Density fluctuations and energy spectra of 3D bacterial suspensions

Measuring collective diffusion coefficients by counting particles in boxes

The collective diffusion coefficient Dcoll is a key quantity for describing the macroscopic transport properties of soft matter systems. However, measuring Dcoll is a fundamental experimental and numerical challenge, as it either relies on nonequilibrium techniques that are hard to interpret or, at equilibrium, on Fourier-based approaches which are fraught with difficulties associated with Fourier transforms. In this work, we investigate the equilibrium diffusive dynamics of a 2D colloidal suspension experimentally and numerically. We use a "Countoscope" technique, which analyses the statistics of particle number counts N(t) in virtual observation boxes of a series of microscopy images at equilibrium, to measure Dcoll for the first time. We validate our results against Fourier-based approaches and establish best practices for measuring Dcoll using fluctuating counts. We show that Fourier techniques yield inaccurate long-range collective measurements because of the non-periodic nature of an experimental image, yet counting exploits this property by using finite observation windows. Finally, we discuss the potential of our method to advance our understanding of collective properties in suspensions, particularly the role of hydrodynamic interactions.

Swarm Autonomy: From Agent Functionalization to Machine Intelligence

Swarm behaviors are common in nature, where individual organisms collaborate via perception, communication, and adaptation. Emulating these dynamics, large groups of active agents can self-organize through localized interactions, giving rise to complex swarm behaviors, which exhibit potential for applications across various domains. This review presents a comprehensive summary and perspective of synthetic swarms, to bridge the gap between the microscale individual agents and potential applications of synthetic swarms. It is begun by examining active agents, the fundamental units of synthetic swarms, to understand the origins of their motility and functionality in the presence of external stimuli. Then inter-agent communications and agent-environment communications that contribute to the swarm generation are summarized. Furthermore, the swarm behaviors reported to date and the emergence of machine intelligence within these behaviors are reviewed. Eventually, the applications enabled by distinct synthetic swarms are summarized. By discussing the emergent machine intelligence in swarm behaviors, insights are offered into the design and deployment of autonomous synthetic swarms for real-world applications.

Transport and energetics of bacterial rectification

Randomly moving active particles can be herded into directed motion by asymmetric geometric structures. Although such a rectification process has been extensively studied due to its fundamental, biological, and technological relevance, a comprehensive understanding of active matter rectification based on single particle dynamics remains elusive. Here, by combining experiments, simulations, and theory, we study the directed transport and energetics of swimming bacteria navigating through funnel-shaped obstacles-a paradigmatic model of rectification of living active matter. We develop a microscopic parameter-free model for bacterial rectification, which quantitatively explains experimental and numerical observations and predicts the optimal geometry for the maximum rectification efficiency. Furthermore, we quantify the degree of time irreversibility and measure the extractable work associated with bacterial rectification. Our study provides quantitative solutions to long-standing questions on bacterial rectification and establishes a generic relationship between time irreversibility, particle fluxes, and extractable work, shedding light on the energetics of nonequilibrium rectification processes in living systems.

Scaling Transition of Active Turbulence from Two to Three Dimensions

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model we develop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organized systems.

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Active Darcy's Law

While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.

Multiflagellarity leads to the size-independent swimming speed of peritrichous bacteria

To swim through a viscous fluid, a flagellated bacterium must overcome the fluid drag on its body by rotating a flagellum or a bundle of multiple flagella. Because the drag increases with the size of bacteria, it is expected theoretically that the swimming speed of a bacterium inversely correlates with its body length. Nevertheless, despite extensive research, the fundamental size-speed relation of flagellated bacteria remains unclear with different experiments reporting conflicting results. Here, by critically reviewing the existing evidence and synergizing our own experiments of large sample sizes, hydrodynamic modeling, and simulations, we demonstrate that the average swimming speed of Escherichia coli, a premier model of peritrichous bacteria, is independent of their body length. Our quantitative analysis shows that such a counterintuitive relation is the consequence of the collective flagellar dynamics dictated by the linear correlation between the body length and the number of flagella of bacteria. Notably, our study reveals how bacteria utilize the increasing number of flagella to regulate the flagellar motor load. The collective load sharing among multiple flagella results in a lower load on each flagellar motor and therefore faster flagellar rotation, which compensates for the higher fluid drag on the longer bodies of bacteria. Without this balancing mechanism, the swimming speed of monotrichous bacteria generically decreases with increasing body length, a feature limiting the size variation of the bacteria. Altogether, our study resolves a long-standing controversy over the size-speed relation of flagellated bacteria and provides insights into the functional benefit of multiflagellarity in bacteria.

Active nematic liquid crystals simulated by particle-based mesoscopic methods

Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.

Giant vortex dynamics in confined bacterial turbulence

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

Response of vesicle shapes to dense inner active matter

We consider experimentally the Takatori-Sahu model of vesicle shape fluctuations induced by enclosed active matter, a model till present tested only in the absence of collective motion because few enclosed bacteria were used to generate the desired active motion (S. C. Takatori and A. Sahu, Phys. Rev. Lett., 2020, 124, 158102). Using deformable giant unilamellar vesicles (GUVs) and phase contrast microscopy, we extract the mode-dependence of GUV shape fluctuations when hundreds of E. coli bacteria are contained within each GUV. In the microscope focal plane, patterns of collective bacteria flow include vortex flow, dipolar flow, and chaotic motion, all of which influence the GUV shapes. The Takatori-Sahu model generalizes well to this situation if one considers the moving element to be the experimentally-determined size of the collecively-moving flock.

Mesoscopic simulations of active nematics

Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a substantial role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarse-grained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multiparticle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active nematic MPCD (AN-MPCD) simulations not only exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing simulations of composite active-passive systems.

Crack patterns of drying dense bacterial suspensions

Drying of bacterial suspensions is frequently encountered in a plethora of natural and engineering processes. However, the evaporation-driven mechanical instabilities of dense consolidating bacterial suspensions have not been explored heretofore. Here, we report the formation of two different crack patterns of drying suspensions of Escherichia coli (E. coli) with distinct motile behaviors. Circular cracks are observed for wild-type E. coli with active swimming, whereas spiral-like cracks form for immotile bacteria. Using the elastic fracture mechanics and the poroelastic theory, we show that the formation of the circular cracks is determined by the tensile nature of the radial drying stress once the cracks are initiated by the local order structure of bacteria due to their collective swimming. Our study demonstrates the link between the microscopic swimming behaviors of individual bacteria and the mechanical instabilities and macroscopic pattern formation of drying bacterial films. The results shed light on the dynamics of active matter in a drying process and provide useful information for understanding various biological processes associated with drying bacterial suspensions.

The colloidal nature of complex fluids enhances bacterial motility

The natural habitats of microorganisms in the human microbiome, ocean and soil ecosystems are full of colloids and macromolecules. Such environments exhibit non-Newtonian flow properties, drastically affecting the locomotion of microorganisms^1-5. Although the low-Reynolds-number hydrodynamics of swimming flagellated bacteria in simple Newtonian fluids has been well developed^6-9, our understanding of bacterial motility in complex non-Newtonian fluids is less mature^10,11. Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in polymer solutions are still under debate^12-23. Here we show that flagellated bacteria in dilute colloidal suspensions display quantitatively similar motile behaviours to those in dilute polymer solutions, in particular a universal particle-size-dependent motility enhancement up to 80% accompanied by a strong suppression of bacterial wobbling^18,24. By virtue of the hard-sphere nature of colloids, whose size and volume fraction we vary across experiments, our results shed light on the long-standing controversy over bacterial motility enhancement in complex fluids and suggest that polymer dynamics may not be essential for capturing the phenomenon^12-23. A physical model that incorporates the colloidal nature of complex fluids quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Our findings contribute to the understanding of motile behaviours of bacteria in complex fluids, which are relevant for a wide range of microbiological processes²⁵ and for engineering bacterial swimming in complex environments^26,27.

Microscopic Swarms: From Active Matter Physics to Biomedical and Environmental Applications

Microscopic swarms consisting of, e.g., active colloidal particles or microorganisms, display emergent behaviors not seen in equilibrium systems. They represent an emerging field of research that generates both fundamental scientific interest and practical technological value. This review seeks to unite the perspective of fundamental active matter physics and the perspective of practical applications of microscopic swarms. We first summarize experimental and theoretical results related to a few key aspects unique to active matter systems: the existence of long-range order, the prediction and observation of giant number fluctuations and motility-induced phase separation, and the exploration of the relations between information and order in the self-organizing patterns. Then we discuss microscopic swarms, particularly microrobotic swarms, from the perspective of applications. We introduce common methods to control and manipulate microrobotic swarms and summarize their potential applications in fields such as targeted delivery, in vivo imaging, biofilm removal, and wastewater treatment. We aim at bridging the gap between the community of active matter physics and the community of micromachines or microrobotics, and in doing so, we seek to inspire fruitful collaborations between the two communities.