Intermediate scattering function of an anisotropic Brownian circle swimmer

TL;DR

This paper provides a theoretical analysis of the intermediate scattering function for anisotropic Brownian circle swimmers, revealing how their circular motion affects measurable dynamical properties across different regimes.

Contribution

It introduces an exact solution for the intermediate scattering function of Brownian circle swimmers using Mathieu functions, highlighting different dynamical regimes.

Findings

Identification of regimes: translational diffusion, circular motion, enhanced diffusion.

Characteristic oscillations in the scattering function due to circular motion.

Exact analytical solution for the scattering function.

Abstract

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.