Mass variation of a thin liquid film driven by an acoustic wave

In this work, we investigate the dynamics of a thin liquid film subjected to an acoustic field in its bounding vapor space. For large acoustic wavelengths, the field imposes a spatially uniform, temporally periodic temperature and pressure at the vapor side of the film interface, which leads to a periodic driving force for mass exchange with the vapor. Neglecting the dynamics of the vapor space, we adopt the "one-sided" model for evaporation/condensation of thin liquid films. In the interest of determining the effect of oscillatory mass exchange on film stability, we consider films in thermodynamic equilibrium with the mean vapor conditions. The effects of oscillatory phase change on both linear stability and nonlinear dynamics are investigated for slightly inclined ceiling films that are destabilized by gravity and subject to thermocapillary effects. At linear order, this mass exchange is not found to alter the band of unstable wave numbers and only marginally affects the growth rates. Additionally, the mass exchanged during evaporation is balanced by condensation so that the total mass of the liquid film is conserved. However, due to nonlinear effects, we find that traveling waves encouraged by the inclination are subject to net mass loss. It is then found that normal thermocapillary effects enhance this loss, and that anomalous thermocapillarity mitigates or even reverses the loss to a mass gain.