@article{a12c60a260ec44f08186294844aa68ea,
title = "Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler",
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).",
keywords = "Granular flow, Mixing, Non-Fickian diffusion",
author = "Christov, {Ivan C.} and Stone, {Howard A.}",
note = "Funding Information: This work was initiated while I.C.C. was working with H.A.S. at Princeton University. At that time, I.C.C. was supported by the U.S. National Science Foundation (NSF) under grant no. DMS-1104047 . I.C.C. would like to further acknowledge the hospitality of the University of Nicosia, Cyprus, where this version was completed thanks to a Fulbright U.S. Scholar award from the U.S. Department of State. Funding Information: This paper is dedicated to memory of the late Prof. Denis L. Blackmore for his contributions to continuum models of granular flows (e.g. [65,66]). I.C.C. would also like to acknowledge discussions (circa 2014) on wave phenomena [33] with the late Prof. A.M. Samsonov. This work was initiated while I.C.C. was working with H.A.S. at Princeton University. At that time, I.C.C. was supported by the U.S. National Science Foundation (NSF) under grant no. DMS-1104047. I.C.C. would like to further acknowledge the hospitality of the University of Nicosia, Cyprus, where this version was completed thanks to a Fulbright U.S. Scholar award from the U.S. Department of State. Publisher Copyright: {\textcopyright} 2023 Elsevier Ltd",
year = "2023",
month = may,
doi = "10.1016/j.mechrescom.2023.104100",
language = "English (US)",
volume = "129",
journal = "Mechanics Research Communications",
issn = "0093-6413",
publisher = "Elsevier Limited",
}