Axisymmetric thermophoresis of an aerosol particle in a spherical cavity

Abstract

The thermophoretic motion of a spherical particle located at an arbitrary position in a gaseous medium inside a spherical cavity is investigated semi-analytically. The temperature gradient is applied along the line connecting the particle and cavity centers. In the slip-flow regime for the gas motion, the temperature jump, frictional slip, thermal creep, and thermal stress slip are permitted at the solid surfaces. The energy and momentum equations are solved using two spherical coordinate frames with respect to the cavity and particle and the boundary conditions at the solid surfaces are satisfied by a collocation method. Results of the thermophoretic velocity are obtained for various values of the relative thermal and surface properties of the particle and cavity, their radius ratio, as well as the normalized distance between their centers (eccentricity of the particle position). In the particular case of the migration of a spherical particle at the center of the cavity, these results agree excellently with the analytical solutions. Interestingly, the contribution to the particle velocity from the thermoosmotic flow at the cavity wall can be equivalent to or even much more important than that from the wall-corrected thermophoretic driving force. The dimensionless thermophoretic velocity of the confined particle decreases significantly with an increase in the normalized distance between the particle and cavity centers or the particle-to-cavity radius ratio. This velocity increases with an increase in the relative thermal conductivity of the solid phases for a specified configuration.