Spontaneous oscillations and geometric cutoff in confined bacterial swarms

Abstract

Self-organized dynamic patterns in dense active matter are striking manifestations of non-equilibrium physics. A prominent example is the macroscopic elliptical motion observed in quasi-2D bacterial suspensions, which has lacked a physical explanation. Here, we examine a minimal linear response framework coupling bacterial swimming dynamics with fluid flow, treating long-range hydrodynamic interactions as a macroscopic communication channel. We demonstrate that microscopic swim motion, via Jeffery coupling, manifests as a ``phase-leading'' response to local shear flows. System-wide sustained oscillations, on the other hand, require both a critical bacterial density and strict geometric confinement. By analytically predicting the onset cell density and maximum film thickness, our model achieves excellent quantitative agreement with experiments, establishing a unified physical framework for self-organized periodic motion of elongated body in active fluids.

Figures (3)

• Figure 1: (a) An active film composed of run-and-tumble bacteria in a thin liquid layer atop an agar plate. Uniform circular motion parallel to the plate was observed, as reported in Ref. Wu17. (b) Proposed laminar flow profile that serves as a communication channel for alignment among swimmers.
• Figure 2: Conditions for active response. (a) Frequency-resolved nematic tilt response function $\chi=\chi'+i\chi"$ to sinusoidal laminar shear flow at two different values of the Péclet number ${\rm Pe}_{\rm s}$. Here $\Lambda_{\rm T}=1$, and $\omega$ in units of $D_R$. At ${\rm Pe}_{\rm s}=10$, $\chi"(\omega)<0$ for $0<\omega<\omega_0$, i.e., the cell population develops phase-leading response in this frequency range. (b) Regions of passive and active response in the ${\rm Pe_s}$-$\Lambda_{\rm T}$ plane, separated by the orange line where the slope of $\chi"(\omega)$ vanishes at $\omega=0$. Contour lines of $2\pi/\omega_0=\tau, 2\tau,\ldots$ are shown inside the active phase, with $\tau=1/D_R$.
• Figure 3: (a) Onset cell density and (b) oscillation frequency predicted by the model, using rheological parameters in Ref. Wu17. Red dashed lines indicate corresponding values measured in the experiment. Spontaneous oscillations disappear when the film exceeds a maximal thickness around 10 $\mu$m.