Session J22: Focus Session: Collective Dynamics of Self-Driven Particles

From cell extracts to fish schools to granular layers: the universal hydrodynamics of self-driven systems

Collections of self-driven or ``active'' particles are now recognised as a distinct kind of nonequilibrium matter, and an understanding of their phases, hydrodynamics, mechanical response, and correlations is a vital and rapidly developing part of the statistical physics of soft-matter systems far from equilibrium. My talk will review our recent results, from theory, simulation and experiment, on order, fluctuations, and flow instabilities in collections of active particles, in suspension or on a solid surface. Our work, which began by adapting theories of flocking to include the hydrodynamics of the ambient fluid, provides the theoretical framework for understanding active matter in all its diversity: contractile filaments in cell extracts, crawling or dividing cells, collectively swimming bacteria, fish schools, and agitated monolayers of orientable granular particles.   

Simulations of Interacting Magnetic Micro-swimmers

Following a recent realization of artificial micro-swimming (Dreyfus et. al., \emph{Nature}, \textbf{437}, 862-865), we conduct simulations of a swimmer whose mechanism of propulsion is the magnetically driven undulation of a flagellum-like tail composed of chemically linked paramagnetic beads. In our model, the tail is treated as a series of spheres tied together by inextensible, bendable links. The spheres interact magnetically through mutual dipole interactions, and hydrodynamic interactions are achieved by the force-coupling method. Building on our previous results, we examine the interactions between multiple swimmers employing a flagellum beating strategy as well as those using a rotary propulsion scheme. In addition to swimmer-swimmer interactions, the effects of a nearby surface on the behavior of a micro-swimmer will be discussed.   

Response and Fluctuations in an Active Bacterial Suspension

An active bacterial bath consists of a population of rod-like motile or self-propelled bacteria suspended in a fluid environment. In this talk, we present a two-fluid model for the dynamics of a bacterial bath, and show, in particular, that the non-equilibrium contribution to the stress arising from the swimming of the bacteria and the non-equilibrium couplings between the alignment tensor and bacterial density, lead to i) a $1/\sqrt{\omega}$ scaling in the power spectrum of the active stress fluctuations, and ii) anomalous density fluctuations in the bacteria themselves. These predictions are observed in a recent experiment.   

Collective dynamics of concentrated swimming micro-organisms

Approximately close packed populations of the cylindrical self-propelled bacteria Bacillus subtilis intermittently form domains of aligned, co-directionally swimming organisms. The velocities of these phalanxes are often ``high'' compared to the speed of individual swimmers. They vary with the depth of the suspension of organisms. Although the Reynolds number is $<$1, this collective dynamic phase, the ``Zooming BioNematic'' (ZBN), appears turbulent. Remarkable spatial and temporal correlations of velocity and vorticity, associated with the spontaneous appearance and decay of these surging phalanxes, were measured using appropriately modified Particle Imaging Velocimetry (PIV). These new data, together with measurements of the trajectories of individual cells, provide ingredients for a rational bio-fluid-dynamical theory of the ZBN.   

Large scale flows and density fluctuation in ensembles of swimming bacteria

We study experimentally self-organization of concentrated ensembles of swimming bacteria Bacilus Subtilis. Experiments are performed in a very thin (of the order of 1 bacterium diameter) fluid film spanned between four supporting fibers. Small amplitude electric field is used to adjust dynamically the density of bacteria inside the experimental cell. Our experiments revealed only gradual increase of the large scale flow correlation length with the increase in number density of bacteria, and no sharp transition. The fluctuation of density of bacteria as a function of thickness of the film was explored.   

Chemotaxis and Target Finding using Chemical Echolocation

Chemotaxis is usually modeled by cellular responses to an imposed, exogenous chemoattractant gradient. Here, we consider a scenario in which a single agent releases a chemical that diffuses and is converted to, or signals the production of another chemical upon contact with a target. This secondary chemical can diffuse back to the agent, which uses it as a chemoattractant. We show that this mechanism has interesting features depending on how the probe chemical is produced, and how the product chemoattractant is sensed. Although involving more steps than conventional chemotaxis that relies on a single chemoattractant, we show that this chemical ``pinging'' mechanism can provide cells with flexibility in regulating behavior and finding different targets.   

Dynamics of Gas-Fluidized Bipolar Rods

We study a driven, non-equilibrium two-dimensional system consisting of bipolar rods in a gas-fluidized bed. The rods have an aspect ratio of 4 and occupy an area fraction of 42{\%}, chosen both to minimize the effects of ordering as well as to ensure a uniform density of particles across the system. We are able to track the position and orientation of the particles as a function of time. From this, we measure the dynamics of the system with the advantage that our temporal resolution allows us to observe ballistic motion at the shortest time scales. We calculate the mean squared displacement (MSD) in both the lab frame and the particle's frame in which displacements are measured as either perpendicular or parallel to the rod's long axis. In contrast to a comparable system of isotropic particles in which the dynamics are thermal, our system exhibits distinctly athermal behavior. Specifically, the effective temperature along the parallel direction is greater than that along the perpendicular direction. Furthermore, the parallel MSD remains superdiffusive at the longest time scales we are able to measure before the particles have reached the wall whereas the perpendicular component experiences cross-over to diffusive motion. This is emphasized by the power law decay of the velocity autocorrelation function (VAF). In comparison to a thermal fluid, the parallel VAF decays much more slowly whereas the perpendicular VAF decays more rapidly. With these characteristics in mind, ours is a simple experimental system that could be used to compare to biological models of active particles as well as to generalize the framework of statistical mechanics to non-equilibrium, athermal systems.   

Simulation of suspensions of hydrodynamically interacting self-propelled particles

Simulations of large populations of hydrodynamically interacting swimming particles are performed at low Reynolds number in periodic and confined geometries. Each swimmer is modeled as a rod containing beads with a propulsion force exerted on one bead (with an equal and opposite force exerted on the fluid) and excluded volume potentials at the beads. At small concentrations, the swimmers behave analogously to a dilute gas in which the hydrodynamic interactions perturb the ballistic trajectories into diffusive motion. Simple scaling arguments can explain the swimmer behavior as well as the behavior of passive tracer particles. As the concentration increases, the hydrodynamic interactions lead to large-scale collective motion.   

Hydrodynamics of self-propelled hard particles.

Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a physical model of the collective dynamics of self-propelled hard particles on a substrate in two dimensions. The particles have finite size, interact via excluded volume and are frictionally damped by the interaction with the substrate. Starting from a microscopic model of dynamics that includes non-thermal noise sources, we derive a continuum description of the system. The hydrodynamic equations are then used to characterize the possible steady states as a function of the particles' packing fraction and examine their stability. Research support by the NSF award number DMR-0305407.   

Traffic jams in driven intracellular transport on parallel lanes

Microtubules, the intracellular tracks for molecular motors like dynein or kinesin, are built of 12-14 parallel lanes. Although it has been revealed that the motor proteins typically remain on one track while proceeding on the microtubule, the statistics of deviations (random lane changes) is so far unknown. We investigate the effects of a small, but finite number of such lane changes by studying driven transport on two parallel lanes with simple site exclusion [1]. As a result, traffic jams emerge in the stationary density profiles, their location can be controlled by the particle fluxes at the boundaries. We obtain analytical results on the shape of the density profiles as well as resulting phase diagrams by a mean-field approximation and a continuum limit. \newline \newline [1] T. Reichenbach, T. Franosch, E. Frey, Phys. Rev. Lett. 97, 050603 (2006)   

DNA multi-ring formation via evaporation process

We present a study of multi-ring pattern formation of DNA aggregates during the solvent evaporation of a DNA droplet. When the contact line of a droplet is pinned at a solid substrate, a `coffee ring' pattern is often observed due to the outward flow during evaporation which carries the nonvolatile solute to the edge of the contact line. Here we report a remarkable observation of multiple rings of DNA stain, where stretched DNA molecules connect each ring. We use a high-speed confocal scanning microscope to investigate the kinetics of the multi-ring formation, when DNAs aggregate at the contact-line and cause a stick-slip receding process with periodic depinning of the contact line. A saw-tooth pattern in measured contact angle during droplet evaporation confirms the stick-slip receding dynamics, and a miscible viscous fingering pattern further confirms the stagnation flow responsible for the formation of consecutive rings. We also report a scaling behavior of the multi-ring wavelength with DNA concentration, droplet size and evaporation temperature, consistent with our proposed mechanism.