Session V16: Active Matter Under Confinement II

Active Self-Assembled Spinners: dynamic crystals, transport and induced surface flows

Strongly interacting colloids driven out-of-equilibrium by an external periodic forcing often develop nontrivial collective dynamics. Active magnetic colloids proved to be excellent model experimental systems to explore emergent behavior and active (out-of-equilibrium) self-assembly phenomena. Ferromagnetic micro-particles, suspended at a liquid interface and energized by a rotational homogeneous alternating magnetic field applied along the supporting interface, spontaneously form ensembles of synchronized self-assembled spinners with well-defined characteristic length. The size and the torque of an individual self-assembled spinner are controlled by the frequency of the driving magnetic field. Experiments reveal a rich collective dynamics in large ensembles of synchronized magnetic spinners that spontaneously form dynamic spinner lattices at the interface in a certain range of the excitation parameters. Non-trivial dynamics inside of the formed spinner lattices is observed. Transport of passive cargo particles and structure of the underlying self-induced surface flows is analyzed. The research was supported by the U.S. DOE, Office of Basic Energy Sciences, Division of Materials Science and Engineering   

Active colloids as assembly machines

Controlling motion at the microscopic scale is a fundamental goal in the development of biologically-inspired systems. We show that the motion of active, self-propelled colloids can be sufficiently controlled for use as a tool to assemble complex structures such as braids and weaves out of microscopic filaments. Unlike typical self-assembly paradigms, these structures are held together by geometric constraints rather than adhesive bonds. The out-of-equilibrium assembly that we propose involves precisely controlling the two-dimensional motion of active colloids so that their path has a non-trivial topology. We demonstrate with proof-of-principle Brownian dynamics simulations that, when the colloids are attached to long semi-flexible filaments, this motion causes the filaments to braid. The ability of the active particles to provide sufficient force necessary to bend the filaments into a braid depends on a number of factors, including the self-propulsion mechanism, the properties of the filament, and the maximum curvature in the braid. Our work demonstrates that non-equilibrium assembly pathways can be designed using active particles.   

Self Propelled Hard Disks Against a Membrane : Mechanical Pressure and Instability

We experimentally study the mechanical pressure exerted by an assembly of respectively isotropic/diffusive and polar/self-propelled disks onto a flexible unidimensional membrane. For the isotropic disks, the mechanical pressure, inferred from the shape of the membrane, is independent of the length of the membrane and follows the equilibrium equation of state of hard disks. On the contrary, for the self-propelled disks, the mechanical pressure depends on the membrane length and is thus not a state variable. When self propelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for Active Brownian Particles against a soft wall. The weaker the pressure difference across the membrane, the largest is the amplitude of the instability.   

Free and constrained expansion of fire ant aggregations

We revisit the classical free and constrained expansion of ideal gases with fire ant aggregations. We use rectangular parallel plates to confine fire ants to two-dimensions and watch how these expand when the plates are horizontal or when these are vertical. In the first case, the ants expand in a rather disorganized fashion, while in the second case, when there is work involved, the expansion is rather organized. The behavior is reminiscent of what is expected from the so called reversible process theorems of classical thermodynamics despite the ant aggregation is intrinsically out of equilibrium. This talk will focus on these results and in related observations in the same experimental setting.   

Predesigned surface patterns and topological defects control the active matter.

Active matter exhibits remarkable patterns of never-ending dynamics with giant fluctuations of concentration, varying order, nucleating and annihilating topological defects. These patterns can be seen in active systems of both biological and artificial origin. A fundamental question is whether and how one can control this chaotic out-of-equilibrium behavior. We demonstrate a robust control of local concentration, trajectories of active self-propelled units and the net flows of active bacteria \textit{Bacillus Substilis} by imposing pre-designed surface patterns of orientational order in a water-based lyotropic chromonic liquid crystal. The patterns force the bacteria to gather into dynamic swarms with spatially modulated concentration and well-defined polarity of motion. Topological defects produce net motion of bacteria with a unidirectional circulation, while pairs of defects induce a pumping action. The qualitative features of the dynamics can be explained by interplay of curvature and activity, in particular, by ability of mixed splay-bend curvatures to generate threshold-less active flows. The demonstrated level of control opens opportunities in engineering materials and devices that mimic rich functionality of living systems.   

Droplet swimmers in complex geometries: Autochemotaxis and trapping at pillars.

Autochemotaxis is a key feature of communication between microorganisms, via their emission of a slowly diffusing chemoattractant or repellent. We present a well-controlled, tunable artificial model to study autochemotaxis in complex geometries, using microfluidic assays of self-propelling liquid crystal droplets in an aqueous surfactant solution. Droplets gain propulsion energy by micellar solubilisation, with filled micelles acting as a chemical repellent by diffusive phoretic gradient forces. We can tune the key parameters swimmer size, velocity and persistence length. If a swimming droplet approaches a wall, it will provide a boundary to both the hydrodynamic flow field and the spread of phoretic gradients, determining the interaction between swimmer and wall. Pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and in the case of attachment bending its trajectory and forcing it to revert to its own trail. We observe different behavior based on the interplay of wall curvature and negative auto-chemotaxis, i. e., no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.   

Bimetallic microswimmers speed up in confining channels

Synthetic microswimmers are envisioned to be useful in numerous applications, many of which occur in tightly confined spaces. It is therefore important to understand how confinement influences swimmer dynamics. Here we study the motility of bimetallic microswimmers in linear and curved channels. Our experiments show swimmer velocities increase, up to 5 times, with the degree of confinement, and the relative velocity increase depends weakly on the fuel concentration and ionic strength in solution. Experimental results are reproduced in a numerical model which attributes the swimmer velocity increase to electrostatic and electro-hydrodynamic boundary effects. Our work not only helps to elucidate the confinement effect of phoretic swimmers, but also suggests that spatial confinement may be used as an effective control method for them.   

Statistical mechanics of an ideal active fluid confined in a channel

The statistical mechanics of ideal active Brownian particles (ABPs) confined in a channel is studied by obtaining the exact solution of the steady-state Smoluchowski equation for the 1-particle distribution function. The solution is derived using results from the theory of two-way diffusion equations, combined with an iterative procedure that is justified by numerical results. Using this solution, we quantify the effects of confinement on the spatial and orientational order of the ensemble. Moreover, we rigorously show that both the bulk density and the fraction of particles on the channel walls obey simple scaling relations as a function of channel width. By considering a constant-flux steady state, an effective diffusivity for ABPs is derived which shows signatures of the persistent motion that characterizes ABP trajectories. Finally, we discuss how our techniques generalize to other active models, including systems whose activity is modeled in terms of an Ornstein-Uhlenbeck process.   

Usefulness and limits of equilibrium mappings for confined active particles

Predicting the response of active particles to external potentials is notoriously difficult. Gaussian colored models have recently allowed some progress, including a systematic way to map an active system onto an equilibrium one. When the external potential represents hard walls, another approach exists, which tracks the dynamics along the walls. I will compare the analytical predictions of these two approaches with each other and with numerical simulations of various active particles (Gaussian colored noise, active Brownian, run-and-tumble) and discuss what they tell us about the scope of equilibrium mappings for active particles in external potentials.   

Large-scale particle-based simulations of active nematic fluids in bulk and under confinement

Active nematics are liquid crystals which are driven out of equilibrium by energy-dissipating active stresses. Experiments and theory have demonstrated that in such systems the ordered nematic state is unstable to the proliferation of topological defects, which undergo birth, streaming dynamics, and annihilation to yield a seemingly chaotic dynamical steady state. In this talk we describe large-scale simulations of a particle-based computational model for active nematic, motivated by an experimental active nematic system containing extensile bundled microtubules and molecular motor proteins. Extending upon previous theoretical and computational work, our model explicitly describes degrees of freedom internal to bundles. We explore how the properties of these internal modes affect large-scale emergent behaviors, such as defect shapes and inter-defect correlations, in bulk and under confinement. We quantitatively compare these defect behaviors observed in bulk and confined experimental systems.   

Active matter and Curvature

Coupling between active motion and curvature is an integral part of many fundamental biological processes such as gastrulation and intestinal crypt fission. However, to date very little is known about how curvature affects active motion. Here we use a particle-based model to study the interplay between activity and curvature in dense systems. Using detailed numerical simulations and simple physical arguments, we show that the presence of curvature results in a number of steady-state configurations that have no analogues in flat geometries. These states are particularly interesting if topological constraints require the presence of defects in the ground states in the passive limit. We focus on polar and nematic active systems confined to move on the surface of a sphere and show that activity can lead to the formation of moving band and multidefect states. We extend our model to self-propelled filaments confined to a plane or the surface of a sphere. We show that the activity leads to an effective softening of the polymer chain. As a result of this softening, with the increase in activity, the system transitions between a jammed polymer-melt state, an active turbulent state characterised by a proliferation of hair-pin defects, to a region dominated by phase segregation (MIPS), finally followed by the onset of a homogenous state characterised by spiral motion of individual polymers.   

Defects in an active nematic confined to a toroid

Active materials are driven far from the ground state by the motion of their constituent particles, thereby making them inherently non-equilibrium materials. For an active nematic, this results in a continuous creation and annihilation of $\pm 1/2$ defect pairs. Here, we confine an active nematic to the surface of a toroid and show that the topological charge of the defects couples to the Gaussian curvature of the underlying surface. However, in our experiments this defect unbinding happens on average, illustrating that despite subtle differences, the role of activity is reminiscent of the role of temperature in conventional nematics. This is confirmed by computer simulations which clearly illustrate that defect unbinding depends on activity. Overall, our results illustrate the role of confinement and curvature on the defect behavior of active nematic liquid crystals.   

Soft inclusion in a confined fluctuating active fluid

We study the dynamics of an inclusion in a 1D confined active fluid with athermal fluctuations. To highlight various features and to appeal to different contexts, we treat the inclusion in turn as a rigid element, a passive elastic element and an active elastomer. We show that in general, the active dynamics of the shape and position of the inclusion are described by coupled Langevin equations with a confining potential and {\it multiplicative} noise. The steady state distribution computed exactly from the resulting Fokker-Planck equation, exihibits a transition as a function of the relative strength of the confining potential and athermal noise. Our study is of relevance to the positioning and shape of (i) the nucleus embedded in the active cytoplasm, (ii) chromosomes within the nucleus, (iii) nuclei in multi-nucleated cells, and (iv) the fluctuations of a cell within a developing tissue.