Nonlinear stability of evaporating/condensing liquid films

Abstract

We consider horizontal static liquid layers on planar solid boundaries and analyse their instabilities. The layers are either evaporating, when the plates are heated, or condensing, when the plates are cooled. Vapour recoil, thermocapillary, and rupture instabilities are discussed, along with the effects of mass loss (or gain) and non-equilibrium thermodynamic effects. Particular attention is paid to the development of dryout. We derive long-wave evolution equations for the interface shapes that govern the two-dimensional nonlinear stability of the layers subject to the above coupled mechanisms. These equations are analysed and their predictions discussed. Previous theoretical and experimental results are reviewed and compared with the present results. Finally, we discuss limitations of the modelling and extend our derivation to the case of three-dimensional disturbances.

Weakly nonlinear study of Marangoni instabilities in an evaporating liquid layer

“…Eqs. (12) express that the temperature, pressure and vapor concentration are fixed at the top of the system and that a constant flux of the gas mixture is extracted from the system at z = H * . At the interface (z = h * (t)):…”

“…We work in the quasi-steady assumption [12] which means that close to the time t 0 , the time scale of the interface displacement is much larger than the time scale of heat and mass diffusion. This assumption is possible thanks to the large value of the latent heat of vaporization L leading to low evaporation rates (this can be seen through the dimensional form of equation (17) which writes as: JL − λ g ∂ z T g + λ l ∂zT l = 0) and thus slow interface displacements.…”

“…Most of the theoretical studies on evaporative convection ( [6], [10]- [12]) assume that the liquid layer is in contact only with its own vapor. In this paper we consider in addition the presence of an inert gas in the vapor phase, not only because in most experimental setups the liquid evaporates in a gas (air for example), but also because the presence of a gas strongly stimulates Marangoni-Bénard instabilities, as shown in [13] and [14] (In this case indeed, the temperature perturbations at the interface are related to the variations of the vapor partial pressure instead of being related to the variations of the total gas pressure).…”

“…Under certain conditions it is possible to reduce the full two-phase problem to a one-sided model which accounts for the effect of evaporation through a generalized heat transfer condition at the liquid surface, as done in [12], [16], [8], [13] and [14]. A 3D-numerical integration of such a one-sided model was also performed in [17].…”

Dry-spot nucleation in thin liquid films on chemically patterned surfaces

“…Sharma and Ruckenstein (1986) determined the stability of spatially non-homogeneous stationary solutions and found a faster rate of thinning and shorter dominant wavelength as compared to the linear theory. Burelbach et al (1988) considered the instability of volatile, evaporating or condensing liquid films.…”