Session A03: Active Matter I: Active Turbulence

Polymers in Swarming Bacterial Turbulence

In this talk, we will show recent experiments on the effects of polymer additives on the collective dynamics of swarming Serratia marcescens in quasi two-dimensional (2D) liquid films. Particle image velocimetry resutls show that even minute amounts of polymers (~ 20 ppm) can significantly enhance swimming speed and promote large-scale coherent structures. Velocity statistics show that polymers suppress large velocity fluctuation, transforming the velocity distributions from super-Gaussian to Gaussian. Spatial and temporal correlation functions suggest that polymers increase both the size and lifetime of flow structures. The energy spectra show an exponential decay at low wavenumbers, with a characteristic length scale increasing with polymer concentration. Overall, these result show polymers can mediate bacteria interaction and promote large-scale coherence in dense active suspensions.   

Do bacteria go with the flow in bacterial turbulence?

A dense suspension of swimming bacteria displays mesmerizing jets and vortices reminiscent of inertial turbulent flow. How an individual bacterium navigates this “bacterial turbulence” generated by its neighbors remains unknown. Here, we image the motion of individual fluorescently-tagged E. coli tracers in bacterial turbulence at different bacterial densities. By comparing the motions of actively swimming cells and immobile cell bodies, we quantify the relative contributions of self-propulsion and background advection to the motion of an individual bacterium in bacterial turbulence. At densities sufficient to induce bacterial turbulence, weak advective flows are generated. At these densities, the swimming of active bacteria contributes to their motion resulting in them being faster than their immobile counterparts. However, at higher densities, the turbulent advection gets stronger, and active and immobile cells are transported at the same speed. Thus, the density of the bacterial suspension controls the coupling between the motion of an individual bacterium and the advective flows of bacterial turbulence. Finally, our findings highlight crucial differences between the transport properties of externally driven inertial turbulence and self-propulsion driven bacterial turbulence.   

Friction-enhanced lifetime of bundled quantum vortices

Some physical systems consist of components which interact with each other not only

directly, but also indirectly by changing the common background. A typical example

of this interplay is hydrodynamic cooperation characterising systems of active agents

such as aqueous suspensions of self-propelled bacteria, fungal spores dispersed in air, road

racing cyclists in pelotons and particle pairs trapped in optical vortices; in these systems

self-organized structures emerge from collective energy-saving mechanisms.

Here we report a similar collective effect existing in superfluid helium at finite temperatures.

By performing cutting-edge numerical simulations of superfluid helium dynamics, we show

that a toroidal bundle of quantized vortex rings generates a large-scale wake

in the normal fluid which reduces the overall friction experienced by the bundle, thus

greatly enhancing its lifetime, as observed in experiments.

This remarkable collective effect - the reduction of dissipation via

hydrodynamic cooperation - displays similar features than the ones observed in particle drafting in optical

vortices. Superfluid helium can hence be considered as a peculiar kind of active fluid,

where hydrodynamic interactions determine the characteristics of turbulence in both superfluid and normal fluid components.   

Active Turbulence - Statistical Analysis

An active suspension consists of a fluid, usually Newtonian, and a large number of active particles. The latter term describes objects which exert a force onto the surrounding fluid and propel themselves through the suspension. At specific particle densities the emerging patterns of an active suspension at low Reynolds numbers show similarities to turbulence, leading to the term "active turbulence". 

We show simulation results for an active suspension, obtained with the fluid-particle solver module of the BoSSS framework  (https://github.com/FDYdarmstadt/BoSSS). Position, orientation and velocity data are used to calculate probability density functions (PDF) describing the statistics of the active suspension.  These data are compared to theoretical results, which are based on the infinite hierarchy of PDF-equations, derived in Deußen et al. (Phys. Fluids, 33, 061902, 2021). We derive Lie symmetries for the PDF-equations, which are then used to obtain group invariant solutions. Comparing the simulation data to the solutions connects the observed turbulent phenomenons to the underlying theory and, subsequently, contributes to the understanding of active suspensions.    

Motility-induced phase separation in the presence of hydrodynamic interactions

Free of the constraints of equilibrium statistical physics, active matter systems exhibit a variety of unexpected phenomena. Their origin lies in detailed balance being broken by self-propulsion and interactions between active particles at the microscopic level. Such systems can often be classified as either 'dry' or 'wet' active matter when dominated by friction with their surroundings and long-ranged hydrodynamic interactions (HI), respectively. In dry active matter, an archetypal example is given by the motility-induced phase separation, while in wet active matter, the same role is played by bacterial turbulence-largescale collective motion of dilute suspension of motile organisms.

In this talk we consider a system that incorporates elements of both dry and wet active matter. We study collective motion in a 2D layer of model microswimmers suspended in a viscous fluid. In the absence of HI, we observe motility-induced phase separation, while the presence of 2D HI only trivially changes the phase diagram of such systems. However, when the microswimmer layer is suspended in a 3D bulk fluid, we find that the growth of motility-induced clusters is arrested, leading to microphase separation. We discuss the mechanism of such arrest and explain the origin of the emergent lengthscale.

    

Emergent length-scale in microswimmer suspensions

Recent years witnessed a significant interest in physical, biological and engineering properties of self-propelled particles, such as bacteria or synthetic microswimmers. One of the most striking features of interacting microswimmers is the appearance of collective motion: at densities high enough, the system is characterised by jets and vortices comprising many individual swimmers. Although many experimental and theoretical works have shown the appearance of a length-scale intrinsic to the ensuing collective flow, its precise origin is not understood.

In this work, we investigate the statistical properties of self-propelling particles with hydrodynamic interactions. Starting from the kinetic theory of microswimmers, we derive a closed set of mean-field moment equations. Performing large-scale pseudo-spectral simulations, we calculate the corresponding energy spectra, and spatial correlations for various values of the mean particle density. Our results demonstrate the emergence of a typical length-scale in the collective phase and we show that it is set by the microswimmer run-length and the inter-particle distance. This length-scale determines the size of strongly correlated regions: it is infinite at the point of the mean-field transition to collective motion, and decreases with increasing microswimmer density. At large scales, the system effectively behaves as a gas of non-interacting swimmers.   

Irreversiblity in Bacterial Turbulence: Insights from the Mean-Bacterial-Velocity Model

We use the mean-bacterial-velocity model to investigate the \textit{irreversibility} of two-dimensional (2D) \textit{bacterial turbulence} and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. We demonstrate how the statistical properties of these particles help us to uncover an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large but negative (or large and positive) values of the \textit{activity} (or \textit{friction}) parameter, the probability distribution functions of energy increments, along tracer trajectories, or the power are \textit{positively} skewed; so irreversibility in bacterial turbulence can lead, on average, to \textit{particles gaining energy faster than they lose it}, which is the exact opposite of what is observed for tracers in 2D fluid turbulence.   

Motility-induced droplet self-propulsion and multifractal interface fluctuations

We develop a minimal phase-field model to study phase separation in an assembly of contractile micro-swimmers confined to a binary-emulsion droplet. Our model uses two scalar order parameters: one to capture the droplet's interface and another to capture the density of the contractile swimmers. Our model reveals, at low activity, straight-line motion of the centre-of-mass (CM) of the droplet powered by an emergent vortex dipole. With increasing activity, the CM displays chaotic super-diffusive motion, which we characterize by its mean-square-displacement; the active field generates low-Reynolds-number turbulence inside the droplet, which leads to multifractal interfacial deformations.   

Lagrangian structure and stretching in bacterial turbulence

Dense suspensions of active, self-propelled agents spontaneously exhibit large-scale, chaotic flow structures. Descriptions of their dynamics have predominately focused on characterization of spatiotemporal correlation of the velocity field, but their transport and mixing properties remain largely unknown. In this work, we use Lagrangian analysis techniques to study the chaotic flow fields generated by "bacterial turbulence'" in dense suspensions of Bacillus subtilis. High-resolution velocity fields are simultaneously measured along with individual tracer and cell trajectories across a range of bacterial swimming speeds. The flow kinematics are quantified through the Lagrangian stretching field and used to characterize the mixing induced by the stretching and folding of the active bacterial colony. The distribution of the finite-time Lyapunov exponent (FTLE) field reveals swimming-speed dependent transitions reminiscent of intermittent dynamics in classical chaotic dynamical systems. Finally, measured trajectories of both passive beads and individual swimming cells directly demonstrate how the striking active Lagrangian flow structures regulate transport in bacterial turbulence.