Rheology of bacterial superfluids in viscous environments.

Viscous environments are ubiquitous in nature and in engineering applications, from mucus in lungs to oil recovery strategies in the earth's subsurface - and in all these environments, bacteria also thrive. The behavior of bacteria in viscous environments has been investigated for a single bacterium, but not for active suspensions. Dense populations of pusher-type bacteria are known to create superfluidic regimes where the effective viscosity of the entire suspension is reduced through collective motion, and the main purpose of this study is to investigate how a viscous environment will affect this behavior. Using a Couette rheometer, we measure shear stress as a function of the applied shear rate to define the effective viscosity of suspensions of Escherichia coli (E. coli), while varying both the bacterial density within the suspension and the viscosity of the suspending fluid. We document the remarkable observation that E. coli decreases the effective suspension viscosity to near-zero (superfluidic regime) for all solvent viscosities tested (1-17 mPa s). Specifically, we observe that the bacterial density needed to trigger this superfluidic regime and the maximum shear rate under which this regime can be sustained both decrease with increasing solvent viscosity. We find that the resulting rheograms can be well approximated by the Carreau-Yasuda law. Using this, we propose a constitutive model as a function of the solvent viscosity and the bacterial concentration only. This model captures the onset of the superfluidic regime and offers promising avenues for the modelling of flow of bacterial suspensions in viscous environments.

Interface evolution during radial miscible viscous fingering.

We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t(1/2), as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability.