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

Evaporating liquid films under shear are utilized across a wide range of systems,

in which substantial improvements can be made by optimizing the liquid interface's

evolution. We investigated the spatio-temporal evolution of an evaporating liquid

film subjected to a shearing gas, whose effect was prescribed as a constant shear

stress along the liquid interface. Long-wave theory was used to derive an equation

governing the evolution of the liquid interface under the various effects involved.

Linear stability theory was used to investigate the temporal and spatio-temporal

stability of the flow, where it was found that the evaporation and thinning of the

film promotes absolute instabilities and can cause convective-absolute transitions.

Moreover, our model predicts that a strong enough counter-flowing gas suppresses

the inertial instability, arming conclusions found previously for a strongly confined

fllm. Additionally, the governing equation was solved numerically to simulate the film's

evolution subject to finite perturbations, which allowed conducting a numerical spatio-

temporal analysis in the nonlinear regime. Finally, we investigated the role of the

shear stress on the film's rupture dynamics through a self-similarity analysis, which

was validated by comparison to numerical data.