Abstract
A common instability in metallurgy and geophysics is the dripping of negatively-buoyant, solid–liquid mixtures. We conducted a numerical study of the finite amplitude evolution of multiphase Rayleigh–Taylor instabilities. For systems with a density-weighted average viscosity of less than 0.2, two time scales of sedimentation were observed. Initially, plumes form and merge, and solids disperse throughout the cavity. Final clarification of the carrier phase by hindered Stoke's settling then occurs. The ratio of the time to clear the mixture to the time for near-uniform dispersal of the solids can be two or three orders of magnitude. Roof sedimentation in more viscous liquids demonstrates a complex time dependence. The solid volume fraction distribution becomes non-topological with features of both viscous and inertially dominated conditions at a given time step. Cyclic sedimentation occurs as the potential energy associated with the initially unstable layer does not decay in a temporally uniform manner.
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