Drag force and transport property of a small cylinder in free molecule flow: A gas-kinetic theory analysis

Analytical expressions are derived for aerodynamic drag force on small cylinders in the free molecule flow using the gas-kinetic theory. The derivation considers the effect of intermolecular interactions between the cylinder and gas media. Two limiting collision models, specular and diffuse scattering, are investigated in two limiting cylinder orientations with respect to the drift velocity. The earlier solution of Dahneke [B. E. Dahneke, J. Aerosol Sci. 4, 147 (1973)] is shown to be a special case of the current expressions in the rigid-body limit of collision. Drag force expressions are obtained for cylinders that undergo Brownian rotation and for those that align with the drift velocity. The validity of the theoretical expressions is tested against experimental mobility data available for carbon nanotubes.