Interfacial instability induced by lateral vapor pressure fluctuation in bounded thin liquid-vapor layers

Abstract

We study an instability of thin liquid-vapor layers bounded by rigid parallel walls from both below and above. In this system, the interfacial instability is induced by lateral vapor pressure fluctuation, which is in turn attributed to the effect of phase change: evaporation occurs at a hotter portion of the interface and condensation at a colder one. The high vapor pressure pushes the interface downward and the low one pulls it upward. A set of equations describing the temporal evolution of the interface of the liquid-vapor layers is derived. This model neglects the effect of mass loss or gain at the interface and guarantees the mass conservation of the liquid layer. The result of linear stability analysis of the model shows that the presence of the pressure dependence of the local saturation temperature mitigates the growth of long-wave disturbances. The thinner vapor layer enhances the vapor pressure effect.We find the stability criterion, which suggests that only slight temperature gradients are sufficient to overcome the gravitational effect for a water/vapor system. The same holds for the Rayleigh-Taylor unstable case, with a possibility that the vapor pressure effect may be weakened if the accommodation coefficient is below a certain critical value.

Effects of convection and diffusion of the vapour in evaporating liquid films

“…However, for thin films the effects of the vapour stress and viscous dissipation are neglected under the long-wave approximation (see Burelbach et al 1988), unless there is an internal or external flow of the gas in the lateral direction, which causes a shear stress on the interface. The former case was considered by Kanatani (2010) and Kanatani & Oron (2011), where the lateral vapour flow arises from the confined geometry of the gas phase. The latter case has been recently addressed in several works (e.g.…”

“…Since the heat flux at the wall is related with the mass flux (see (2.27)), the heat transfer characteristic would also change once the instability occurs and the horizontal diffusion of the vapour takes effect. The dispersion relation of the type of equation (4.4) was already encountered and investigated in the study of evaporating or condensing bilayer systems (Kanatani 2010). It is obvious from (4.4) that the small-wavenumber modes always grow if gravity is absent (G = 0).…”

Rayleigh–Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour

“…Most of the previous theoretical studies on interfacial instability and evaporative convection considered that a volatile liquid layer was in contact only with its own vapour (Palmer 1976;Burelbach et al 1988;Kliakhandler et al 2002;Guo & Narayanan 2010;Kanatani 2010;Kanatani & Oron 2011) and that the atmosphere has a constant vapour pressure (Bestehorn & Merkt 2006). Later, some numerical investigations have considered ambient gas as a mixture of the vapour and an inert (non-condensable) gas in the presence of vapour diffusion by linear or weakly nonlinear analysis (Haut & Colinet 2005;Margerit, Dondlinger & Dauby 2005;Sultan, Boudaoud & Amar 2005).…”

Instabilities in a horizontal liquid layer in cocurrent gas flow with an evaporating interface

“…More recently, Kanatani and Oron [11] have studied the nonlinear dynamics of the same system as that in Ref. [10]. In these two papers, the Hertz-Knudsen equation has also been applied to describe the dynamics of the interface.…”

“…Liu and Liu [8] gave up the assumption of interfacial chemical potential equilibrium and used a more general empirical relation, i.e., the Hertz-Knudsen equation [9], to describe the relation between the mass flux and the local temperature and the pressure of vapor. Kanatoni [10] has studied the interfacial instability induced by lateral vapor pressure fluctuation in a vapor-liquid system with an evaporating interface. More recently, Kanatani and Oron [11] have studied the nonlinear dynamics of the same system as that in Ref.…”