Viscosity of bacterial suspensions: Hydrodynamic interactions and self-induced noise

Abstract

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system.

Non-Newtonian Viscosity ofEscherichia coliSuspensions

“…This last result validates the use of the Newtonian approximations for the extraction of our viscosity measurements. In the semi-dilute regime (here for volume fractions greater than 1%), we observe a strong increase of the viscosity consistent with numerical simulations by Ryan et al [23]. Our results represent the first experimental validation of the non-Newtonian rheology of an active suspension of pushers under controlled shear conditions.…”

“…In our case this regime is observed for concentrations above approximately 1%. Similar behavior was also observed by Sokolov et al [12] using vortex decay in a suspension of Bacilus subtilis confined in a soap film and has been predicted by Ryan et al [23] in their simulations. So far we have measured the shear viscosity of the suspensions as a function of the maximum shear rate assuming a parabolic velocity profile.…”

Flexibility of bacterial flagella in external shear results in complex swimming trajectories

“…The flow produced in dense bacterial colonies in the course of swarming can be very complex because of the interaction between the bacteria and the fluid [3][4][5][6][7]. While the flow might visually resemble the turbulent motion emerging in rapidly stirred fluids, there is a fundamental difference: in hydrodynamic turbulence, the mechanical energy is injected at the macroscopic scale, e.g.…”

Geometry-dependent viscosity reduction in sheared active fluids

“…In particular, recent shear experiments suggest that Escherichia coli bacteria can create effectively inviscid flow if their concentration and activity are sufficiently large to support coherent collective swimming [18]. From a theory perspective, it is desirable to formulate a minimal hydrodynamic model that is analytically tractable and can account for all the aforementioned experimental observations without overfitting.Previous theoretical work [19][20][21][22][23][24] identified potential viscosity reduction mechanisms [15,18] in certain classes of active suspensions, but the complexity and specific nature of the underlying multi-field models have made analytical insight, time-resolved dynamical studies and comparison with experiment challenging. To better understand the general conditions under which active fluids can develop spontaneous symmetry-breaking and quasi-inviscid behavior, we pursue here an alternative approach by focusing on the generic phenomenological properties of non-Newtonian fluids that exhibit biologically, chemically or physically driven pattern formation.…”