Suppression of Wave Instability in a Liquid Film Flow Down a Non-Uniformly Heated Slippery Inclined Plane Using Odd Viscosity

Abstract

We study the effects of odd viscosity on the stability of a thin Newtonian liquid film flowing down a nonuniformly heated plane under a slip boundary condition. The effect of odd viscosity arises in classical fluids when the time-reversal symmetry breaks down. Due to the odd viscosity, the odd part of the Cauchy stress tensor consists of symmetric and antisymmetric parts and shows several striking effects. We apply the Navier slip boundary condition for the slippery inclined plane at the solid–liquid interface. For our problem, we first derive an evolution equation whose solution describes the film thickness. The equation contains parameters considering the effect of inertia, thermocapillarity, slip length, and odd viscosity. We then perform the linear stability analysis and find that odd viscosity can significantly suppress the combined destabilizing effects of the thermocapillarity and slip length. Next, we analyze the dynamics using the weakly nonlinear approach, which provides details of different subregions of the instability zone. We observe that as the influence of the odd viscosity increases, the supercritical stable and explosive zones shrink while the unconditional stable and subcritical unstable zones expand. We also perform numerical investigation and observe that linear analysis, weakly nonlinear theory, and numerical results are consistent.