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The transport of small particles in the free-molecule regime is investigated on the basis of gas kinetic theory. Drag force formulations were derived in two limiting collision models-namely, specular and diffuse scattering-by considering the potential force of interactions between the particle and fluid molecules. A parametrized drag coefficient equation is proposed and accounts for the transition from specular to diffuse scattering as particle size exceeds a critical value. The resulting formulations are shown to be consistent with the Chapman-Enskog theory of molecular diffusion. In the limit of rigid-body interactions, these formulations can be simplified also to Epstein's solutions [P. S. Epstein, Phys. Rev. 23, 710 (1924)].

Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime