liquid film with a free charged surface resting on a solid charged substrate by performing a general OrrSommerfeld (O-S) analysis complemented by a long-wave (LW) analysis. An externally applied field generates an electroosmotic flow (EOF) near the solid substrate and an electrophoretic flow (EPF) at the free surface. The EPF retards the EOF when both the surfaces have the same sign of the potential and can even lead to the flow reversal in a part of the film. In conjunction with the hydrodynamic stress, the Maxwell stress is also considered in the problem formulation. The electrokinetic potential at the liquidair and solidliquid interfaces is modelled by the PoissonBoltzmann equation with the DebyeHuckel approximation. The O-S analysis shows a finite-wavenumber shear mode of instability when the inertial forces are strong and an LW interfacial mode of instability in the regime where the viscous force dominates. Interestingly, both the modes are found to form beyond a critical flow rate. The shear (interfacial) mode is found to be dominant when the film is thick (thin), the electric field applied is strong (weak), and the zeta-potentials on the liquidair and solidliquid interfaces are high (small). The LW analysis predicts the presence of the interfacial mode, but fails to capture the shear mode. The change in the propagation direction of the interfacial mode with the zeta-potential is predicted by both O-S and LW analyses. The parametric range in which the LW analysis is valid is thus demonstrated.