Spatio-temporal evolution of evaporating liquid films sheared by a gas

Abstract

The main purpose of this work is the investigation of the spatio-temporal characteristics of an evaporating liquid film under the in uence of inertia, hydrostatic pressure, thermocapillary effects, vapor recoil, and shear stress imparted by a gas. The effects of the shearing gas are included via the introduction of a constant shear agent quantity modeling the effect of a constant shear stress applied along the liquid interface. Subsequently, long wave theory is used to derive an interface evolution equation accounting for all the previous effects which then is used to analyze the linear stability characteristics of the film for different parameter combinations. First a temporal analysis is performed to determine the stable/unstable parameter sets, followed by spatio-temporal analysis to differentiate the absolute/convective stability domains. It is demonstrated that the shear agent acts as a modifier to the base ow's existing inertia and therefore doesn't change perturbation growth rates in a stationary base ow, however it does have a strong effect on the phase speed. Therefore it can cause convective/absolute transitions of thermal instabilities. As for its effect on inertial instabilities, namely the H-mode, positive values of the shear agent promote its growth, while negative ones suppress it, to the point of completely eliminating it for sufficiently negative values. As for the effects of evaporation it is found that the reduction in film height due to evaporation suppresses the advection of perturbations through the film and therefore promotes absolute instabilities. In order to investigate the non-linear evolution of the interface, the evolution equation is solved numerically. Initially, the interface evolution is simulated for infinitesimal perturbations over a periodic domain for the purposes of validation by comparison to the linear temporal stability results, and also to existing literature. Once the numerical procedure is validated, the non-linear evolution of the interface is studied. Finally, the shear gas's effect on film rupture location nd time are studied where it is found that the shear agent can strongly affect rupture location and time, but doesn't change the self-similar rupture mechanics as the minimum film height approaches zero.