Theory of thermophoresis. II. Low-density behavior

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Abstract
Kinetic theory, in the repeated-ring approximation, is employed to calculate the general expressions for thermophoretic forces and velocities which were obtained in the preceding paper (I). The velocity is not renormalized by the repeated-ring terms, since they all cancel. The thermophoretic force, on the other hand, is strongly renormalized by these terms, since the friction constant is. The latter changes from Boltzmann-type behavior at low densities of the host gas to Stokes-type behavior. In the limit in which the guest particle is represented by a hard-sphere potential we regain known results in the Boltzmann regime. These results are at variance with experiment. A realistic attractive tail, added to the hard-sphere potential yields a vanishingly small correction because of the typical short ranges of such tails. When accommodation processes are included, one obtains excellent agreement with experiment, provided the longitudinal and transverse momentum have different accommodation coefficients.