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arXiv · 1902.01200

Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler

Ivan C. Christov·Howard A. Stone
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Abstract

We provide new concepts for understanding transport phenomena in flows of granular materials by using a non-Fickian macroscopic model of axial diffusion of a granular material in a finite cylindrical tumbler. The model accounts for diffusion induced by particle collisions only in a thin surface flowing layer due to localization of shear within the cross-section of the drum. All model parameters are related to measurable quantities in a granular flow. It is shown that the proposed model is a member of the general class of linear constitutive relations with memory. An exact solution for the spreading of a finite-width pulse initial condition under the proposed non-Fickian model is derived and compared to the solution of a Fickian model (i.e., the ``classical'' diffusion equation).

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BibTeXRIS

Ivan C. Christov, Howard A. Stone. 2019-01-30. Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler. https://doi.org/10.1016/j.mechrescom.2023.104100

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