The effect of the evaporation coefficient and temperature jumps on the thermophoresis of a particle in a binary gas mixture in view of thermodiffusion and Stefan effects

Abstract

A theory of uniform thermophoretic motion of a solitary spherical volatile particle in an unbounded incompressible binary mixture of gases with a phase transition of one of the components on the surface of the condensed phase is constructed on the basis of hydrodynamic method under slip conditions. Analysis is performed of the direct relative effect of the evaporation coefficient and boundary temperature jumps on the distribution of the velocity, temperature, and concentration of the volatile component and on the rate of thermophoresis of a moderately large highly viscous sphere. The thermodiffusion terms, Stefan effects, and the heat flux associated with convective transfer of evaporating mass are taken into account. A generalization is performed by taking into account the internal circulation of the matter of a large liquid one-component droplet and the thermocapillary phenomena. The inferences made in this paper disagree with those of the traditional theories in the cases of thermophoresis of a solitary aerosol particle under conditions of weak and moderately strong diffusion evaporation. Analysis has revealed that, in the case of weak evaporation of a large particle, the difference between the results increases as the binary gas mixture is saturated with vapors of the volatile component. Apparently, the calculation formulas for the rate of thermophoretic transfer have a wider range of validity than those previously obtained, all other things being equal.