Pressure force transition and mixture morphology evolution in heterogeneous mixtures

Abstract

The pressure gradient terms in multifluid dynamical descriptions with separate momentum equations for each species or material have different forms depending on the mixture morphology. As the mixture evolves from chunk to molecular mixing, the form of the pressure gradient terms should evolve accordingly. This paper presents a new formulation of the pressure gradient terms which exhibits the appropriate smooth transition in form as the mixture evolves from chunk to molecular mixing, including intermediate stages in which both types of mixing are present. This transition is accomplished by introducing appropriate mixture morphology variables βi to describe the degree of molecular vs. chunk mixing for each species. A simple provisional relaxation-time model for the time evolution of the βi is also presented.