Thermophoretic Deposition of a Sphere Normal to a Plane Surface

Abstract

An analytical study is presented for the thermophoresis of a sphere constant applied temperature gradient perpendicular to a plane surface. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. asymptotic formulas for the temperature and velocity fields in the quasisteady situation are obtained by using a method of reflections. The plane surface may be a wall or a free surface. The boundary effect on the thermophoretic motion is found to be weaker than that on the motion driven by a gravitational force. Even so, interaction between the plane and the particle can be very strong when the gap thickness approaches zero. For the motion of a particle normal to a solid plane, the effect of the plane surface is to reduce the thermophoretic velocity of the particle. For case of particle migration toward a free surface owing to thermophoresis, the particle velocity can be either greater or smaller than...