  Motivated by recent experiments, we consider the hydrodynamic capture of a
microswimmer near a stationary spherical obstacle. Simulations of model
equations show that a swimmer approaching a small spherical colloid is simply
scattered. In contrast, when the colloid is larger than a critical size it acts
as a passive trap: the swimmer is hydrodynamically captured along closed
trajectories and endlessly orbits around the colloidal sphere. In order to gain
physical insight into this hydrodynamic scattering problem, we address it
analytically. We provide expressions for the critical trapping radius, the
depth of the "basin of attraction," and the scattering angle, which show
excellent agreement with our numerical findings. We also demonstrate and
rationalize the strong impact of swimming-flow symmetries on the trapping
efficiency. Finally, we give the swimmer an opportunity to escape the colloidal
traps by considering the effects of Brownian, or active, diffusion. We show
that in some cases the trapping time is governed by an Ornstein-Uhlenbeck
process, which results in a trapping time distribution that is
well-approximated as inverse-Gaussian. The predictions again compare very
favorably with the numerical simulations. We envision applications of the
theory to bioremediation, microorganism sorting techniques, and the study of
bacterial populations in heterogeneous or porous environments.
