Self-Concentration and Large-Scale Coherence in Bacterial Dynamics

Suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy. We find in sessile drops that flows related to those in the Boycott effect of sedimentation carry bioconvective plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions in both geometries exhibit transient, reconstituting, high-speed jets straddled by vortex streets. A mechanism for large-scale coherence is proposed based on hydrodynamic interactions between swimming cells.

Figure 1

Bioconvection in a sessile drop of diameter $1\mathrm{c}\mathrm{m}$. Top: images $5\mathrm{m}\mathrm{i}\mathrm{n}$ apart show the traveling-wave bio-Boycott convection that appears first at the drop edge. Bottom: images $2\min $ apart show self-concentration seen from above, beginning as vertical plumes which migrate outward.

Figure 2

Dark-field side views of self-concentrative flows between two coverslips spaced $1\mathrm{m}\mathrm{m}$ apart: (a) uniform initial concentration; (b),(c) development of depletion layer as cells swim upward; (d)–(f) plumes carried to nose of drop, dragged by surface layer. Depletion and accumulation layer thicknesses $l$ and $d$ are shown. The scale bar is $1\mathrm{m}\mathrm{m}$.

Figure 3

Bacterial “turbulence” in a sessile drop, viewed from below through the bottom of a petri dish. Gravity is perpendicular to the plane of the picture, and the horizontal white line near the top is the air-water-plastic contact line. The central fuzziness is due to collective motion, not quite captured at the frame rate of $1/30\mathrm{s}$. The scale bar is $35\mu \mathrm{m}$.

Figure 4

Flows at the bottom of a pendant drop. Instantaneous bacterial swimming vector field. The arrow at right denotes a speed of $35\mu \mathrm{m}/\mathrm{s}$.

Figure 5

Correlation functions in a pendant drop: (a) average spatial correlation $I(r)$ (solid) along with several traces at particular times; (b) Average temporal correlation $J(t)$ (solid) with two particular traces.