Concentration Effects on the Thermophoresis of Aerosol Spheres

The thermophoretic motion of a homogeneous suspension of identical spherical particles of arbitrary thermal conductivity and surface properties is considered under conditions of small Knudsen, Peclet, and Reynolds numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of energy and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the thermophoretic migration velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. Comparisons between the ensemble-averaged thermophoretic velocity of a test particle in a dilute suspension and our cell-model results are made. A parallel analysis for the sedimentation of aerosol spheres is also presented. Copyright 1999 Academic Press.