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Plenary: investigating the intermediate granular flow regime

Monday 5th January 2009 - 10:20 to 11:00
INI Seminar Room 1
Hydrodynamic modelling of gas-solid systems and granular materials traditionally focus on two flow regimes: slow dense flow, usually referred to as quasi-static flow, and fast dilute flow, usually referred to as rapid flow. In the first regime, dry particles interact via enduring contacts and the flow is often described through the Coulomb frictional law. In the second regime, dry particles interact via fast collisional contacts and the flow displays mainly viscous stresses usually described according to the kinetic theory of granular flow. Between the rapid flow and the quasi-static flow, a less understood intermediate flow might exist; in the window of intermediate flow regime, strong evidences support the argument that flow induced fluctuations and enduring contacts coexist. Researchers have attempted three different modelling approaches of the intermediate regime: (1) the kinetic-frictional approach which uses an ad hoc patching together of the stress from the two limiting regimes at a specific solid fraction (e.g., Johnson and Jackson, J. of Fluid Mech., 210, 501, 1978); (2) the switching from one regime to another using different solid stress formulations (e.g., Makkawi and Ocone, Kona, 23, 49, 2005); (3) the fluid mechanic approach allowing for smooth transition from one regime to another using a unified model (e.g., Tardos et al., Powder Tech., 131, 23, 2003). In this talk, a one-dimensional fully developed gas-solid flow model for horizontal flow is used to review the various treatments of the solid stresses; the sensitivity of the flow predictions to the frictional stress is assessed. In addition, the boundaries between rapid-intermediate-dense flow regimes are established, based on the dimensionless shear rate (ë) and a modified Reynolds number (Re).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons