A model of droplet evaporation: New mathematical developments

Abstract

A previously developed model for mono-component droplet evaporation is revisited using new mathematical tools for its analysis. The analysis is based on steady-state mass, momentum, and energy balance equations for the vapor and air mixture surrounding a droplet. The previously obtained solution to these equations was based on the assumption that the parameter ϵ (proportional to the squared ratio of the diffusion coefficient and droplet radius) is equal to zero. The analysis presented in the paper is based on the method of integral manifolds, and it allowed us to present the droplet evaporation rate as the sum of the evaporation rate predicted by the model based on the assumption that ϵ = 0 and the correction proportional to ϵ. The correction is shown to be particularly important in the case of small water and methanol droplets (diameters less than 5 μm) evaporating in air at low pressure (0.1 atm.). In this case, this correction could reach 35% of the original evaporation rate. In the case of evaporation of relatively large droplets (with radii more than 10 μm) in air at atmospheric and higher pressures, these corrections are shown to be small (less than 10-3 of the evaporation rate predicted by the model based on the assumption that ϵ = 0).