Stability analysis of volatile liquid films in different evaporation regimes

We investigate the role of the evaporation regime on the stability of a volatile liquid film flowing over an inclined heated surface using a two-fluid system that considers the dynamics of both the liquid phase and the diffusion of its vapor into the ambient environment. Consequently, the evaporation process is necessarily governed by the competition between (1) the thermodynamic disequilibrium tied to the liquid film's local thickness and (2) the diffusion effects dependent on the interface's curvature. We (1) modify the kinetic-diffusion evaporation model of Sultan et al. [J. Fluid Mech. 543, 183 (2005)] to allow for the reduction in film thickness caused by evaporative mass loss and (2) combine it with the liquid film formulation of Joo et al. [J. Fluid Mech. 230, 117 (1991)], and then (3) utilize long-wave theory to derive a governing equation encapsulating the effects of inertia, hydrostatic pressure, surface tension, thermocapillarity, and evaporation. We employ linear stability theory to derive the system's dispersion relationship, in which the Marangoni effect has two distinct components. The first results from surface tension gradients driven by the uneven heating of the liquid interface and is always destabilizing, while the second arises from surface tension gradients caused by imbalances in its latent cooling tied to vapor diffusion above it, and is either stabilizing or destabilizing depending on the evaporation regime. These two components interact with evaporative mass loss and vapor recoil in a rich and dynamic manner. Moreover, we identify an evaporation regime where the kinetic and diffusion phenomena are precisely balanced, resulting in a volatile film that is devoid of the vapor recoil and mass loss instabilities. Additionally, we clarify the dependence of the mass loss instability on the wave number under the two-fluid formulation, which we attribute to the presence of a variable vapor gradient above the liquid's surface. Furthermore, we investigate the effect of film thinning on its stability at the two opposing limits of the evaporation regime, where we find its impact in the diffusion-limited regime to be dependent on the intensity of evaporative phenomena. Finally, we conduct a spatiotemporal analysis which indicates that the strength of vapor diffusion effects is generally correlated with a shift towards absolute instability, while the thinning of the film is observed to cause convective-to-absolute-to-convective transitions under certain conditions.