Anomalous diffusion in silo drainage

Abstract

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well defined relationship ($\gamma =2/(3-q)$) between the anomalous diffusion exponent $\gamma$ and the entropic parameter $q$ introduced by the non-extensive formalism to fit the PDF of the fluctuations.

18 pages, 6 figures. Substantially enlarged with new results. Accepted for EPJ-E

References in corpus (9)

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• Self-diffusion in dense granular shear flows
• Jamming During the Discharge of Grains from a Silo Described as a Percolating Transition
• Diffusion and mixing in gravity-driven dense granular flows
• Size Segregation of Granular Matter in Silo Discharges
• Velocity profile of granular flows inside silos and hoppers
• The statistics of particle velocities in dense granular flows
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• Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation
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• Some Open Points in Nonextensive Statistical Mechanics
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• Collisional regime during the discharge of a 2D silo
• Pathway Model and Nonextensive Statistical Mechanics
• Reorganization of a granular medium around a localized transformation
• T. Dauxois' "Non-Gaussian distributions under scrutiny" under scrutiny