On the Motion of Small Spheres in Gases

Using the general theory developed by the author in the previous paper, the problems of thermophoresis and diffusio-phoresis have been examined with a view to elucidating the effect of a general gas-surface scattering law on the associated forces. It is found that, in thermo-phoresis, there exists a close coupling between the first anisotropic moment of the gas-surface scattering law and the solution of the Chapman-Enskog conductivity equation. Explicit calculations indicate that for an arbitrary combination of any type of purely elastic scattering, e. g. specular, Lambert or backward, there is no change in the creep velocity of the particle. On the other hand, diffuse scattering with redistribution, leads to a marked decrease in the creep velocity. These conclusions are independent of the force law between gas atoms and depend only on the gas-surface interaction. In diffusio-phoresis, using only the simplest Chapman-Enskog solution for a binary mixture, it is found that unless the gas-surface laws differ greatly for the two species, there is virtually no influence of gas-surface scattering on the particle motion: the effect is due almost entirely to the mass difference and concentration ratio. We also investigate the way in which particles move in gas streams close to boundaries; slip flow is used as an example and it is shown that for diffuse reflection a particle at the wall travels with a speed which is about 60% of the gas speed at the wall.