New solutions to the species diffusion equation inside droplets in the presence of the moving boundary

Two new solutions to the equation, describing the diffusion of species during multi-component droplet evaporation, are suggested. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient species equation to the solution of the Volterra integral equation of the second kind. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. The analytical solution has been incorporated into a zero dimensional CFD code and applied to the analysis of a bi-component droplet evaporation. The case of an initial 50% ethanol–50% acetone mixture and droplets with initial diameter equal to 142.7 μm moving in air at atmospheric pressure has been considered. To separate the effect of the moving boundary on the species diffusion equation from a similar effect on the heat conduction equation inside droplets, described earlier, a rather artificial assumption that the droplet temperature is homogeneous and fixed has been made. It has been pointed out that the effect of the moving boundary slows down the increase in the mass fraction of ethanol (the less volatile substance in the mixture) and leads to the acceleration of droplet evaporation.