A mechanical model for phase separation in debris flow

Abstract

Understanding the physics of phase separation between solid and fluid phases as a mixture mass moves down-slope is a long-standing challenge. Here, we propose an extension of a two phase mass flow model (“Pudasaini (2012), A general two-phase debris flow model, Journal of Geophysical Research, 117, F03010, doi:10.1029/2011JF002186”) by including a new mechanism, called separation-flux, that leads to strong phase separation in avalanche and debris flows while balancing the enhanced solid flux with the reduced fluid flux. The relative velocity between the phases is key in triggering the phase separation mechanism, which is induced by the effective forces that appear in the system. The novel separation-flux can be written as a product of the separation-rate, solid and fluid volume fractions, and the flow depth which amplify the separation-flux. Its magnitude is further controlled by the separation-rate-intensities which are functions of volume fractions and the density ratio. The separation-fluxes are multi-directional. One of the most important characteristics of the separation-flux is that phase separation ceases as soon as one of the components in the mixture vanishes. As the solid density approaches the fluid density, the phase separation intensity is reduced. Furthermore, as the drag increases, the phase separation decreases. The separation velocity emerges from the separation-flux as a function of the relative phase velocity, volume fraction of solid or fluid, and the respective separation-rate-intensity. The separation-rate takes into account different dominant physical and mechanical aspects of the mixture flow, such as the hydraulic pressure gradients, topography induced pressure gradients, the gradients of the volume fractions of solid and fluid phases, flow depths, grain size, densities, friction, viscosities, and buoyancy. The separation-flux mechanism is capable of describing the dynamically evolving phase separation and levee formation in a multi-phase, geometrically three-dimensional debris flow. These are often observed phenomena in natural debris flows and industrial processes that involve the transportation of particulate solid-fluid mixture material. Due to the inherent separation mechanism, as the mass moves down-slope, more and more solid particles are transported to the front and the sides, resulting in solid-rich and mechanically strong frontal surge head, and lateral levees followed by a weaker tail largely consisting of viscous fluid. The primary frontal solid-rich surge head followed by secondary fluid-rich surges is the consequence of phase separation. Such typical and dominant phase separation phenomena are revealed for two-phase debris flow simulations. Finally, changes in flow composition, that are explicitly considered by the new modelling approach, result in significant changes of impact pressure estimates. These are highly important in hazard assessment and mitigation planning and highlight the application potential of the new approach.