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Instabilities in Flows of Solid Particles

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Date and time:Ìý

Thursday, February 7, 2013 - 3:15pm

Abstract:Ìý

The rapid flow of solid particles, be it in a strictly granular flow or in conjunction with a gas-phase, are often rarefied in nature since the separation of scales is often not great enough to neglect Knudsen-type effects a priori. The hydrodynamic description of such flows is further complicated, relative to their molecular counterparts, due to the dissipative nature of particle collisions. This dissipation can give rise to a host of phenomena with no molecular counterpart, such as vortex and clustering instabilities. Although hydrodynamic descriptions of rapid granular flows often take the form of Navier-Stokes order equations, such approaches have been called into question for the reasons listed above – i.e., the lack of a strict adherence to separation of scales and the presence of large local gradients (higher Knudsen numbers) in flows with vortex and clustering instabilities. In this work, we present a number of recent examples of the success of Navier-Stokes order equations for systems where Knudsen effects are non-negligible. The focus here is on moderate concentrations, with the Enskog equation used as the starting point for the hydrodynamic description. Collectively, these results demonstrate the success of Navier-Stokes order hydrodynamics for a wide class of rapid granular flows at moderate concentrations.