Transient two-dimensional dynamics in the upper conduit of a rhyolitic eruption: A comparison of closure models for the granular stress

Abstract

To elucidate the role of particle collisions in redistributing momentum after fragmentation, a numerical study was performed comparing the behavior of an inviscid, or collision-less, granular material with a granular material whose viscosity and pressure were modeled using kinetic theory. The granular viscosity calculation is sensitive to particle size and three particle sizes were considered: 0.0002 m, 0.002 m, and 0.02 m. A critical volume fraction of gas (0.75) identifies the onset of fragmentation, dividing the region of rhyolitic magma with dispersed bubbles from the region of turbulent gas with dispersed particles. The transient simulations can be divided into two dynamic regimes: an initial shock followed by a transition to steady state. During the initial shock phase, treatment of the granular pressure and viscosity led to greater particle velocities relative to the inviscid calculation due to the development of higher gas pressure at fragmentation. However, as steady state is approached the viscosity slows the particle phase relative to the inviscid counterpart for particles greater than a millimeter. The modeled sub-millimeter particle velocity was insensitive to the treatment of the granular pressure and viscosity. Centimeter-scale particles have a much higher granular viscosity (up to 10 −1 Pa·s) and the kinetic theory calculation is thus relevant in these conditions. After reaching steady state, the differential velocity between gas and particles at the conduit exit correlates with particle size for both the inviscid and granular viscosity calculations: negligible differential velocity develops for sub-millimeter particles, but centimeter-scale particles exit the conduit with >5% differential velocity between phases.