Thermophoretic motion of an aerosol sphere in a spherical cavity

Abstract

A theoretical investigation of the quasi-steady thermophoresis of an aerosol sphere located arbitrarily in a spherical cavity normal to the line of their centers is presented. In the slip-flow regime for the gas motion, the thermal creep, thermal stress slip, frictional slip, and temperature jump are permitted at the solid surfaces. The general solutions to the conservative equations governing the temperature and fluid velocity distributions in the two spherical coordinate systems with respect to the particle and cavity centers are superimposed, and the boundary conditions are satisfied by a collocation technique. The translational and angular velocities of the particle are determined as functions of the scaled center-to-center distance between the particle and cavity (eccentricity of the particle position), their radius ratio, and their relative thermal and surface properties. The results indicate that the boundary effect on the thermophoretic motion is significant, interesting, and complicated. When the particle is located at the cavity center, its migration velocity agrees well with the available analytical solution. In general, the thermophoretic mobility decreases with increases in the particle-to-cavity size ratio and in the normalized distance between the particle and cavity centers, but there exist some exceptions. The circulating cavity-induced thermoosmotic flow can increase or decrease the thermophoretic migration and retard the particle rotation, even reverse their directions, depending on the geometric and characteristic parameters. The boundary effect on the thermophoretic migration normal to the line through the particle and cavity centers is slightly weaker than that along the line.