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On force balance in Brinkman fluids under confinement

Published online by Cambridge University Press:  28 March 2025

Abdallah Daddi-Moussa-Ider Open the ORCID record for Abdallah Daddi-Moussa-Ider [Opens in a new window]  and
Andrej Vilfan Open the ORCID record for Andrej Vilfan [Opens in a new window]
Abdallah Daddi-Moussa-Ider
Affiliation:
School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
Andrej Vilfan*
Affiliation:
Jožef Stefan Institute, Ljubljana 1000, Slovenia
*
Corresponding author: Andrej Vilfan, [email protected]
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Abstract

A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning.

JFM classification

Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A11
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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