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Viscous flow around three-dimensional macroscopic cavities in a granular material

Published online by Cambridge University Press:  26 November 2021

Osamu Sano
Affiliation:
Tokyo University of Agriculture and Technology, Fuchu, Tokyo183-8538, Japan
Timir Karmakar
Affiliation:
Department of Mathematics, National Institute of Technology Meghalaya, Shillong, Meghalaya793003, India
G.P. Raja Sekhar*
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur721302, India
*
Email address for correspondence: rajas@iitkgp.ac.in

Abstract

Viscous flow around spherical macroscopic cavities in a granular material is investigated. The Stokes equation inside and the Darcy–Brinkman equation outside the cavities are considered. In particular, the interaction of two equally sized cavities positioned in tandem is examined in detail, where the asymptotic effect of the other cavity is taken into account. The present analysis gives a reasonable estimate on the volume flow into the cavity and the local enhancement of stresses. This is applicable to predict the microscale waterway formation in that material, onset of landslides, collapse of cliffs and river banks, etc.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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