Photophoresis of an aerosol sphere normal to a plane wall

A combined analytical-numerical study is presented for the quasisteady photophoretic motion of a spherical aerosol particle of arbitrary thermal conductivity and surface properties exposed to a radiative flux perpendicular to a large plane wall. The Knudsen number is assumed to be so small 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 radiation-absorbing particle. In the limit of small Peclet and Reynolds numbers, the appropriate equations of conservation of energy and momentum for the system are solved using a boundary collocation method and numerical results for the photophoretic velocity of the particle are obtained for various cases. The presence of the neighboring wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is enhanced or reduced by the wall, thereby speeding up or slowing down the particle; second, the wall increases viscous retardation of the moving particle. The net effect of the wall can decrease or increase the particle velocity, depending upon the relative conductivity and surface properties of the particle as well as the relative particle-wall separation distance. In general, the boundary effect of a plane wall on the photophoresis of an aerosol particle can be quite significant in some situations. In most aerosol systems, the boundary effect on photophoresis is weaker than that on the motion driven by a gravitational field.