Thermocapillary instability in the presence of uniform normal electric field: effect of odd viscosity

The stability and dynamics of a gravity-driven, viscous, Newtonian, thin liquid film with broken time-reversal symmetry draining down a nonuniformly heated inclined plane in the presence of a uniform normal electric field is examined within the finite-amplitude regime. The presence of odd part of the Cauchy stress tensor with odd viscosity coefficient brings new characteristics in thin film flow as it gives rise to new terms in the pressure gradient of the flow. Employing the classical long-wave expansion technique, a nonlinear evolution equation of Benney-type is derived in terms of film thickness h(x, t). The linear stability analysis is performed using the normal mode approach and a critical Reynolds number is obtained. The linear study reveals that the critical Reynolds number increases with odd viscosity and decreases with the electric field. It is also observed that thermocapillarity promotes instability. In other words, odd viscosity has a stable effect while the electric field and thermocapillarity have destabilizing tendency on the flow dynamics. The method of multiple scales is used to investigate the weakly nonlinear stability of the flow and it is observed that both supercritical stable and subcritical unstable zones are possible for this type of film flow. Scrutinizing the effect of odd viscosity, Marangoni and electric Weber numbers on the amplitude and speed of waves, it is found that in the supercritical region, the threshold amplitude decreases with the increase in odd viscosity. Finally, the spatially uniform solution is obtained sideband stable in the supercritical region for the considered parameter range.