Boundary effects on a thermophoretic sphere in an arbitrary direction of a plane surface

Abstract

AbstractThe thermophoresis of a sphere in a constant applied temperature gradient in an arbitrary direction with respect to a plane surface was analytically studied. The Knudsen number was assumed small to describe the fluid flow by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. The asymptotic formulas for the temperature and velocity fields in the quasi‐steady situation were obtained by a method of reflections. The plane surface can be a solid wall or a free surface. The boundary effect on the thermophoretic motion was weaker than that on the motion driven by a body force. Even so, the interaction between the plane and particle can be very significant when the gap thickness gets small. For a particle motion normal to a solid wall, plane surface effect reduces the thermophoretic velocity of the particles; however, this solid wall may be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in the case of a particle migrating close to a free surface due to thermophoresis, the particle velocity can be either greater or smaller than what would exist in the absence of the plane surface, depending on the relative thermal conductivity and surface properties of the particle and its relative distance from the plant. The thickness of the thermophoretic interacting region was also evaluated by considering the thermophoretic mobility. A free surface generally exerts less influence on the particle movement than does a solid surface.