Effects of internal circulation and particle mobility during nanofluid droplet evaporation

Abstract

The effect of internal circulation on evaporation of fluid droplets containing nano-sized particles is analytically investigated, where internal circulation is caused by viscous effects at the liquid–gas interface in the convective environment. The competing time scales of liquid diffusion, convection, and particle diffusion are first analyzed as influenced by gas phase velocity, relative viscosities of gas and liquid phases, and the droplet size. The results reveal the importance of internal recirculation for droplets of practical sizes. To demonstrate the role of internal circulation plays on particle distribution and shell formation during the evaporation process, a symmetric Hill vortex and strong circulation are assumed for solving a one-dimensional governing equation, which to yield (i) the particle redistribution during the evaporation process, (ii) the time and the size upon shell formation (i.e., the end of the first-stage evaporation/drying) due to inclusion of particles at the droplet surface, and (iii) internal particle distribution that forecast possible morphologies of particle aggregates once the drying process is complete. These results are found to be dependent upon (a) the relative time scales of liquid diffusion and particle mobility (the effect of Lewis number, Le), and (b) the relative importance or evaporation rate (K) and particle mobility (the effect of Peclet number, Pe). Comparisons with previous results without internal circulation are made, as related to the time for shell formation and possible morphologies. Such comparisons reveal some distinctly different, and surprising, phenomena during and at the end of the first-stage evaporation.