Microorganism Billiards

TL;DR

This paper investigates the complex dynamics of microorganisms reflecting off surfaces with a fixed departure angle, revealing stable, chaotic, and trapping behaviors, and proposes a passive sorting device based on these properties.

Contribution

It introduces a novel billiard-like model for microorganism reflection, analyzing its dynamics in polygonal domains and patterned environments, with implications for sorting and trapping.

Findings

Dynamics can be stable or chaotic depending on geometry and angle.

Passive sorting device can separate swimmers by departure angle.

Trajectories can be trapped or diffusive based on environment pattern.

Abstract

Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of a body with this empirical reflection law inside a regular polygon and show that the dynamics can settle on a stable periodic orbit or can be chaotic, depending on the swimmer's departure angle and the domain geometry. The dynamics are often found to be robust to the introduction of weak random fluctuations. The Lyapunov exponent of swimmer trajectories can be positive or negative, can have extremal values, and can have discontinuities depending on the degree of the polygon. A passive sorting device is proposed that traps swimmers of different departure angles into separate bins. We also study the external problem of a microorganism swimming in a patterned environment of square obstacles, where the departure angle dictates the possibility of trapping or diffusive trajectories.