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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 Open the ORCID record for Osamu Sano [Opens in a new window] ,
Timir Karmakar Open the ORCID record for Timir Karmakar [Opens in a new window]  and
G.P. Raja Sekhar Open the ORCID record for G.P. Raja Sekhar [Opens in a new window]
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
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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.

JFM classification

Geophysical and Geological Flows: Hydraulic control Granular media: Avalanches Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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