Droplet evaporation in inert gases

Abstract

A general mixed kinetic-diffusion boundary condition is formulated to account for the out-of-equilibrium kinetics in the Knudsen layer. The mixed boundary condition is used to investigate the problem of quasi-steady evaporation of a droplet in an infinite domain containing inert gases. The widely adopted local thermodynamic equilibrium assumption is found to be the limiting case of infinitely large kinetic Péclet number ${{Pe}_k}$ , and it introduces significant error for ${{Pe}_k} \leqslant O(10)$ , which corresponds to a typical droplet radius $a$ of a few micrometres or smaller. When compared with experimental data, solutions based on the mixed boundary condition, which take into account the temperature jump across the Knudsen layer, better predict the time evolution of $a$ than the classical $D^2$ -law (i.e. $a^2 \propto t$ , where $t$ denotes time). In the slow evaporation limit, an analytical solution is obtained by linearising the full formulation about the equilibrium condition, which shows that the $D^2$ -law can be recovered only in the large ${{Pe}_k}$ limit. For small ${{Pe}_k}$ , where the process is dominated by kinetics, a linear relation, i.e. $a \propto t$ , emerges. When the gas phase density approaches the liquid density (e.g. at high-pressure or low-temperature conditions), the increase in the chemical potential of the liquid phase due to the presence of inert gases needs to be accounted for when formulating the mixed boundary condition, an effect largely ignored in the literature so far.