Anomalous diffusion in silo drainage
Department of Physics and Applied Mathematics, University of Navarra, E-31080, Pamplona, Spain
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Published online: 2 July 2007
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 (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.
PACS: 45.70.-n Granular systems – / 45.70.Mg Granular flow: mixing, segregation and stratification – / 45.50.-j Dynamics and kinematics of a particle and a system of particles –
© EDP Sciences/Società Italiana di Fisica/Springer-Verlag, 2007