Session G08: Biofluids: Collective Behavior and Active Matter I

Optimal tracking strategies in a turbulent flow

We show how to apply optimal control theory to catch a passive drifting target in a turbulent flow by an autonomous flowing agent with limited maneuverability. For the case of a perfect knowledge of the environment, we show that optimal control theory can overcome chaotic dispersion capturing the Lagrangian target in the shortest possible time [1]. We also provide baselines using heuristic strategies based on local-only hydrodynamic cues. How to extend this approach to model-free data-driven tools is also briefly discussed [2]. One possible application of the present results is the control of microswimmers/minirobots at small scales, while it may be of interest to extend the present work to multi-agent systems.

   Data are open downloadable from TURB-Lagr [3], a database of more than 300K three-dimensional trajectories of tracer particles advected by a fully developed homogeneous and isotropic turbulent flow.

[1] Calascibetta, C., Biferale, L., Borra, F., Celani, A. and Cencini, M. Optimal tracking strategies in a turbulent flow - arXiv preprint arXiv:2305.04677, (2023). 

[2] Calascibetta, C., Biferale, L., Borra, F., Celani, A. and Cencini, M. Taming Lagrangian chaos with multi-objective reinforcement learning. Eur. Phys. J. E 46, 9 (2023).

[3] https://smart-turb.roma2.infn.it/   

Active turbulence in suspensions of bacterial mimetics

Swimming bacteria exhibit self-organizing behavior, forming macro-scale patterns such as swarms and dynamic clusters. At high concentrations, bacterial suspensions display turbulent-like motion characterized by erratic flow and characteristic vortex size. In contrast to classical hydrodynamic turbulence, which occurs at high Reynolds numbers and is dominated by inertia with energy injected at the macroscale and cascading down to the microscales, bacterial turbulence occurs at very small Reynolds numbers where inertia is negligible. Instead, it is energized by the motion of microswimmers. The energy spectrum in classical turbulence follows a power-law dependence on the wavenumber, with E ∼ k^(−5/3). However, for bacterial turbulence, the energy dependence of E ∼ k^(−8/3) has been reported, although experimental results are limited and inconclusive. In this study, we present a model system to study the emergence of coherent structures and large-scale flows in active fluids that mimic bacterial suspensions under well-defined conditions. In this system, we utilize the Quincke instability to design motile colloids that execute a random walk. By experimentally investigating the collective dynamics of these Quincke random walkers at different levels of activity, density, and types of random walk, we aim to gain insights into the turbulent-like behaviors in low-Reynolds-number active flows.   

Control of bacteria turbulence through surfaces

Hydrodynamic instabilities appear in E. coli suspensions at high concentrations. Controlling such instabilities could allow extracting energies at the microscales. We achieved control of the collective motion size in a sample confined between two parallel solid surfaces at a distance of H. By measuring the velocity correlation function in the center of the sample, we determined that the decay length scales increase linearly with the value of H up to 800 µm. We also tracked passive beads inside the bacteria turbulence and determined the impact of this scaling in the mixing properties of the bath. These results show that controlling the size of the collective motion is possible even at larger scales, revealing the importance of surface effects in the properties of the active suspension.   

Two-dimensional bacterial turbulence at a liquid-air interface

Many ecological issues at a liquid-air interface are complicated due to the non-equilibrium and multi-scale nature of the interface. Active matter such as bacterial suspension at an interface drives the system even further from equilibrium. In this talk, we show our recent results on active turbulence at a 2D interface. In experiments, 2D bacterial turbulence is normally formed in a thin layer of liquid above solid, or between two liquid phases. It is difficult to quantify how hydrodynamic interactions influence the structure of active turbulence, since the 2D suspension is either too far or too close to a no-slip boundary that is parallel to the bacterial motion. Here, we use concentrated Serratia marcescens bacteria that swim at a liquid-air interface to form 2D active turbulence. By cell culture, we obtain bacteria with lengths from 1μm to 10μm to tune the hydrodynamic dipole lengths. By using a microbubble assay, the thickness of the liquid layer can be adjusted from 1μm to several mm. The mean vortex size of bacterial turbulence scales with hydrodynamic dipole lengths. More interestingly, the vortex size decreases exponentially with the distance to the solid wall, which we believe is a unique feature of the 2d bacterial suspension at a water-air interface.   

Collective dynamics of micro-swimmers in Brinkman flows

Micro-swimmers live and have evolved in multiplex environments containing inert particles, obstacles, and impurities which affect their motion. Understanding the swimmers' locomotion and interactions in such inhomogenous environments viscous fluids is crucial to understanding their emerging dynamics.

We derive a model for rigid active particles immersed in viscous Brinkman flows -- which approximate with a linear resistance term the presence of much smaller inert impurities or stationary obstacles.  We show that resistance alters the disturbance flow generated as each active particle swims, and as such alters the hydrodynamical interactions between swimmers and ultimately modifies their coupled dynamics. Simulations implemented using the Immersed Boundary Method  show that resistance inhibits correlated collective dynamics in micro-swimmer suspensions because resistance hinders each individual's motion and its interactions with others. We analyze the resulting dynamics for varying resistance strengths, and show that a high resistance, in accordance with results from analysis of the related continuum model, can fully suppress the emergence of macroscopic collective motion.