Effect of odd viscosity on the stability of a falling thin film in presence of electromagnetic field

Abstract

Abstract In the presence of an electromagnetic field, we studied the stability of a conductive thin liquid film flowing on a non-conductive inclined plate taking the effect of odd viscosity into account. Using the lubrication theory, a new liquid–gas interface evolution equation involving odd viscosity effect is derived. By analyzing the linear and non-linear stability of the evolution equation, we find that the odd viscosity and the magnetic field stabilize the flow, while the electric field destabilizes the flow. Linear study shows that the larger odd viscosity leads to the higher critical Reynolds number. The weakly nonlinear study reveals that in the limited amplitude range, the supercritical stable region and the explosion region will decrease with the increase of the odd viscosity. Conversely, the unconditionally stable region increases and the subcritical unstable region keeps almost unchanged.