On the Motion of Small Spheres in Gases. I. General Theory

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Abstract
We have developed a global scattering kernel which describes the scattering of gas atoms by spherical particles which are small compared with a mean free path in the gas. The global kernel, which is analogous in many ways to the thermal neutron scattering kernel employed in neutron thermalization studies, is given in terms of the gas-surface scattering law for the particle. Thus the global kernel can be studied as a function of specular reflection and incomplete accommodation. The recent model of KUŠČER and of CERCIGNANI is used for the latter investigation and we find that on the average the angular distribution of the scattered gas atoms depends sensitively on the tangential momentum accommodation coefficient but only very weakly on the energy coefficient. However, the phenomenon is strongly dependent on the speed of the approaching gas atom and, for low speed gas atoms, the sensitivity to energy accommodation becomes much more important. The net scattering rate is obtained and put in a form convenient for later calculations to be described in a series of companion papers.

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