Investigations into the evolution of heated liquid films

Abstract

The evolution of the free surface of a heated liquid film is directly tied to the performance and efficiency of various industrial systems. Therefore, we investigate the spatiotemporal evolution of heated liquid films across a range of different settings by formulating distinct of hydro-thermal models taking into account the effects of inertia, thermocapillarity, evaporation, gas shear, and thermal radiation, where we direct our modeling efforts in each problem on the most dominant physical phenomena. In liquid flows characterized by relatively low Reynolds numbers belonging to the drag-gravity flow regime, we model the hydrodynamics of the film using the long-wave expansion (LWE) methodology and perform linear stability analyses focused on the thermocapillary and evaporative instabilities, as they have a primary influence on the film’s evolution in this flow regime. Consequently, the evaporation process is governed by the competition between thermodynamic disequilibrium and diffusion effects dependent on the interface’s curvature. We modify the kinetic-diffusion evaporation model of Sultan et al. [Sultan et al., J. Fluid Mech. 543, 183, (2005)] and combine it with long-wave theory to derive a governing equation encapsulating the coupled dynamics. We then utilize linear stability theory to derive the system’s dispersion relationship, in which the Marangoni effect has two components. The first results from surface tension gradients driven by the uneven heat flux, while the second arises from surface tension gradients caused by imbalances in vapor diffusion. These two components interact with evaporative mass loss and vapor recoil in a rich and complex manner. Moreover, we identify an evaporation regime where a volatile film is devoid of evaporation instabilities. 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 vapor diffusion effects are correlated with a shift towards absolute instability. In the second problem, we study the spatiotemporal evolution of an evaporating liquid film sheared by a gas and consider both the inertial and thermal instability modes, where the shearing gas is modeled by imposing a constant shear stress along the liquid’s interface. Interestingly, it’s inclusion in the problem allows the utilization of a one-sided evaporation model, which is precisely the transfer-rate-limited case of the first system we investigated. Once more long-wave theory is used to derive the an evolution for the liquid film which incorporates the role of the shearing gas. Afterwards, linear stability theory is used to investigate the temporal and spatiotemporal characteristics of the flow, where it is found that the evaporation of the film promotes absolute instabilities and can cause convective/absolute transitions. We also find that counter-flowing shearing gas can suppress the inertial instability affirming similar conclusions found by previous studies for a strongly confined isothermal film. Furthermore, the evolution interface equation was solved numerically to explore the film’s nonlinear stability. Moreover, we employ self-similarity analysis to probe the shear stress’s effect on the film’s rupture mechanics. In the third problem we research, the liquid flow’s Reynolds number is relatively high, and hence we utilize the weighted-residual integral boundary layer (WIBL) technique [C. Ruyer-Quil and P. Manneville,” Eur. Phys. J. B, 15, 357, (2000)], and direct our attention at directly simulating the temperature field across the film using reduced models. The WIBL hydrodynamic equations are derived expressions obtained via the boundary layer approximation, while the thermal profile is modeled by employing an asymptotic expansion which produces a hierarchy of models in which enhanced sophistication is offset by higher complexity and computational cost. These models are solved numerically revealing how the temperature field across the film is governed by a balance between the conduction across both the liquid film and the solid surface, and their respecitve radiative emissions, wherein these two transfer phenomena are linked through two corresponding dimensionless numbers associated with both the liquid film and the solid surface.