Thermophoresis of an aerosol sphere parallel to one or two plane walls

Abstract

AbstractThe steady thermophoretic motion of a spherical particle in a gaseous medium located in an arbitrary position between two infinite parallel‐plane walls is studied theoretically in the absence of fluid inertia and thermal convection. The Knudsen number is assumed small to describe the fluid flow by a continuum model with a temperature jump, thermal slip, and frictional slip at the particle surface. The imposed temperature gradient is constant and parallel to the two plane walls, which may be insulated or prescribed with the far‐field temperature distribution. The presence of neighboring walls causes two basic effects on the particle velocity: the local temperature gradient on the particle surface is enhanced or reduced by the walls, to speed up or slow down the particle; the walls increase viscous retardation of the moving particle. A boundary collocation method is used to solve the thermal and hydrodynamic governing equations of the system. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded gaseous medium are presented for various relative thermal conductivity and surface properties of the particle, as well as relative separation distances between the particle and two plates. For thermophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by a method of reflections. The presence of lateral walls can reduce or enhance the particle velocity, depending on the relative thermal conductivity and surface properties of the particle, the relative particle‐wall separation distances, and the thermal boundary condition at the walls. In general, the boundary effect on thermophoresis is complicated and weaker than that on sedimentation.