A multiphase virtual mass model for debris flow

Abstract In a rapidly moving multiphase mass flow, drag and virtual mass forces are important interfacial forces. However, in many existing literatures, virtual mass force has often been ignored or employed empirically. In this contribution, we construct analytical, full and explicit expressions for the virtual mass coefficients in the true three-phase typical debris flow consisting of coarse-solid, fine-solid and fluid. Similar to virtual mass coefficients, three different linear functions are introduced to connect the volume fractions and velocities of three distinct bulks of phases with other three entrapped fields, namely fine-solid entrapped in coarse-solid, and fluid entrapped in coarse-solid and fine-solid. This results in the emergence of three fundamentally different virtual mass forces expressed as analytical functions of phase-fractions, phase-densities, and the capacity of the solid-type material to hold the fluid-type materials in the mixture. Emergence of the virtual mass force coefficients induced enhanced viscosities, phase fractions, drags, viscous stresses and gravity forces of the coarse-solid and fine-solid indicate the further importance of the newly constructed multiphase mass flow model. For different local distributions of the viscous fluid and the fine particle concentrations, the model can be applied to the different flow regimes of the mixture from dilute to dense so as to cover the whole spectrum of the mixture rheology for each phase limit. In our generic model, entrapment coefficients, viscous rheology and drag coefficients can be used according to the nature of the materials involved and the flow situation. The reductions to existing two-phase mass flow models further indicate that the developed model is more generalized than the existing two-phase models. The reduced virtual mass coefficients for two-phases are still more generalized than the existing two-phase models. The simulation results using the new virtual mass coefficient with two different values of the entrapment coefficients reveal dynamically different flow-obstacle-interactions resulting in more phase-separation for the lower value of the entrapment coefficient.