Evaluation of evaporation coefficient for micro-droplets exposed to low pressure: A semi-analytical approach

Abstract

Evaporation rate of water is strongly influenced by energy barrier due to molecular collision and heat transfer limitations. The evaporation coefficient, defined as the ratio of experimentally measured evaporation rate to that maximum possible theoretical limit, varies over a conflicting three orders of magnitude. In the present work, a semi-analytical transient heat diffusion model of droplet evaporation is developed considering the effect of change in droplet size due to evaporation from its surface, when the droplet is injected into vacuum. Negligible effect of droplet size reduction due to evaporation on cooling rate is found to be true. However, the evaporation coefficient is found to approach theoretical limit of unity, when the droplet radius is less than that of mean free path of vapor molecules on droplet surface contrary to the reported theoretical predictions. Evaporation coefficient was found to reduce rapidly when the droplet under consideration has a radius larger than the mean free path of evaporating molecules, confirming the molecular collision barrier to evaporation rate. The trend of change in evaporation coefficient with increasing droplet size predicted by the proposed model will facilitate obtaining functional relation of evaporation coefficient with droplet size, and can be used for benchmarking the interaction between multiple droplets during evaporation in vacuum.