Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G24: Granular Flows: Mixing, Segregation and Separation
8:00 AM–9:57 AM,
Monday, November 24, 2014
Chair: Sylvain Joubaud, Ecole Normale Superieure de Lyon
Abstract ID: BAPS.2014.DFD.G24.1
Abstract: G24.00001 : Continuum modeling of diffusion and dispersion in dense granular flows*
8:00 AM–8:13 AM
Preview Abstract Abstract
Ivan C. Christov
(Theoretical Division \& Center for Nonlinear Studies, Los Alamos National Laboratory)
Howard A. Stone
(Mechanical \& Aerospace Engineering, Princeton University)
Continuum modeling of granular flows remains a challenge of modern statistical physics. Granular materials do not perform Brownian motion, yet diffusion and shear dispersion can be observed in such systems when agitation causes inelastic collisions between particles. In a number of canonical flow regimes (e.g., in a rotating container or down an incline), granular materials can behave like fluids. We formulate and solve the granular counterparts to two basic fluid mechanics problems: diffusion of a pulse and shear dispersion of a pulse for dense granular materials in rapid flow. We provide a theory to account for the concentration-dependent diffusivity of bidisperse granular mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process for which an exact self-similar analytical solution does not exist. For shear dispersion, we show that the effective dispersivity of the depth-averaged concentration of the dispersing powder varies as the P\'eclet number squared, as in classical Taylor--Aris dispersion of molecular solutes. The calculation is extended to generic shear profiles, showing a significant enhancement for convex profiles due to the shear-rate dependence of the diffusivity of granular materials.
*ICC was supported by NSF Grant DMS-1104047 and the U.S. DOE through the LANL/LDRD Program; HAS was supported by NSF Grant CBET-1234500.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.DFD.G24.1
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