Bacterial turbulence at compressible fluid interfaces

Abstract

Dense bacterial suspensions at fluid interfaces provide a natural platform to explore active turbulence in a dimensional mismatch: active units are restricted to a two-dimensional surface, while the induced flows extend into the surrounding three-dimensional liquid. Using hydrophobic Serratia marcescens at the air-water interface, we realize interfacial bacterial turbulence as a distinct class of active turbulence. The system exhibits compressible in-plane flows, with vortex size initially increasing with the thickness of the underlying fluid and saturating near 100 $μ$ m, independent of bacterial length. This behavior contrasts sharply with bulk active turbulence, where correlation length typically scales with system size. Hydrodynamic theory, together with direct measurements of the three-dimensional flow field, shows that the coupling between interfacial and bulk flows sets the emergent length scale. Our results uncover the fundamental physics of interfacial bacterial turbulence and open new strategies for geometric control of collective active flows.

Figures (3)

• Figure 1: Experimental setup, particle tracking, and vortices at the air-water interface. (a) A monolayer of hydrophobic Serratia marcescens bacteria swims in 2D at an air-water interface. The interface is pinned and kept flat at the open end of an air-filled tube, that is partially immersed in water. H denotes the fluid thickness above the solid substrate and $L$ represents the total bacterial length, including the flagella. (b) Schematic illustrating a bacterium trapped at the interface. The arrows indicate the direction of flow fields generated both at the interface and in the underlying liquid. (c) 3D particle-tracking experiments show passive particles being advected into the interfacial layer. The red circle indicates the range of Brownian diffusion over the same time interval. (d) Instantaneous flow fields, represented by vorticity color maps superimposed with streamlines, illustrate the smallest vortices (mean radius $R=3.8~\mu$m), and (e) the largest vortices ($R=53.3~\mu$m) observed under the conditions $L=8~\mu$m, H$=1~\mu$m and $L=23~\mu$m, H$=800~\mu$m.
• Figure 2: Fluid thickness controlling vortex size. (a) The correlation length $R$ as a function of fluid thickness H for bacteria of varying lengths $L$. Each data point represents measurements from at least three independent bacterial batches, with error bars indicating standard deviations. Solid blue triangles denote the vortex size of wild-type bacteria ($L=10~\mu$m), calculated using the Okubo–Weiss method. (b) Normalized correlation length $R/L$ for interfacial S. marcescens suspensions (open symbols) and three-dimensional confined E. coli suspensions (filled stars) as a function of H. The dashed line indicates an exponential fit, $R/L=2.1-1.6e^{-\text{H}/20}$, and serves as a guide to the eye.
• Figure 3: Growth rate, correlation lengths, viscous couplings. (a) Growth rate as a function of wavevector for the interfacial 2D system (I2D) ($Q\neq 0$) and the purely two-dimensional system (P2D) ($Q=0$). Inset: Schematic of the flow flux generated by a bacterium at a fluid interface. (b) Contour plot illustrating the variation of $\mathscr{A}$ with respect to fluid thickness H (y-axis) and wavevector $k$ (x-axis), with the color bar indicating $\mathscr{A}$ values. Dashed black lines represent the onset of instability, $\mathscr{A}=\lambda$, with contour levels at 0.5, 1.0, and 1.5 $s^{-1}$. (c) Normalized vortex size from experiments plotted against the instability length predicted by mean-field kinetic theory at a tumbling rate of $\lambda=0.5~s^{-1}$. (d) Ratio of parallel to total flow velocity as a function of fluid thickness. The curve shows the same dependence on H as $R$. The dashed line represents the same exponential function as in Fig. \ref{['fig2']}, scaled by a factor of $(2.1 - 1.6 e^{-\text{H}/20})/0.38$.