Abstract
Tracer particles immersed in suspensions of biological microswimmers such as E. coli or C. reinhardtii display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers in active suspensions can be expected to exhibit even more complex behaviour than spherical ones, due to the presence of a nontrivial translation-rotation coupling. Using large-scale lattice Boltzmann simulations of model microswimmers described by extended force dipoles, we study the motion of ellipsoidal point tracers immersed in 3-dimensional microswimmer suspensions. We find that the rotational diffusivity of tracers is much less affected by swimmer-swimmer correlations than the translational diffusivity. We furthermore study the anisotropic translational diffusion in the particle frame and find that, in pusher suspensions, the diffusivity along the ellipsoid major axis is higher than in the direction perpendicular to it, albeit with a smaller ratio than for Brownian diffusion. Thus, we find that far field hydrodynamics cannot account for the anomalous coupling between translation and rotation observed in experiments, as was recently proposed. Finally, we study the probability distributions (PDFs) of translational and rotational displacements. In accordance with experimental observations, for short observation times we observe strongly non-Gaussian PDFs that collapse when rescaled with their variance, which we attribute to the ballistic nature of tracer motion at short times.
Highlights
Active transport of particles is of importance in many biological contexts, such as intracellular transport [1], absorption of nutrients in intestines [2] and by microorganisms [3], and possibly mass transport in oceans [4]
In contrast to experimental results for ellipsoidal tracers in E. coli suspensions [14], we find that the ratio D /D⊥ is above unity, indicating that far-field hydrodynamics cannot account for the anomalous coupling between translation and rotation seen in experiments
SUMMARY AND CONCLUSION In this study, we computationally investigated the dynamics of ellipsoidal tracer particles in three-dimensional microswimmer suspensions, using large-scale lattice Boltzmann simulations
Summary
Active transport of particles is of importance in many biological contexts, such as intracellular transport [1], absorption of nutrients in intestines [2] and by microorganisms [3], and possibly mass transport in oceans [4]. For Brownian diffusion, these PDFs are Gaussian, while in biological microswimmer suspensions they become strongly non-Gaussian at low swimmer densities and short observation times [16,17,32] This effect is explained by the fact that tracer displacements result from just a small number of swimmer-tracer scattering events, so that the central limit theorem does not apply [33,34,35], and has been reproduced in computational models of microswimmers [21,23,35]. In addition to the enhanced overall diffusion seen for spherical tracers, these studies found significantly increased rotational diffusion coefficients DR They found that ellipsoidal tracers display a qualitatively anomalous anisotropic diffusion compared to the Brownian case, in that the ratio D /D⊥ of diffusion coefficients parallel and perpendicular to the particle major axis is below unity in the case of pusher-type swimmers (E. coli) at high densities [14]. In contrast to experimental results for ellipsoidal tracers in E. coli suspensions [14], we find that the ratio D /D⊥ is above unity, indicating that far-field hydrodynamics cannot account for the anomalous coupling between translation and rotation seen in experiments
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