Session P19: Focus Session: Interfacial Active Matter III

Interfacial dynamics of active microtubule nematics

Phase-separated systems minimize their interfacial area by producing rounded droplets that coalesce and eventually bulk separate. Non-equilibrium driving can fundamentally alter such dynamics. Conventional non-equilibrium systems rely on the input of energy through macroscopic boundaries, which cause shear flows that deform and elongate the interface. In contrast, in active matter energy is injected at the microscopic scale, and from there it propagates upward to create large-scale turbulent-like flows. To study coupling of active matter with soft interfaces, we have developed an experimental phase-separated active system by merging a microtubule-based isotropic active fluid with phase-separating polymers. The system spontaneously partitions into an active phase containing the microtubules and kinesin motors, and a passive phase. The two phases are separated by an interface with an ultralow surface tension that is deformed by active flows, resulting in large fluctuations. Sufficiently strong active stresses destabilize interfaces altogether, resulting in droplet break-up. We quantify the fluctuations of a single interface, examine how activity fundamentally alters the course of phase separation and produces surprising emergent states like spontaneous wetting.   

Modeling active fluids via physically constrained machine learning

We investigate an experimental fluid flow driven by microtubules confined to an oil/water interface. Deriving a mathematical model of this active fluid from first principles is difficult, as not all the relevant physical processes are well understood. Instead, we use sparse physics-informed discovery of empirical relations (SPIDER) to learn the governing equations directly from experimental data. General physical constraints such as locality, causality, and symmetry are used to construct libraries of candidate relations between the flow field and the director field describing the orientation of microtubules. Sparse regression is then used to identify a parsimonious two-dimensional model of this system. Three PDEs are identified from data: an incompressibility condition and momentum balance describing the fluid flow and a separate equation for the director field. The latter two governing equations are distinct from those appearing in the literature. In particular, neither the advection terms nor the time derivative of the flow velocity appears in the momentum equation, consistent with the low Reynold's number of the flow. We also find that elastic effects cannot be described by weakly nonlinear terms in the evolution equation for the director field.   

Phase separation in magnetic chiral fluids

Phase separation in active particle systems and the spatio-temporal organization of chiral

fluids are two prominent research areas of continuous interest. I will describe the collectively self-organiztion of spinning ferromagnetic rotors  that interact both via hydrodynamic

and dipolar forces into  circulating clusters, At   high spinning frequency, hydrodynamics dominate over attractive magnetic interactions and impede

coarsening,. A  minimal numerical model brings insight into  the fundamental role of

hydrodynamics and of the boundary plane in the organization process. These results highlight  the importance of fluid mediated long range interactions in the assembly of active spinning materials.   

Computational Dynamics of Interfaces in Multispecies Active Fluids

Capturing the behavior of interactions between the collective motion of mismatched swarms of active agents is critical to the understanding of natural phenomena and several new developments in engineering and medicine. The simple locomotive rules applied to each agent give way to emergent behavior of the whole swarms and the interface between them. Here we define the interface as the curve delimiting the region where one species predominates, and study how its evolution is related to the swimming properties. We focus in particular on the emergence of spontaneous structures, and investigate whether these structures can be compared to traditional crystals. We use a multi-scale mean-field continuum model to simulate the motion of active agents, without tracking agents themselves, and couple their governing equations with that of the surrounding fluid. The resulting continuum system is solved using a level-set based hybrid Finite Difference-Finite Volume solver on a Quadtree grid for high computational efficiency. This work is an advancement on the method presented by us earlier and continues to pave the way for future studies of systems which can be described as the collective motion of active agents, such as bacterial colonies, wound healing, colloidal swimmers, and programmable active matter. In nature, swarming species certainly interact, and we seek to understand the mechanisms which govern the behavior of the collective motion of active agents when encountering another swarm.   

Numerical simulation of electric field-induced concentration patterns at fluid interfaces

Experiments have shown that DNA molecules attached to the liquid-liquid interface of an aqueous two-phase system form concentration patterns when subject to an electric field normal to the interface. Electroosmotic flow due to the Debye layer around the molecules induces the formation and interaction of clusters and connecting filaments. Previous findings have revealed concentration patterns in which shorter-wavelength modes destabilize at later times with progressively faster growth rates. We use a pseudo-spectral Fourier method to solve the governing non-linear integro-differential equation and propose an additional term to account for the crowding of molecules. Simulation results for the pattern formation as well as the interaction and merging of DNA clusters agree well with experimental observations. We further characterize the dynamics by identifying inherent scales for the time of pattern formation and the average distance between clusters.   

Roughening instability of growing three-dimensional bacterial colonies

How do growing bacterial colonies get their shape? While this process of morphogenesis is well-studied in 2D, many bacterial colonies inhabit 3D environments, such as gels and tissues in the body, or soils, sediments, and subsurface media. Here, we describe a morphological instability exhibited by dense colonies of non-motile bacteria growing in 3D. Using experiments in transparent 3D media, we show that colonies of Escherichia coli and Vibrio cholerae generically roughen as they consume nutrients and grow, eventually forming branched, finger-like patterns. This behavior reflects a key difference between 2D and 3D colonies: while 2D colonies can more easily access the nutrients needed for growth, the 3D colonies inevitably become nutrient-limited in their interior, driving a transition to rough, branched growth. We elucidate this behavior using linear stability analysis and numerical simulations of a continuum active fluid model, which indeed reveal that when the size of the growing colony far exceeds the nutrient penetration length, nutrient depletion drives a transition to roughening with a characteristic universal shape that can be compared with experiments.   

Developmentally driven self-assembly and dynamics of living chiral crystals

The emergent dynamics exhibited by collections of living organisms often shows signatures of symmetries that are broken at the single-organism level. At the same time, early organism development itself is accompanied by a sequence of symmetry breaking events that eventually establish the body plan. Combining these key aspects of collective phenomena and embryonic development, we describe here the spontaneous formation of hydrodynamically stabilized active crystals made of hundreds of starfish embryos during early development. As development progresses and embryos change morphology, crystals become increasingly disordered and eventually stop forming. We introduce a minimal hydrodynamic model that is fully parameterized by experimental measurements of single embryos. Using this theory, we can quantitatively describe the stability, formation and rotation of crystals, as well as the emergence of long-lived chiral deformation waves. Our work thereby quantitatively connects developmental symmetry breaking events on the single-embryo level with the remarkable macroscopic properties of a novel living chiral crystal system.   

Bifurcations and pattern formation in active suspensions

We consider the Saintillan--Shelley [2008] kinetic model of active rodlike particles in Stokes flow, for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings. We determine exactly how the isotropic steady state loses stability in different parameter regimes. Through weakly nonlinear analysis accompanied by numerical simulations, we study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behavior near these bifurcations provides both a means of verifying the predictive power of the model against experimental observations as well as a theoretical means of comparing this model with other systems which transition to turbulence.   

Hydrodynamic interactions induce microphase separation in active systems

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 the 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, respectively. Manifestations of broken detailed balance often comprise novel phases that are absent in equilibrium. 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' - large-scale collective motion of a dilute suspension of motile organisms. In this talk we introduce a model that simultaneously includes long-range hydrodynamic interactions between microswimmers and microscopic ingredients necessary for the formation of motility-induced clusters. We demonstrate that the model yields a variety of new phases. Most importantly, we find that the growth of motility-induced clusters is arrested by hydrodynamic interactions leading to microphase separation. We discuss its mechanism and propose a phase diagram for such systems.   

Active carpets drive non-equilibrium diffusion and enhanced molecular fluxes

Biological activity is often highly concentrated on surfaces, across the scales from molecular motors and ciliary arrays to sessile and motile organisms. These 'active carpets' locally inject energy into their surrounding fluid. Whereas Fick's laws of diffusion are established near equilibrium, it is unclear how to solve non-equilibrium transport driven by such boundary-actuated fluctuations. Here, we derive the enhanced diffusivity of molecules or passive particles as a function of distance from an active carpet. Following Schnitzer's telegraph model, we then cast these results into generalised Fick's laws. Two archetypal problems are solved using these laws: First, considering sedimentation towards an active carpet, we find a self-cleaning effect where surface-driven fluctuations can repel particles. Second, considering diffusion from a source to an active sink, say nutrient capture by suspension feeders, we find a large molecular flux compared to thermal diffusion. Hence, our results could elucidate certain non-equilibrium properties of active coating materials and life at interfaces.     

Emergent order in Hydrodynamic Spin Lattices

In this talk, we will introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own wave fields. By virtue of the coupling with their wave fields, these walking droplets, or 'walkers', extend the range of classical mechanics to include certain features previously thought to be exclusive to the microscopic, quantum realm. Walkers may be impelled to walk in small circles (corresponding to `spin states') in either clockwise or counterclockwise directions, through the influence of submerged circular wells.  When many such spin states are arranged in a regular 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. Through experiments and mathematical modeling, we demonstrate the spontaneous emergence of coherent droplet rotation dynamics for different types of lattices. For sufficiently strong pair-coupling, wave interactions between neighboring walkers may induce local spin flips leading to `ferromagnetic' or `antiferromagnetic' states, as arise when neighboring droplet pairs orbit in the same or opposite sense, respectively. Transitions between these two forms of collective order can be induced through variations in non-equilibrium driving, lattice geometry and Coriolis forces mimicking an external magnetic field. Theoretical predictions based on a generalized Kuramoto model derived from first principles rationalize our experimental observations, establishing HSLs as a generic paradigm for active phase oscillator dynamics.   

Effective diffusivity of a microswimmer in a lattice

Microswimmers display various patterns when they swim in complex environments, and their trajectories are studied both experimentally and theoretically for a wide range of geometries. In recent years, confinement in gel structure receives a great amount of attentions where swimmers exhibite a diffusive behavior in long time scales. In order to understand the effective diffusivity, we consider a 2-D active Brownian swimmer navigating through homogenous gel media. The swimmer travels with constant speed and its direction of swimming changes according to a Brownian process. The gel media are modelled by a periodic lattice grid, whose dimensions are large compared to the size of the swimmer. In this case, hydrodynamic interactions with boundaries are negligible since boundaries are lattice points. Steric interactions on the other hand, play an important role and they depend on a swimmer's shape. To avoid making ad-hoc assumptions on the swimmer's behavior near the lattice points, we only assume a swimmer can not penetrate lattice points and absorb the shape into a no-flux boundary condition. The invariant density of the swimmer then satisfies a Fokker--Planck equation, and we solve the effective diffusivity tensor in space asymptotically.