On force balance in Brinkman fluids under confinement

TL;DR

This paper analyzes force distribution in Brinkman fluids under confinement, using the Lorentz reciprocal theorem and analytical solutions, with implications for cellular processes like cytoplasmic streaming.

Contribution

It provides a detailed force analysis in confined Brinkman fluids across various geometries, combining theoretical and analytical approaches.

Findings

Force balance is maintained by various forces depending on geometry.

Analytical solutions validate the force distribution calculations.

Implications for cellular processes such as cytoplasmic streaming.

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.