Turning Bacteria Suspensions into Superfluids

The rheological response under simple shear of an active suspension of Escherichia coli is determined in a large range of shear rates and concentrations. The effective viscosity and the time scales characterizing the bacterial organization under shear are obtained. In the dilute regime, we bring evidence for a low-shear Newtonian plateau characterized by a shear viscosity decreasing with concentration. In the semidilute regime, for particularly active bacteria, the suspension displays a “superfluidlike” transition where the viscous resistance to shear vanishes, thus showing that, macroscopically, the activity of pusher swimmers organized by shear is able to fully overcome the dissipative effects due to viscous loss.

Figure 1

Shear stress response for an E. coli suspension (ATCC9637 strain, $T=25°\mathrm{C}$). (a) Shear stress $\mathrm{\Sigma }$ rescaled by the applied shear rate $\dot{\gamma }$ during the rotation to display an effective viscosity $\mathrm{\Sigma }/\dot{\gamma }$ in the sheared regime. Gray and black lines: Fluid without bacteria ($\varphi =0$). Colored solid lines: Fluid with bacteria ($\varphi =0.67\%$). Various $\dot{\gamma }$ are applied ranging from 64 (dark blue line) down to $0.022{\mathrm{s}}^{-1}$ (dark red line). (b) Relative viscosity $\eta /{\eta }_0$ averaged over three realizations as a function of $\dot{\gamma }$ (empty square, $\varphi =0.11\%$; empty circle, $\varphi =0.21\%$; empty triangle, $\varphi =0.44\%$; empty diamond, $\varphi =0.67\%$). The solid line is an adjustment by the Carreau law: $\eta /{\eta }_0=1.08-0.795/[1+(\dot{\gamma }/0.6{)}^2]$. The vertical dashed line shows ${\dot{\gamma }}_c$; below this shear rate $\eta (\dot{\gamma })/{\eta }_0$ is less than 1. (c) Values of the plateau viscosity ${\eta }_p/{\eta }_0$ as functions of the bacteria volume fraction $\varphi$ for very low shear rates (empty circle, $\dot{\gamma }=0.022{\mathrm{s}}^{-1}$; empty square, $\dot{\gamma }=0.04{\mathrm{s}}^{-1}$; empty triangle, $\dot{\gamma }=0.075{\mathrm{s}}^{-1}$).

Figure 2

(a) Shear stress response $\mathrm{\Sigma }$ rescaled by the shear rate $\dot{\gamma }$ for the ATCC9637 strain (blue lines) and RP437 strain (red lines). All experiments are performed with $\dot{\gamma }=0.04{\mathrm{s}}^{-1}$. In some cases, the stress response can reach negative values. (b) Variation of the viscosity ${\eta }_p/{\eta }_0$ as a function of the volume fraction of bacteria $\varphi$ in oxygenated conditions (filled symbols) and deoxygenated conditions (empty symbols). Dashed lines are meant as guides only. (c) Relaxation time ${\tau }_r$ obtained by adjusting exponentially the stress relaxation at the start of the shear (rotation) and at the end of the shear (relaxation) as a function of the mean distance ($\xi ={\varphi }^{-(1/3)}$) between bacteria (empty symbols, deoxygenated conditions; filled symbols, oxygenated conditions; blue symbols, ATCC9637 strain; red symbols, RP437 strain).