Thermophoresis at small but finite P?clet numbers

Abstract

The thermophoretic motion of a spherical particle suspended in a gaseous medium possessing a uniform temperature gradient is analytically studied for a small but nonzero P?clet number Pe. The Knudsen number is small for the gas motion in the slip-flow regime, and the thermal creep, temperature jump, frictional slip, and thermal stress slip are allowed over the particle surface. Through the use of a method of matched asymptotic expansions, the energy and momentum equations governing the problem are solved and an expansion formula for the thermophoretic velocity of the particle good to O(Pe3) is obtained in closed form. This singular perturbation analysis shows that the perturbed temperature and velocity fields are of O(Pe3), but the first correction to the particle velocity is of O(Pe2). This correction can be either negative or positive depending on several thermal and interfacial parameters, indicating that the effect of heat convection is complex and can retard or enhance the thermophoresis of the particle. The convection effect is generally negligible as Pe?0.1 but significant as Pe equals about unity. ? 2018 American Association for Aerosol Research. ? 2018, ? 2018 American Association for Aerosol Research.