Influence of thermal fluctuations on active diffusion at large Péclet numbers

Abstract

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 P eclet 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 eclet 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 eclet 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 nonmonotonic 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)].

Optimal Ratchet Potentials for Run-and-Tumble particles

“…Typical values for E. coli are D = 0.2 µm 2 /s for the thermal diffusion constant, w = 40 µm/s for the self-propulsion speed and γ = 1s −1 for the tumble rate [41,42], producing values between Pe = 1000 and Qe = 125 for L = 5 µm and Pe = 2 • 10 4 and Qe = 5 • 10 4 for L = 100 µm. For these parameters we expect the optimal potential to be akin to Fig.…”

Interplay between Brownian and hydrodynamic tracer diffusion in suspensions of swimming microorganisms

“…Furthermore, the effect of Brownian motion on enhanced tracer diffusion was analysed theoretically by Kasyap, Koch & Wu (2014) for a model of slender-body swimmers, showing that is a non-monotonic function of , with first showing a small increase for intermediate , before falling below the athermal value as grows larger. In a more recent study of finite-size spherical tracers in microswimmer suspensions, Dyer & Ball (2021) analysed numerically the combined effect of thermal fluctuations and near-field flows on the size-dependent tracer dynamics, finding non-monotonic behaviour similar to that observed experimentally. In this paper, we will revisit the problem of the interplay between Brownian and hydrodynamic diffusion for the simple case of point-like tracers immersed in a dilute suspension of microswimmers described via a regularised dipolar flow field.…”

“…Thus, even though Brownian motion is unlikely to provide a significant dependence of on for tracers immersed in suspensions of biological microswimmers, there are several other mechanisms that need to be studied to explain the non-monotonic dependence observed experimentally (Patteson et al. 2016) and computationally (Dyer & Ball 2021). First, the effect of tracer entrainment by the near field flows of the swimmer is strongly dependent on the size ratio between the swimmer and the tracer (Jeanneret et al.…”

“…2016), although we expect this term to be small for micron-sized tracer particles in E. coli suspensions. Second, the finite size of the tracer will change the equation of motion (2.1) into the Faxén equation that takes into account the nonlinearity of the flow field (Kim & Karrila 1991), an effect that was included implicitly in the wavelet Monte Carlo simulations by Dyer & Ball (2021), and, together with tracer entrainment, is a significant explanation of their observed dependence of . Finally, non-hydrodynamic interactions such as direct collisions, electrostatic interactions and artefacts due to container walls are likely to depend in a non-trivial manner on the tracer size for each system in question.…”

Anisotropic diffusion of ellipsoidal tracers in microswimmer suspensions

“…Furthermore, in the concentration regime where swimmer-swimmer correlations are sufficiently weak, D T displays a linear scaling with swimmer density [8,11,16]. For dilute, 3dimensional microswimmer suspensions, this enhanced tracer diffusion has been rationalised from the superposition of independent hydrodynamic swimmer-tracer scattering events due to the swimmers' long-ranged dipolar * joakim.stenhammar@fkem1.lu.se flow fields [8,[20][21][22][23][24][25], while, at much higher densities, for finite-size particles, or in confined geometries, direct swimmer-tracer collisions [26][27][28] and near-field hydrodynamic effects [13,29] also become significant. Furthermore, for the case where microswimmers are significantly larger than the tracer particles, so-called tracer entrainment can occur, leading to isolated, very large displacements of individual tracers and a qualitative change in the displacement statistics [25,30,31].…”