Instability of liquid film with odd viscosity and slip effect under the action of external electric field

Abstract

The influence of odd viscosity on the instability of a liquid film flowing along a porous inclined plane under a normal electric field is investigated. It is assumed that the flow at the porous inclined plane satisfies the Beavers–Joseph slip boundary condition. By utilizing the long-wave approximation and employing the method of systematic asymptotic expansion, a nonlinear evolution equation for the film thickness under the influence of the electric field is derived. The stability analysis of this evolution equation reveals that the odd viscosity of the film has a stabilizing effect, while the electric field has a destabilizing effect. Additionally, the permeability of the porous inclined plane enhances the instability of the liquid film flow. Numerical simulations are conducted using a fast Fourier transform algorithm to solve the nonlinear evolution equations. The numerical results demonstrate that, within the stable region and with all parameters fixed, the wave amplitude decreases as the evolution time increases, indicating a gradual stabilization of the liquid film flow. Conversely, in the unstable region, the opposite behavior is observed. As the evolution time increases, the fluctuation amplitude grows larger, resulting in a gradual destabilization of the liquid film flow. Furthermore, when the evolution time is kept constant and the odd viscosity coefficient is nonzero, the film exhibits greater stability. The amplitude of the wave increases with the electrical parameter E. In the unstable region, an increase in the permeability β of the porous medium leads to a tendency for the film flow to stabilize.