Effect of chattering collisions on the self-diffusion coefficient of a dilute gas composed of infinitely thin hard needles

Abstract

The self-diffusion coefficient of a dilute gas composed of infinitely thin hard needles was studied by classical trajectory calculations in relation to the moment of inertia of the needle, I. The calculated self-diffusion coefficient was compared with the value obtained by the independent collision approximation (ICA) in which each collision is assumed to be uncorrelated. Both the self-diffusion coefficient and the collision frequency increase with decreasing moment of inertia of the needle as expected by the ICA. The increasing rate of the self-diffusion coefficient was proportional to I -0.83 at I→0, that is larger than I -1/2 by the ICA. However, the ICA gives a larger self-diffusion coefficient at large moment of inertia; the correlation between the impulses during the chattering collisions changes its sign from positive to negative with decreasing moment of inertia. The thermal rotational motion at the initial configuration reduces the effect of the collision-induced rotational motion that leads to the positive correlation. The rapid thermal rotational motion at small moment of inertia makes the chattering collisions a kind of reciprocating motion in the orientation of the needles.