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

Ivan C. Christov, Howard A. Stone

Research output: Contribution to journalArticlepeer-review


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).

Original languageAmerican English
Article number104100
JournalMechanics Research Communications
StatePublished - May 2023
Externally publishedYes

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • Granular flow
  • Mixing
  • Non-Fickian diffusion

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