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

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)].