Non-Newtonian Viscosity ofEscherichia coliSuspensions

Abstract

The viscosity of an active suspension of E-Coli bacteria is determined experimentally in the dilute and semi dilute regime using a Y shaped micro-fluidic channel. From the position of the interface between the pure suspending fluid and the suspension, we identify rheo-thickening and rheo-thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the micro-channel.PACS numbers: 47.57.Qk,The fluid mechanics of microscopic swimmers in suspension have been widely studied in recent years. Bacteria [1, 2], algae [3,4] or artificial swimmers [5] dispersed in a fluid display properties that differ strongly from those of passive suspensions [6]. The physical relationships governing momentum and energy transfer as well as constitutive equations vary drastically for these suspensions [7,8]. Unique physical phenomena caused by the activity of swimmers were recently identified such as enhanced Brownian diffusivity [1,[8][9][10]] uncommon viscosity [4,12,13], active transport and mixing [11] or the extraction of work from isothermal fluctuations [13,16]. The presence of living and cooperative species may also induce collective motion and organization at the mesoscopic or macroscopic level [17,18] impacting the constitutive relationships in the semi-diluted or dense regimes. The E.Coli bacterium possesses a quite sophisticated propulsion apparatus consisting of a collection of flagella (7-10 µm length) organized in a bundle and rotating counter-clockwise [20]. In a fluid at rest, the wild-type strain used here has the ability to change direction by unwinding some flagella and moving them in order to alter its swimming direction (a tumble) approximately once every second [21]. In spite of the inherent complexity of the propulsion features, low Reynolds number hydrodynamics impose a long range flow field which can be modeled as an effective force dipole. Due to the thrust coming from the rear, E.coli are described as "pushers", hence defining a sign for the force dipole which has a crucial importance on the rheology of active suspensions [7]. For a dilute suspension of force dipoles, Haines et al [22] and Saintillan [24] derived an explicit relation relating viscosity and shear rate. They obtained an effective viscosity similar in form to the classical Einstein relation for dilute suspensions : η = η 0 (1 + Kφ) (η 0 being the suspending fluid viscosity and φ the volume fraction). These theories predict a negative value for the coefficient K for pushers at low shear rates, meaning the suspension can exhibit a lower viscosity than the suspending fluid. The theoretical assessment of shear viscosity relies on an assumed statistical representation of the orientations of the bacteria, captured by a Fokker-Plank equation and a kinematic model for the swimming trajectories [25,26].Despite the large number of theoretical studies, few experimen...

Hydrodynamic length-scale selection in microswimmer suspensions

“…Comparing Eq. (13) against experimental data yields good agreement with recent measurements in 3D bacterial [24,25] and algal [26] suspensions (Fig. 2).…”

“…The active stress tensor σ represents the forcing of the fluid by the swimmers [8,16,17]. For dense suspensions, the bulk viscosity μ contains contributions from the solvent as well as passive and active contributions from the microswimmers [23][24][25][26][27][28]. For simplicity, we assume that the passive contribution is approximately given by the Batchelor-Einstein relation for spherical colloids, μ = μ 0 (1 + k 1 φ + k 3 φ 2 ), where μ 0 is the "bare" solvent viscosity, φ is the volume fraction, and k i are positive constants [23,[29][30][31].…”

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

“…Although such low strain-rates cannot be practically realized with extensional rheometers currently, they are accessible in shear rheometers. This intriguing effect has been demonstrated by Gachelin et al 7 with E. coli in a microfluidic device. This effect is likely to be much more dramatic with sperm suspensions: the parameters we have obtained for sperm lead to a very large negative zero-Pe limit [η] 0 =χ (2 9 +β 15 (γ +σ − 1 β ) ) = −1.9 × 10 3 .…”

Destabilization of a flow focused suspension of magnetotactic bacteria

“…However, thinking along these lines would require defining for the effective active fluid physical properties such as viscosity or surface tensions. If some viscosities of active systems have been characterized [27][28][29][30], there has been, so far, no studies on the viscosity of suspensions of magnetotactic bacteria. As for the idea of generalizing the surface tension in active systems, it has only emerged very recently [31].…”