The dynamics of liquid films, as described by the diffuse-interface model

Abstract

The dynamics of a thin layer of liquid, between a flat solid substrate and an infinitely-thick layer of saturated vapor, is examined. The liquid and vapor are two phases of the same fluid, governed by the diffuse-interface model. The substrate is maintained at a fixed temperature, but in the bulk of the fluid the temperature is allowed to vary. The slope $\epsilon$ of the liquid/vapor interface is assumed to be small, as is the ratio of its thickness to that of the film. Three asymptotic regimes are identified, depending on the vapor-to-liquid density ratio ${\rho }_v/{\rho }_l$. If ${\rho }_v/{\rho }_l\sim 1$ (which implies that the temperature is comparable, but not necessarily close, to the critical value), the evolution of the interface is driven by the vertical flow due to liquid/vapor phase transition, with the horizontal flow being negligible. In the limit ${\rho }_v/{\rho }_l\to 0$, it is the other way around, and there exists an intermediate regime, ${\rho }_v/{\rho }_l\sim {\epsilon }^{4/3}$, where the two effects are of the same order. Only the ${\rho }_v/{\rho }_l\to 0$ limit is mathematically similar to the case of incompressible (Navier--Stokes) liquids, whereas the asymptotic equations governing the other two regimes are of different types.

References in corpus (4)

• Shock formation in the collapse of a vapor nano-bubble
• Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability
• Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model
• Nonexistence of two-dimensional sessile drops in the diffuse-interface model

Cited by in corpus (5)

• Capillary condensation of saturated vapor in a corner formed by two intersecting walls
• The multicomponent diffuse-interface model and its application to water/air interfaces
• Dynamics of a drop floating in vapor of the same fluid
• Nonexistence of two-dimensional sessile drops in the diffuse-interface model
• Nonisothermal evaporation