Three-dimensional model for the effective viscosity of bacterial suspensions

Abstract

We derive the effective viscosity of dilute suspensions of swimming bacteria from the microscopic details of the interaction of an elongated body with the background flow. An individual bacterium propels itself forward by rotating its flagella and reorients itself randomly by tumbling. Due to the bacterium's asymmetric shape, interactions with a prescribed generic (such as planar shear or straining) background flow cause the bacteria to preferentially align in directions in which self-propulsion produces a significant reduction in the effective viscosity, in agreement with recent experiments on suspensions of Bacillus subtilis.

Motility induced changes in viscosity of suspensions of swimming microbes in extensional flows

“…Recent studies by Haines et al 9 and Saintillan 10 have modeled the statistics of an axisymmetric self-propelled particle that stochastically changes its swimming direction while moving in an externally imposed homogeneous extensional flow, and then obtained an expression relating [η] to motility characteristics and strain-rate. We summarize here Saintillan's analysis for a slender rod to explain the physical significance of the key parameters in the expression for [η] in an active suspension.…”

“…8 The observations appear to clearly confirm a key generic feature of the rheology of active suspensions. Quantitative microstructural models relating particle size, shape, concentration and motility to rheological properties are just beginning to emerge, [9][10][11][12] but thus far there have been no systematic comparison of their predictions against experimental data. We present here such a comparison for suspensions of wild-type strains of the microalga Dunaliella tertiolecta, the bacterium Escherichia coli and mouse spermatozoa.…”

Sheared active fluids: Thickening, thinning, and vanishing viscosity

“…[11] as the appearance of bulk shear bands accommodating a range of macroscopic shear-rates at zero stress. Finally, the predicted activity-induced thinning of bacterial suspensions has been demonstrated in recent experiments in Bacillus subtilis [12][13][14].…”

“…This directed motion occurring in polar suspensions contributes to a nonequilibrium local stress of the form σ β ij ∼ β (∂ i p j + ∂ j p i ). Most theoretical work has focused on the rheology of active nematic (β = 0), while the shear response of active polar suspensions is far less explored [12,14]. We find that for a fixed value of β, the behavior of active suspensions depends on the interplay between the local contractile/tensile stresses, embodied in the parameter α, and the flow-aligning behavior of liquid crystalline particles, described by the flow alignment parameter, λ [?…”

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.…”