Hydrodynamic Attraction and Hindered Diffusion Govern First-passage Times of Swimming Microorganisms

Abstract

The motion of microorganisms in their natural habitat is strongly influenced by their propulsion mechanisms, geometrical constraints, and random fluctuations. Here, we study numerically the first-passage-time (FPT) statistics of microswimmers, modeled as force-dipoles, to reach a no-slip wall. Our results demonstrate that hindered diffusion near the wall can increase the median FPT by orders of magnitude compared to "dry" agents, while the intricate interplay of active motion and hydrodynamic attraction speeds up the arrival at large Péclet numbers (measuring the importance of self-propulsion relative to diffusion). Strikingly, it leads to a non-monotonic behavior as a function of the dipole strength, where pushers reach the wall significantly faster than pullers. The latter become slower at an intermediate dipole strength and are more sensitive to their initial orientation, displaying a highly anisotropic behavior.