Interfacial phase change effect on a viscous falling film having odd viscosity down an inclined plane

Abstract

Abstract We investigate the phase change effect at the thin film interface with broken time-reversal-symmetry falling down an inclined flat wall. We consider the impact of evaporation and as well as condensation at the fluid-vapor interface separately. The non-zero odd part of the Cauchy stress tensor with the odd viscosity coefficient, which arises due to broken-time-reversal-symmetry, adds an attractive characteristic in the flow by stabilizing the effect of evaporation/condensation. We study the long-wave instabilities of the ununiform film by deriving a non-linear evolution equation in the classical long wave expansion method framework. The one-equation model can track the free surface evolution and accounts for viscosity, gravity, surface tension, and phase change (evaporation/condensation) effects. Linear stability analysis confirms that the odd viscosity has no significant impact on the instability threshold of an evaporating film as a contrast of condensate film, where the critical Reynolds number increases with the odd-viscosity parameter μ . While studying the weakly non-linear waves, we use the method of multiple scales to obtain the Complex Ginzburg Landau equation that shows both supercritical and subcritical solutions are possible for evaporating and condensate film. Interestingly, while one subcritical region is visible for an evaporating film, two subcritical unstable regions are found for condensate film. The numerical solution of the free-surface equation illustrates the finite-amplitude behavior that tends to dry out for evaporating film and rapidly increase film thickness for condensate film. The presence of odd viscosity slows down both the film thinning process for evaporation and the film thickening process for condensation. Furthermore, odd-viscosity cannot prevent film rupture in case of evaporation.