Boundary effects on thermophoresis of aerosol cylinders

An analytical study is presented for the thermophoretic motion of a circular cylindrical particle in a gaseous medium with a transversely imposed temperature gradient near a large plane wall parallel to its axis in the quasisteady limit of negligible Peclet and Reynolds numbers. 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 particle surface. The presence of the confining wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhance the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the thermophoresis of the aerosol cylinder are computed for various cases. The presence of the plane wall can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distance, and the direction of the applied temperature gradient. The direction of the thermophoretic motion of a cylindrical particle near a plane wall is different from that of the prescribed thermal gradient, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the thermophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.