Power of a Brinkman sheet ($P_{+}=\frac{1}{2}\mu b^{2}k{\omega }^{2}s(s+1)$)

For $s=\sqrt{1+(\alpha /k{)}^2}$, the leading work per projected area on one side of a transverse Brinkman swimming sheet is $\mu b^{2}k{\omega }^{2}s(s+1)/2$. Two fluid sides double it. Work includes viscous dissipation and drag against the matrix, giving a greater fixed-stroke cost than in the unscreened fluid.