Stability of a condensing liquid film in a binary vapor mixture system

作者：Kanatani Kentaro^*

来源：International Journal of Heat and Mass Transfer, 2013, 58(1-2): 413-419.

DOI：10.1016/j.ijheatmasstransfer.2012.11.060

• Marangoni dropwise condensation
• Binary mixture
• Stability analysis
• Thin liquid film

We study stability of a condensing liquid film of a binary vapor mixture. When a binary vapor mixture of some kind is cooled on a substrate, a condensing liquid film emerges to take an inhomogeneous form such as a droplet one due to the solutal Marangoni effect. In order to analyze this phenomenon, we apply the long-wave approximation to the condensing liquid film and derive a nonlinear partial differential equation describing the spatio-temporal evolution of the film thickness. An interfacial boundary condition taking account of an effect of mass gain of the liquid film is adopted. Based on this model, we perform a linear stability analysis around a flat-film solution. We obtain an evolution equation of the amplitude of a disturbance, from which the cutoff and fastest growth wavenumbers are deduced. The maximum value of the cutoff wavenumber relative to the film thickness and its film thickness are estimated for water-ethanol mixture at atmospheric pressure. We numerically verify the long-wave nature of the instability of the condensate liquid film in this system. A significant difference in their values is found for low-ethanol fractions of the ambient vapor whether or not the temperature dependence of the mass transfer coefficient is considered. The wavenumber of a pattern of the liquid film observed in the experiment has the same parameter dependence as that of the fastest growth wavenumber.

• 出版日期2013-3