Mathematical Modelling of Heating and Evaporation of a Spheroidal Droplet

Most of the currently used models of droplet heating and evaporation are based on the assumption that droplets are perfect spheres. At the same time the shapes of many observed droplets in engineering applications are far from spherical. We have studied the influence of droplet non-sphericity, approximating droplet shapes using prolate spheroids. The evaporation process of a spheroidal droplet in a gaseous atmosphere has been modelled. The previously developed exact solutions to the heat and mass transfer equations for the gas phase surrounding a spheroidal droplet have been used to perform numerical analysis of spheroidal droplet heating and evaporation. The temperature gradient inside droplets and the changes in their shape during the evaporation process have been taken into account. Our results show that significant changes in evaporation rate can be observed even for uniform droplet surface temperature. However, higher evaporation at the droplet surface regions with higher curvature does not mean that droplet eccentricity tends towards 1 (i.e. the droplet does not become more spherical). Our results demonstrate that temperature of a deformed droplet becomes uniform very quickly and after that the deformation parameter remains almost constant during the process of evaporation.