By increasing the sensitivity of an established technique, researchers have shown that swimming bacteria can make frictionless fluids — with potential applications in areas such as microfluidics.
The viscosity of a liquid is a measure of its resistance to flow. In general, denser fluids are more viscous and require more energy to get them to flow through a pipe. Flow with no energy dissipation is a hallmark of exotic states of matter such as superfluidity and superconductivity. Key to these exotic states are quantum effects that dominate at ultralow temperatures — turning liquid helium, for example, into a superfluid that flows without friction through cracks as thin as molecules. Writing in Physical Review Letters, López et al.1 demonstrate that Escherichia coli bacteria swimming in a fluid can organize themselves to counterbalance the energy loss resulting from viscous dissipation and thereby dramatically lower the fluid's viscosity, driving it to vanish or even to become negative.
In 2004, it was predicted2 that unicellular swimming organisms could substantially change the viscosity of a fluid on the basis of a hydrodynamic theory3 of active fluids (liquids consisting of self-propelled particles). This suggestion was confirmed by numerical solutions4,5 of the theory, which revealed the possibility of vanishing viscosity for suspensions of motile bacteria. Pioneering experiments subsequently confirmed a reduction of viscosity in suspensions of the bacteria Bacillus subtilis6 and E. coli7. A concurrent study8 demonstrated the sensitivity of this effect to the microscopic cellular-propulsion mechanism by revealing an increase in viscosity for dilute concentrations of the alga Chlamydomonas reinhardtii; however, this behaviour remains puzzling.
Detailed calculations9,10,11,12 of the response of dilute suspensions of swimmers to an externally imposed shear flow (which induces the velocity profile shown in Fig. 1a) have provided quantitative expressions for viscosity changes for small volume fractions of bacteria. Demonstrating that a bacterial suspension can achieve a state of vanishing, or even negative, viscosity was previously impossible, however, because this requires measurements of tiny shear stresses.
López and colleagues overcame this problem by adapting an old-fashioned rheometer — a device used to measure fluid viscosity. A simple rheometer consists of inner and outer cylinders that can rotate relative to each other. A fluid is placed in the annulus between the cylinders and one of the cylinders is rotated at a set rate, shearing the fluid. The liquid drags the other cylinder, exerting a torque on it. From measurements of this torque, one can infer the shear stress and thus the fluid viscosity, defined as the ratio of stress to the applied shear rate.
The authors modified this device by controlling the rotation of the inner cylinder using a computerized feedback mechanism. This set-up maintains zero torque, allowing highly sensitive measurements of ultralow shear stresses. The researchers also suspended bacteria in a medium that allows the microbes to remain motile but not to divide, enabling control of the bacterial concentration.
Importantly, López et al. were able to demonstrate the existence of states of arbitrarily small viscosity, in a regime in which the viscosity did not depend on the imposed shear rate and was therefore a legitimate material property. The development of a macroscopic device capable of sensing the rheological response of microorganisms is a remarkable experimental achievement. It paves the way for the quantitative characterization of the flow behaviour of a wide range of microorganisms, and for understanding the role of different propulsion mechanisms.
Suspending non-motile particles in a fluid always increases the fluid's viscosity. Albert Einstein provided the first quantitative formulation of this intuitive effect in 1906 by showing that, in a dilute suspension of spheres, the increase in viscosity is linearly proportional to the volume fraction of suspended particles13. So how do swimming bacteria achieve the opposite effect and thin out the suspension, turning it into a frictionless liquid akin to a superfluid?
The answer relies on two key properties of flowing suspensions. First, inactive rod-like particles in an externally imposed shear flow align their long axes along the direction in which the flow 'stretches' the fluid. The rods tilt at a fixed angle that depends on their ratio of length to width; this angle can be close to 45° for long, slender rods (Fig. 1a). Many unicellular organisms, including E. coli, have such a rod-like shape and therefore orient in this way in shear flow.
Second, swimming bacteria exert forces on the surrounding fluids. These forces come in equal and opposite pairs: the force from the beating of their propulsive appendages (flagella or cilia) is balanced by the viscous drag on the cell's body. The spatial profile of these forces depends on the propulsion mechanism. Most bacteria use appendages mounted at the back of their bodies, and are known as pushers. When they move, they push fluid out at their front and back, while sucking it in at the sides.
Elongated pushers thus align their bodies along the stretching axis of the external flow and generate additional flows that further stretch the fluid in the same direction (Fig. 1b). At high enough concentrations, continuum theories suggest that the bacteria act collectively to push the fluid along, effectively thinning it. A microscopic understanding of how bacteria coordinate their response to shear to achieve a state of frictionless flow is still lacking. However, López and co-workers' experiments demonstrate that the viscosity of a suspension of swimming bacteria can indeed decrease with an increasing volume fraction of swimmers, within a range of bacterial concentrations.
By showing that bacteria can completely compensate for fluid friction by allowing the fluid to flow with zero dissipation, the authors have demonstrated that it is possible, in principle, to extract useful macroscopic mechanical power from bacterial activity. This observation is in line with earlier findings14 that bacteria can work together to turn microgears. Although harnessing bacterial power for macroscopic energy generation may still be a dream, it is not such a stretch to imagine that bacteria could be used as mixers to thin and stir the flow in capillary and microfluidic devices. Quantitative characterizations of rheology of the type pioneered by López et al. pave the way to the development of bacterial baths tailored to mix and flow liquids for specific applications.Footnote 1
López, H. M., Gachelin, J., Douarche, C., Auradou, H. & Clément, E. Phys. Rev. Lett. 115, 028301 (2015).
Hatwalne, Y., Ramaswamy, S., Rao, M. & Simha, R. A. Phys. Rev. Lett. 92, 118101 (2004).
Simha, R. A. & Ramaswamy, S. Phys. Rev. Lett. 89, 058101 (2002).
Cates, M. E., Fielding, S. M., Marenduzzo, D., Orlandini, E. & Yeomans, J. Phys. Rev. Lett. 101, 068102 (2008).
Giomi, L., Liverpool, T. B. & Marchetti, M. C. Phys. Rev. E 81, 051908 (2010).
Sokolov, A. & Aranson, I. S. Phys. Rev. Lett. 103, 148101 (2009).
Gachelin, J. et al. Phys. Rev. Lett. 110, 268103 (2013).
Rafaï, S., Jibuti, L. & Peyla, P. Phys. Rev. Lett. 104, 098102 (2010).
Liverpool, T. B. & Marchetti, M. C. Phys. Rev. Lett. 97, 268101 (2006).
Haines, B. M., Sokolov, A., Aranson, I. S., Beryland, L. & Karpeev, D. A. Phys. Rev. E 80, 041922 (2009).
Saintillan, D. Exp. Mech. 50, 1275–1281 (2010).
Ryan, S. D., Haines, B. M., Berlyand, L., Ziebert, F. & Aranson, I. S. Phys. Rev. E 83, 050904(R) (2011).
Einstein, A. Ann. Phys. 19, 289–306 (1906).
Sokolov, A., Apodaca, M. M., Grzybowski, B. A. & Aranson, I. S. Proc. Natl Acad. Sci. USA 107, 969–974 (2009).
Related links in Nature Research
About this article
Radiation Effects and Defects in Solids (2020)
Physical Review E (2020)
Rheologica Acta (2019)
Physica A: Statistical Mechanics and its Applications (2019)