The condensation and evaporation of liquid droplets in a pure vapour at arbitrary Knudsen number

Abstract

A new set of equations describing the growth and evaporation of small liquid droplets in a pure vapour are presented. The equations, which model both mass and heat transfer between the droplet and the vapour, are in simple closed form solution and are suitable for practical calculations at any Knudsen number. The physical model on which the theory is based is essentially that of Langmuir but some novel features are incorporated. For example, the velocity distribution function for molecules approaching the liquid surface is described by a simplified Grad, thirteen-moment distribution. The results of the analysis are in close agreement with other, more complicated and less general theories to be found in the literature. In particular, the temperature jump across the Knudsen layer in the continuum limit is accurately predicted. It is also shown that Maxwell moment methods based on the Lees, two-stream Maxwellian distribution lead to incorrect results.