Some notes on a volume fraction mixture theory and a comparison with the kinetic theory of gases

Abstract

This paper is primarily concerned with the development of a modern mixture theory based on a volume fraction definition of velocity. This definition may be contrasted to that of classical mixture theory which bases the mixture velocity on dispersed densities. The volume fraction theory leads to fundamentally different restrictions for the supply terms governing constituent interactions. An accurate representation of the mass, momentum, and energy supplies is critical to the success of virtually all mixture theory applications. Hence, the differences between the volume fraction theory and the classical theory are substantial and a closer scrutiny of the implications of each is warranted. The two theories are compared with results from the kinetic theory of gases for the case of a diffusing mixture of gases. The results indicate the volume fraction theory is consistent with kinetic theory while the classical theory is not.