The curved kinetic boundary layer of active matter

The finite reorient-time of swimmers leads to a finite run length $\mathrm{\ell }$ and the kinetic accumulation boundary layer on the microscopic length scale $\delta$ on a non-penetrating wall. That boundary layer is the microscopic origin of the swim pressure, and is impacted by the geometry of the boundary [Yan & Brady, $\mathit{\text{J.}}\mathit{\text{Fluid.}}\mathit{\text{Mech.}}$, 2015, $\mathbf{\text{785}}$, R1]. In this work we extend the analysis to analytically solve the boundary layer on an arbitrary-shaped body distorted by the local mean curvature. The solution gives the swim pressure distribution and the total force (torque) on an arbitrarily shaped body immersed in swimmers, with a general scaling of the curvature effect ${\mathrm{\Pi }}^{swim}\sim \lambda {\delta }^2\mathrm{/}L$.