  Achieving macroscopic directed migration of microscale swimmers in a fluid is
an important step towards utilizing their autonomous motion. It has been
experimentally shown that directed motion can be induced, without any external
fields, by certain geometrically asymmetric obstacles due to interaction
between their boundaries and the swimmers. In this paper, we propose a
kinetic-type model to study swimming and directional migration of microscale
bimetallic rods in a periodic array of posts with non-circular cross-sections.
Both rod position and orientation are taken into account; rod trapping and
release on the post boundaries are modeled by empirically characterizing
curvature and orientational dependence of the boundary absorption and
desorption. Intensity of the directed rod migration, which we call the
normalized net flux, is then defined and computed given the geometry of the
post array. We numerically study the effect of post spacings on the flux; we
also apply shape optimization to find better post shapes that can induce
stronger flux. Inspired by preliminary numerical results on two candidate
posts, we perform an approximate analysis on a simplified model to show the key
geometric features a good post should have. Based on that, three new candidate
shapes are proposed which give rise to large fluxes. This approach provides an
effective tool and guidance for experimentally designing new devices that
induce strong directed migration of microscale swimmers.
