Thermophoresis of an Aerosol Sphere in a Circular Cylindrical Pore
Date Issued
2009
Date
2009
Author(s)
Wu, Kuang-Cheng
Abstract
The problem of the thermophoretic motion of a spherical particle in a gaseous medium along the centerline of a circular cylindrical pore is studied theoretically in the steady limit of negligible Reynolds and Peclet numbers. The imposed temperature gradient is uniform and parallel to the pore wall, which may be either insulated or prescribed with the far-field temperature distribution. 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 pore wall causes two basic effects on the particle velocity: first, the local temperature gradients on the particle surface are altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhances the viscous retardation of the moving particle. To solve the equations of conservation of energy and momentum, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various relative thermal conductivity and surface properties of the particle, as well as the relative separation distance between the particle and the pore wall. The collocation results agree well with the approximate analytical solution obtained by using a method of reflections. The wall-corrected particle velocity depends on the surface properties of the particle and the wall, the ratio of particle-to-pore radii, and the thermal boundary condition at the wall. In general, the boundary effect on thermophoresis is quite significant and complicated.
Subjects
Thermophoresis
Aerosol sphere
Fluid mechanics
Boundary effects
Circular cylindrical pore
Type
thesis
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