Thermophoresis of a slightly deformed aerosol sphere

Abstract

An analytical study is presented for the thermophoretic motion of a freely suspended aerosol particle with an arbitrary, slightly deformed spherical surface in a uniformly prescribed temperature gradient. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the surface of the particle. A first attempt is made to obtain analytical approximations for the thermophoretic velocity of the particle in the limit of vanishing Peclet and Reynolds numbers. To the first order in the small parameter characterizing the deformation of the spherical shape of the particle, explicit expressions are derived for its drift and rotational velocities. The angular velocity of a particle undergoing thermophoresis is found to be zero for any shape, which is the first indication that the fluid motion around a single thermophoretic particle of an arbitrary shape is irrotational, as is known to be in the case of thin-double-layer electrophoresis. A comparison of our first-order approximation for the thermophoretic velocity of a spheroid with the available exact solution shows that the agreement is quite good, even for relatively large deformations of the spherical shape of the particle. Our results for the motion of a spheroid demonstrate that its relative physical and surface properties, its aspect ratio, and its orientation relative to the imposed temperature gradient can have significant effects on its thermophoretic mobility.