A continuum approach to phoretic motions: Thermophoresis

A purely continuum theory for the thermophoretic velocity of aerosol and hydrosol particles in the zero Knudsen number, near continuum limit, Kn=0+, valid for both gases and liquids, is proposed. This theoretical result is based upon a fundamentally modified version of the traditional equations governing continuum fluid motion, one which accounts for an intrinsic difference in a fluid's barycentric (mass-based) velocity and its kinematic velocity of volume, this difference arising during molecular transport processes in fluids within which a mass density gradient exists. Our continuum-scale approach contains no free parameters, nor does it rely upon any sub-continuum, molecular concepts, such as Maxwell's thermally-induced velocity-slip condition. The resulting expression for the thermophoretic velocity of a non-Brownian, spherical particle agrees both constitutively and phenomenologically with available correlations of such velocity data in gases, as well as with the more limited data for liquids. Furthermore, the effect of shape and orientation is discussed for the case of non-spherical particles, with specific results furnished for effectively non-conducting particles. Agreement of the theory with the data furnishes explicit experimental support of the non-traditional fluid-mechanical equations utilized herein.