Theory of Thermophoresis of a Large Evaporating Droplet in a Viscous Nonisothermal Binary Gaseous Medium

Abstract

Thermophoretic motion of a spherical evaporating droplet in a viscous binary gas medium at arbitrary relative temperature differences in its vicinity is theoretically described in a quasistationary approximation at low Reynolds and Peclet numbers. A system of gas-dynamic equations is solved, including a velocity-linearized system of Navier–Stokes equations, as well as heat and mass transfer equations. The properties of a gaseous medium are described with account for the power-law dependence of the transfer (viscosity, diffusion, and thermal conductivity) and density coefficients on temperature. The resulting numerical estimates suggest that the dependences of the thermophoretic force and the velocity of the droplet on the average temperature of its surface are nonlinear.