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Register a new userDiffusion of an ellipsoid in bacterial suspensions
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Active matter such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. Among these properties, the enhanced diffusion of tracer particles is generally deemed as a hallmark of active matter. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in quasi-two-dimensional bacterial bath. Our study reveals a nonlinear enhancement of both translational and rotational diffusions. More importantly, we uncover an anomalous coupling between translation and rotation that is strictly prohibited in the classic Brownian diffusion. Combining experiments with theoretical modeling, we show that such an anomaly arises from generic stretching flows induced by swimming bacteria. Our work illustrates a universal organizing principle of active matter and sheds new light on fundamental transport processes in microbiological systems.
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Tracer particles immersed in suspensions of biological microswimmers such as E. coli or Chlamydomonas 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.
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazurs method [Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazurs $deltagamma$-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified $deltagamma$ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as $40%$.
The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking non-monotonic dependence of the long-time self-diffusion on the concentration of the DNA in low-salt conditions. This generic non-monotonic behavior results from both the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, and from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.
We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in suspensions of charge-stabilized colloidal spheres. In simulation and theory, the spheres interact by a hard-core plus screened Coulomb pair potential. Intermediate and self-intermediate scattering functions are calculated by accelerated Stokesian Dynamics simulations where hydrodynamic interactions (HIs) are fully accounted for. The study spans the range from the short-time to the colloidal long-time regime. Additionally, Brownian Dynamics simulation and mode-coupling theory (MCT) results are generated where HIs are neglected. It is shown that HIs enhance collective and self-diffusion at intermediate and long times, whereas at short times self-diffusion, and for certain wavenumbers also collective diffusion, are slowed down. MCT significantly overestimate the slowing influence of dynamic particle caging. The simulated scattering functions are in decent agreement with our dynamic light scattering (DLS) results for suspensions of charged silica spheres. Simulation and theoretical results are indicative of a long-time exponential decay of the intermediate scattering function. The approximate validity of a far-reaching time-wavenumber factorization of the scattering function is shown to be a consequence of HIs. Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function and the particle mean squared displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a method to deduce the MSD approximately in DLS is theoretically validated.
We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio $epsilon$ and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where $epsilon = 1$, there are many unconstrained and non-trivial rotational degrees of freedom. These constitute a set of zero-frequency modes that are gradually mobilized into a new rotational band as $|epsilon - 1|$ increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, $omega^*$, the presence of these new degrees of freedom leaves unaltered the basic scenario that the translational spectrum is determined only by the average contact number. Indeed, $omega^*$ depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large $|epsilon - 1|$, where the two bands merge.
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