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.

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• Low Reynolds number flows
• Mathematical physics
• Swimming