A generalized quasi two-phase bulk mixture model for mass flow

We employ full dimensional two-phase mass flow equations (Pudasaini, 2012) [18] to develop a generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The emerging model, as a set of coupled partial differential equations, is characterized by some new mechanical and dynamical aspects of generalized bulk and shear viscosities, pressure, velocities and effective friction for the mixture where all these are evolving as functions of several dynamical variables, physical parameters, inertial and dynamical coefficients and drift factors. These coefficients and factors are uniquely constructed, contain the underlying physics of the system, and reveal strong coupling between the phases. The new model is mechanically described by an extended pressure and rate-dependent Coulomb-viscoplastic rheology of mixture. The model is expected to simulate the velocities and pressure of the bulk mixture much faster than the two-phase mass flow model. Furthermore, the introduction of the velocity and pressure drifts makes it possible to reconstruct the two-phase dynamics. This shows the application potential of the new model presented here.