Thermophoretic interactions of aerosol particles with constant temperatures

This paper presents an analytical study of the thermophoretic motion of two free aerosol spheres with constant temperatures by using a method of reflections. The particles are allowed to differ in radius, in temperature, and in surface properties. The Knudsen numbers are assumed small so that a continuum model describes the fluid flow with a thermal creep and a hydrodynamic slip at the particle surfaces. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single sphere with constant temperature placed in an arbitrarily varying temperature field. The results for two-sphere interactions are correct to O(r12−7), where r12 is the distance between the particle centers. For the special situation of two identical spheres, the effect of particle interactions will drive the pair system approaching each other if the particle temperature is less than the temperature of the surrounding. While the temperature of the particles is higher than the surrounding temperature, the thermophoretic force obtains a repulsive effect between the particles. Based on a microscopic model the results for two-particle interactions are applied to find the effect of particle concentration on the average thermophoretic velocity in a bounded suspension. In general, the effect of interactions on thermophoretic coagulation of particles with constant temperatures can be stronger than that on sedimentation.