Fig. 1: Optimal microswimmer navigation near spherical obstacles.

a Curves represent optimal trajectories for microswimmers (red and green) and for a dry active particle (blue), i.e., in the absence of hydrodynamic interactions (HIs) with obstacles (shown in gray). The swimmers are micron sized and the swimming trajectories are assumed to take place in the plane passing through the centers of the spherical obstacles. Here, σ is the source dipole coefficient and x, z are spatial coordinates. Panels b, c show the flow field streamlines induced by a source dipole at position r = (−3, 3) μm in the presence of a spherical obstacle with radius R = 3 μm. Black arrows indicate the orientation of the swimmers. The fluid-mediated hydrodynamic interactions with the spherical boundary induce a deceleration of the swimming agent for σ > 0 leading to larger speeds as the swimmer gets away from the obstacle. In contrast to that, hydrodynamic interactions cause an acceleration for σ < 0 yielding an increased speed near the obstacle.