Transient stefan flow and thermophoresis around an evaporating droplet

Abstract

The particle scavening efficiency of vapour-grown ice crystals falling from mixed clouds proves to be very high. Stefan flow, an aerodynamic flow originating in the fluid surrounding evaporating or condensing bodies, pushes airborne particles away from the surface of the supercooled droplets evaporating in the vicinity of an ice crystal. The particle Brownian flux towards the surface of the ice crystal (terminal velocity of about 1 m s−1) it, therefore, enhanced. However, the efficiency of this process of airborne-particle removal is strongly reduced as a consequence of the cooling of the evaporating droplet which produces a «thermal force», thermophoresis, which counteracts the particle Stefan flow. At the surface of an evaporating droplet in a quasi-equilibrium state, the two airborne-particle velocity fields practically balance each other. This counteracting effect on particle motion needs to be evaluated in the transient case. An approach is presented which consists of reformulating the transient heat and mass transfer problem in such a way as to convert it into a purely heat transfer problem having a known analytical solution. The approach is discussed and found to be correct. The results of the computations show that the counteracting role of thermophoresis on Stefan-flow particle motion during the residence time of supercooled droplets in the vicinity of an ice crystal (from 10−5 to 10−4s), which is also the time in which evaporation takes place, is considerably weak. It turns out to be practically negligible for large droplets (radius ≥8·10−4 cm).