A Taylor swimming sheet under a finite Brinkman layer

TL;DR

This paper analyzes how a two-dimensional swimming sheet's speed is affected by a finite Brinkman layer, considering factors like porosity, jump stress, and layer thickness, with implications for biological and medical systems.

Contribution

It introduces an asymptotic approach to study the swimming speed of a sheet in a Brinkman layer, incorporating effects of porosity and jump stress, revealing complex behaviors and conditions for maximum speed.

Findings

Swimming speed decreases with increased layer thickness and decreased permeability.

Porosity effects can enhance or reduce swimming speed depending on porosity value.

Coupling jump stress with porosity can lead to maximum swimming speeds exceeding Newtonian cases.

Abstract

An asymptotic approach is employed to study the swimming speed of a two-dimensional Taylor swimming sheet beneath a Brinkman layer of finite thickness. This configuration is representative of a swimmer confined within a porous non-Newtonian boundary and could model microscopic filter feeders like choanoflagellates and sponges or the mucociliary escalator in the lungs. When ignoring the effects of jump stress and porosity, the swimming speed of the sheet decreases as the thickness and lower boundary of the Brinkman layer increase. The same is true as the permeability of the layer decreases. Including porosity effects with a zero jump stress enhances the swimming velocity of the sheet for porosity values near unity and decreases the swimming velocity for smaller porosity values. In the absence of porosity, the swimming speed of the sheet increases for positive-valued jump stresses and decreases for negative ones. Coupling nonzero jump stress with a variable porosity establishes complex behavior, with the sheet's swimming speed attaining a maximum, surpassing that found for the Newtonian case, particularly in thin or low-permeability Brinkman layers.