Influence of thermal fluctuations on active diffusion at large P\'{e}clet numbers

TL;DR

This study uses wavelet Monte Carlo simulations to show that thermal fluctuations significantly influence active diffusion of passive particles near microswimmers, resulting in a weak power-law dependence on Péclet number and a non-monotonic size dependence.

Contribution

It introduces a model incorporating thermal motion into active diffusion analysis at large Péclet numbers, revealing its impact on particle dynamics and diffusivity.

Findings

Thermal motion causes significant decorrelation in particle velocities.

Active diffusivity scales approximately as Pe^{0.2} for small particles.

Diffusivity varies non-monotonically with particle size.

Abstract

Wavelet Monte Carlo dynamics simulations are used to study the dynamics of passive particles in the presence of microswimmers, taking account of the often-omitted thermal motion alongside the hydrodynamic flows generated by the swimmers. Although the P\'{e}clet numbers considered are large, we find the thermal motion to have a significant effect on the dynamics of our passive particles, and can be included as a decorrelation factor in the velocity autocorrelation with a decay time proportional to the P\'{e}clet number. Similar decorrelation factors come from swimmer rotations, e.g.~run and tumble motion, and apply to both entrainment and far field loop contributions. These decorrelation factors lead to active diffusivity having a weak apparent power law close to $Pe^{0.2}$ for small tracer-like particles at P\'{e}clet numbers appropriate for E. coli swimmers at room temperature. Meanwhile, the reduced hydrodynamic response of large particles to nearby forces has a corresponding reduction in active diffusivity in that regime. Together, they lead to a non-monotonic dependence of active diffusivity on particle size that can shed light on similar behaviour observed in experiments by Patteson et al.