Microorganism Billiards

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.

29 pages, 17 figures. Elsevier style. Final published version

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Cited by in corpus (7)

• Curvature-guided motility of microalgae in geometric confinement
• Active particles in periodic lattices
• Swimming in Complex Fluids
• Diffusion of active particles in a complex environment: Role of surface scattering
• Ideal circle microswimmers in crowded media
• Rebound and scattering of motile Chlamydomonas algae in confined chambers
• Boundary shape engineering for the spatial control of confined active particles