Active Caustics

TL;DR

This paper demonstrates that self-propelled particles can form caustic singularities similar to inertial particles in vortical flows, leading to high local concentrations and burst-like encounters, with implications for microbial communication.

Contribution

It reveals that caustic formation occurs in self-propelled particles without inertia, establishing a formal link to inertial particle dynamics and identifying a singular perturbation mechanism.

Findings

Caustics form around vortices in self-propelled particle flows.

Peak caustic activity occurs at intermediate self-propulsion levels.

Numerical simulations show intense caustics in turbulent flow regions.

Abstract

Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds can arise without mechanical inertia for self-propelled particles (SPPs), through a formal correspondence between the dynamics of IPs and SPPs in a generic background flow. We establish that a singular perturbation underlies caustics formation by SPPs around a single vortex, and numerical studies of SPPs in two-dimensional Navier-Stokes turbulence reveal intense caustics in straining regions of the flow, peaking at intermediate levels of self-propulsion. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Reynolds-number swimmers. Caustics generate burst-like encounters through large relative velocities between neighboring swimmers, with potentially significant implications for communication and sexual reproduction. An intriguing open direction is whether the active turbulence of a suspension of swimming microbes could serve to generate caustics in its own concentration