Kinetic Theory of Nonspherical Molecules

A modification of the Boltzmann equation is described in which the rotational motion of nonspherical molecules is considered classically. This Boltzmann equation leads to equations of continuity, motion, and energy balance similar to the equations applying when the molecules are spherical. An additional equation of change arises, however, because of the conservation of angular momentum in collisions. (When the molecules are spherical, this equation is redundant.) Associated with the additional equation of change, there appears an additional ``macroscopic variable'' related to the local density of angular momentum due to the rotational motion of the molecules and an additional flux vector representing the flux or transport of this angular momentum. The Boltzmann equation is solved by a perturbation method similar to the Chapman-Enskog first approximation, and expressions are obtained for the various flux vectors and transport coefficients. Although the equations of change apply under more general conditions, the present treatment is restricted to molecules which may be idealized as rigid nonspherical bodies in which the center of mass is a center of symmetry.