Transport Equations of Multicomponent Systems of Polyatomic Molecules. I

Abstract

The treatment of the transport phenomena starting with the Liouville equation was first given by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] for a one‐component system composed of point molecules. The theory has been extended by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1957)] to multiple‐component point‐molecule systems and by Dahler [J. Chem. Phys. 30, 1447 (1959)] to a one‐component system of diatomic molecules. In the present work, the theory is extended to a multicomponent system composed of polyatomic molecules. The theory treats the translational, rotational, and vibrational motions of fluids but not the electronic motion. From the Liouville equation, the equations of continuity and of linear momentum, angular momentum, and energy transport are developed. The one‐particle and pair densities, involving the one‐particle and the two‐particle distribution functions are expanded in powers of a parameter measuring the small deviations from the state of local thermodynamic equilibrium, but the calculations extend only to the first order in the gradients of the particle densities and temperature. From the general transport equations, the phenomenological equations involving transport coefficients are obtained. These coefficients are formally determined in terms of the laws of intermolecular interaction and of the assumed dependence of the distribution functions on the gradients of the particle densities and of temperature.