Moving boundary and time-dependent effects on mass transfer from a spherical droplet evaporating in gaseous environment

Analytic modelling of drop evaporation is often approached under quasi-steady approximation, disregarding the inherent unsteadiness of such phenomenon and the fact that drop radius shrinking due to evaporation settles a moving boundary problem. Such assumption yields simple and very useful analytical solutions of the species conservation equations. However it is known that, after the sudden immersion of a drop in a gaseous environment, a relaxation time is needed to reach quasi-steadiness and the evaporation rate during this period is expected to be much higher than that under steady conditions. The present work is aimed to define the analytical problem of evaporation in a gaseous environment relaxing the above mentioned approximation. The spherically symmetric, time-dependent species conservation equation for vapour transport in a gaseous environment is derived in nondimensional form accounting for moving boundaries. Numerical solution allows to evaluate the relaxation time as a function of the Spalding mass transfer number and to quantify the evaporated mass during this time lapse.