Influence of thermal fluctuations on active diffusion at large Péclet numbers

Three-dimensional Wavelet Monte Carlo dynamics simulations are used to study the dynamics of passive particles in the presence of microswimmers—both represented by neutrally buoyant spheres—taking into account the often-omitted thermal motion alongside the hydrodynamic flows generated by the swimmers. Although the Péclet 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 Péclet 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 Pe0.2 for small tracer-like particles at Péclet 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 behavior observed in the experiments by Patteson et al. [“Particle diffusion in active fluids is non-monotonic in size,” Soft Matter 12, 2365–2372 (2016)]