Active fluids
"Living matter, while not eluding the 'laws of physics' as established up to date, is likely to involve 'other laws of physics' hitherto unknown, which, however, once they have been revealed, will form just as integral a part of science as the former."
-- Erwin Schrodinger, What is life? (1944)
Few things seem to capture our imagination more reliably than the collective motion of flocking birds, schooling fish or swarming insects. The coordinated maneuvers undertaken by a group of animals with as many as thousands of individual members are so striking that one may even have the illusion that the group has a mind of its own. How do self-driven individuals self-organize into a collective motion with a correlation length orders of magnitude larger than the size of single units? The answer to the question is of fundamental interest far beyond the field of animal ethology. Studies in soft matter physics over the past decade have shown that the collective motion of animal flocks indeed represents a universal feature of a novel class of non-equilibrium systems, known as active matter, which includes biological and physical systems of widely different length scales ranging from vibrated granular rods to mobile colloids and to self-propelled cytoskeleton. Understanding the organizing principles of active matter will provide insights into diverse phenomena such as the formation of biofilms, the self-assembly of active colloids and the behaviors of human crowds in panicked conditions and will likely lead to the next breakthrough in non-equilibrium statistical mechanics.
(1) Diffusion of ellipsoids in bacterial suspensions
Active fluids such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. As a hallmark example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in quasi-two-dimensional bacterial bath. Our study reveals a nonlinear enhancement of both translational and rotational diffusions. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropy in particle diffusions, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our study illustrates an unexpected universal feature of active fluids and transforms the basic understanding of transport processes in microbiological systems.
- Y. Peng, L. Lai, Y.-S. Tai, K. Zhang, X. Xu, and X. Cheng, “Diffusion of ellipsoids in bacterial suspensions”, Phys. Rev. Lett. 116, 068303 (2016). (Selected as “Editors’ Suggestion”)
- O. Yang, Y. Peng, Z. Liu, C. Tang, X. Xu, and X. Cheng, “Dynamics of ellipsoidal tracers in swimming algal suspensions”, Phys. Rev. E 94, 042601 (2016).
(2) Bacterial turbulence
One of the most fascinating features of living systems is the emergence of nonequilibrium collective dynamics at large length and time scales from interactions among microscopic constituents. From the assembly of mitotic spindles during cell division, to multicellular gene-expression patterns in developing embryos, to the coordinated motion of schooling fish and flocking birds, such emergent phenomena arise across multiple levels of biological organization and play essential roles in life processes.
As a premier model of active fluids, dense bacterial suspensions exhibit collective motion in which individual swimmers generate chaotic flows composed of transient vortices and jets, reminiscent of classical turbulence at high Reynolds numbers. This phenomenon—often termed active or bacterial turbulence—is particularly striking given that the Reynolds number of an individual bacterium is on the order of 10⁻⁵. How do individual cells self-organize into coherent flows with correlation lengths far exceeding their own size? Addressing this question lies at the heart of active matter research and is key to understanding emergent dynamics in nonequilibrium systems. From a materials science perspective, bacterial turbulence also exhibits unusual transport properties that may be harnessed for novel engineering applications.
Representative works include our studies of the flow behavior of bacterial turbulence, which reveal the emergence of nonuniform shear profiles that give rise to “bacterial superfluidity.” We have also constructed a phase diagram for three-dimensional E. coli suspensions, spanning bacterial concentration, swimming speed, and the fraction of active swimmers, and identified kinetic pathways leading to turbulent states. In addition, we have characterized anomalous density fluctuations in bulk E. coli suspensions, demonstrating the existence of giant number fluctuations and quantifying their scaling behavior.
S. Guo, D. Samanta, Y. Peng, X. Xu, and X. Cheng, “Symmetric shear banding and swarming vortices in bacterial superfluids”, Proc. Natl. Acad. Sci. USA 115, 7212-7217 (2018).
Y. Peng, Z. Liu, and X. Cheng, “Imaging the emergence of bacterial turbulence: phase diagram and transition kinetics”, Sci. Adv. 7, eabd1240 (2021).
Z. Liu, W. Zeng, X. Ma, and X. Cheng, “Density Fluctuations and Energy Spectra of 3D Bacterial Suspensions”, Soft Matter 17, 10806-10817 (2021). (Featured on the front cover)
Colloidal suspensions
Colloidal suspensions are heterogeneous systems of two separate phases, in which small solid particles or droplets of liquid are dispersed in a liquid medium. The length scale of the dispersed particles is usually between 10 nanometers and 10 micrometers. Familiar examples of colloidal suspensions include blood, paints, inks and milk. Research on colloidal suspensions is very broad. We are particularly interested in rheological properties of suspensions and try to understand these properties based on their microstructural dynamics.
Flow of colloidal suspensions shows various uncommon non-Newtonian behaviors. The viscosity of suspensions can vary by orders of magnitude depending on how quickly they are sheared. Such non-Newtonian flow behaviors show striking effects and are critical for many natural and industrial processes. One example is the shear thinning of commercial paints: paints become much easier to flow when stirred. Another interesting example is the shear thickening of cornstarch-water mixtures. Under shaking or when squeezed, a cornstarch-water mixture turns into a doughy paste which can form different shapes or even support large weights. The following video illustrates the effect vividly.
(1) Glassy dynamics of colloidal suspensions under confinement
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlation. Moreover, by investigating the dynamics of spherically confined samples, we reveal a profound influence of the static correlation on the relaxation of colloidal liquids. In analogy to glass-forming liquids with randomly pinned particles, we propose a simple relation for the change of the configurational entropy of confined colloidal liquids, which quantitatively explains our experimental findings and illustrates a divergent static length scale during the colloidal glass transition.
- B. Zhang and X. Cheng, “Structures and dynamics of glass-forming colloidal liquids under spherical confinement”, Phys. Rev. Lett. 116, 098302 (2016). (Selected as “Editors’ Suggestion” with Synopsis)