On analytical solutions of a two-phase mass flow model

Abstract

We investigate a two-phase mass flow model by constructing analytical solutions with their physical significance. We use the method of splitting and separation of variables to reduce the system of non-linear PDEs modeling the two-phase mass flow into quasilinear PDEs. In particular, the system of non-linear PDEs is reduced into Riccati equations and Burgers equations, thereby making it possible to solve. Starting with simple analytical solutions, we construct analytical solutions with increased complexities for the phase velocities and the phase heights as functions of space and time. Furthermore, we use the Lie group action to generate more analytical solutions and analyze their possible invariance. We also present a perspective called relative non-invariance associated to the underlying physics relevant to multi-phase flows, namely, the relative velocity and relative flow depths between the phases. Finally, we present detailed analysis and discussion on the time and spatial evolutions of the analytical solutions for solid and fluid phase velocities and the flow depths. The obtained analytical solutions corroborate with the physics of two-phase mass flows down a slope.