Concentration Dependence of the Collective Dynamics of Swimming Bacteria

At concentrations near the maximum allowed by steric repulsion, swimming bacteria form a dynamical state exhibiting extended spatiotemporal coherence. The viscous fluid into which locomotive energy of individual microorganisms is transferred also carries interactions that drive the coherence. The concentration dependence of correlations in the collective state is probed here with a novel technique that herds bacteria into condensed populations of adjustable concentration. For the particular thin-film geometry employed, the correlation lengths vary smoothly and monotonically through the transition from individual to collective behavior.

Figure 1

Schematics of experimental setup. A thin film containing bacteria spans two adjustable Pt wires and two dielectric fibers and is stretched by a control screw. Electric current is transmitted between the Pt wires and a small Pt ring lowered onto the film. The cell is within a humidity controlled chamber.

Figure 2

(a) Image illustrating decrease of $p\mathrm{H}$ near the electrodes as a result of transmission of electric current. (b) Concentrated bacteria (darker part of the image). Square indicates field of view of microscope.

Figure 3

Bacteria patterns for low density $\rho =0.14$, no collective swimming (a); high density $\rho =0.47$, well-developed chaotic large-scale flows (b). Vector fields for velocity $\mathbf{V}$ (c) and orientation $\mathit{\tau }$ (d) for the configuration shown in image (b). See also movies 2 and 3 in 15.

Figure 4

Alignment coefficient $C$ [see Eq. (1)] vs threshold $k$ for different values of density $\rho$.

Figure 5

Typical velocity $\overline{V}$ (diamonds) and velocity correlation length $L$ (circles) as the function of bacterial number density $\rho$. Dashed line shows fit of $\overline{V}$ to solution to Eq. (2) with ${\rho }_c\approx 0.28$. Inset: typical dependence of density $\rho$ vs time in the course of experiment.