Session X9: Coordination, Coherence and Synchronization through Hydrodynamic Interactions

Collective motion and density fluctuations in swimming bacteria

The emergence of collective motion such as in fish schools, mammal herds, and insect swarms is a ubiquitous self-organization phenomenon. Such collective behavior plays an important role in a range of problems, such as spreading of deceases in animal or fish groups. Current models have provided a qualitative understanding of collective motion, but progress in quantitative modeling in hindered by the lack of experimental data. Here we examine a model microscopic system, where we are able to measure simultaneously the positions, velocities, and orientations of up to a thousand bacteria in a colony. The motile bacteria form closely-packed dynamic clusters within which they move cooperatively. The number of bacteria in a cluster exhibits a power-law distribution truncated by an exponential tail, and the probability of finding large clusters grows markedly as bacterial density increases. Mobile clusters cause anomalous fluctuations in bacterial density as found in mathematical theories and numerical models. Our results demonstrate that bacteria are an excellent system to study general phenomena of collective motion.   

Collective behavior of spinning particles at fluid/fluid interface

Rotating particles in a viscous fluid can exhibit interesting behavior due to hydrodynamic interactions. When the particles are driven by an external torque, these interactions result in an effective azimuthal force, leading to swirling motion. It has been shown that small numbers of such particles form precessing atom-like structures. The behavior of large collections of spinning particles is, however, still relatively unexplored. We study the phase diagram of a collection of spinning particles in two dimensions using molecular dynamics simulations. The rotors interact via hydrodynamic interactions and short-range repulsion, in the presence of thermal noise. The repulsive interaction yields transitions from a solid to a liquid to a gas as the density of rotors is decreased. The azimuthal hydrodynamic interaction modifies each of these phases in a distinct way. Both long-range and screened hydrodynamic interactions are considered. Some properties of the various phases are shown to depend critically on the range of the interaction.   

Synchronization phenomena in systems with magnetodipolar interactions

Rich pattern formation phenomena under the action of AC field for two dimensional systems of magnetic dipoles floating on the surface of liquid are observed and reproduced numerically by the first-principles model [1]. Here by the study of dynamics of two dipoles interacting with weak dipolar forces it is found that due to series of bifurcations the motion of dipoles in AC field is synchronized. If the dipoles orientation is confined to the plane the synchronous oscillation regime by infinite period bifurcation transforms to the regime of synchronous rotation. This regime is unstable for intermediate values of the field strength and the motion of dipoles is periodic or quasi-periodic. Above the critical value of field strength these regimes transform to rotational regime and the dipoles synchronously rotate in plane. Estimate of the critical parameters of the synchronization according to the dimensionless parameters used in the first-principles model [1] show that the synchronization of the dipoles rotation should be inherent in this model.\\[4pt] [1] M.Belkin, A.Glatz, A.Snezhko, and I.S.Aranson, Phys.Rev.E, 82, 051301(R), (2010)   

Pattern Formation in a Rotating Suspension of Non-Brownian Buoyant Particles

This study examines concentration and velocity patterns observed in a horizontal rotating cylinder completely filled with a monodisperse suspension of non-Brownian buoyant particles. The unique patterns or phases are mapped by varying both the rotation rate and the solvent viscosity. Individual phases are identified using both frontal and axial views. Phase boundaries are compared to those obtained recently for suspensions of non-buoyant particles. Expressing the boundaries in terms of dimensionless parameters unifies the data for several samples at low rotation rates. When centrifugal force dominates, the behavior becomes quite different from previous studies.   

Shear-induced hydrodynamic diffusion of a flowing suspension of elastic capsules

In flowing suspensions of soft and deformable elastic capsules, the shear flow causes hydrodynamic interaction among the capsules, resulting in an effective hydrodynamic diffusion that is not Brownian in origin. Recent experiments have suggested that hydrodynamic diffusion of red blood cells may play an important role in the pathophysiological processes of vasoocclusion and thrombosis. To study hydrodynamic diffusion further, we have developed accurate three-dimensional numerical simulations based on the immersed boundary method and thin shell theory to study the deformation of a large number of elastic capsules enclosed by thin shells moving in a shear flow. Using these simulations, we have calculated the effective hydrodynamic diffusion coefficient and showed how it varies with bulk flow velocity and capsule properties such as the volume fraction, size, and stiffness of spherical and biconcave capsules. We also compared them to scaling arguments and experimental measurements done for red blood cell suspensions.   

Artificial Microfluidic Squirmers

While there is a growing consensus on the propulsion mechanisms of swimmers at low Reynolds' numbers, many questions remain open regarding the hydrodynamic effects on such swimmers, in particular the coupling between swimmers. Here we present experiments on artificial swimmers, where hydrodynamics is seen to be responsible for a wide range of collective behavior and interactions. Using droplet microfluidics with a surfactant laden continuous oil phase, we create monodisperse aqueous droplets containing chemicals that produce a steady source of Bromine ions. The surfactant (mono-olein) reacts at the droplet interface with the Bromine produced within the droplets, and a dynamic instability leads to gradients of interfacial tension at the droplet interface. These gradients set up Marangoni flows propelling the droplets, in a manner similar to the classical squirmer model of swimming. The flow around the swimmers as well as its effect on the droplet motion are measured using particle image velocimetry (PIV). The PIV analysis reveals the far field flows generated by the swimmers in the surrounding liquid, leading to the emergence of bound states and oriented clusters. We discuss the interaction mechanisms and compare it to previous theoretical work and simulations.   

Characterizing particle transport due to actuated cilia with adhesive tips

Biological tissues and organisms commonly utilize arrays of cilia to manipulate microparticles of different sizes. Motivated by biology, we use numerical simulations to study the interaction of microparticles with an array of actuated cilia, immersed in fluidic microchannel. For each cilium in the array, one end is tethered to the wall, while the other end is actuated by an external periodic force. Also, an adhesive force is introduced between the cilia tip and the microparticle. The simulations are performed using the Lattice Boltzmann Method for the flow, with a chain of point-forces, connected by springs, used to represent each cilium. We observe that a combination of hydrodynamic and adhesive forces can lead to size-specific control of microparticle transport. For instance, for certain adhesion strength and particle sizes, it is possible to trap and release particles by varying the actuation frequency. Also, for a given actuation frequency, the average particle speed is maximized at a particular adhesion strength. We will present the parameter range where we can observe the above behavior.   

Harnessing self-oscillating polymer gels to design active ciliated surfaces

Via theory and simulations, we design active surfaces capable of replicating characteristics of biological cilia. Our approach harnesses the use of polymer gels that undergo photosensitive Belousov-Zhabotinsky (BZ) reaction. Powered by internalized BZ reaction these polymer gels swell and de-swell autonomously due to the chemo-mechanical transduction and therefore are ideal materials for designing our system. We have successfully developed an efficient hybrid approach by combining our three dimensional gel lattice spring model (3D-gLSM) and Lattice Boltzmann Method (LBM) which allows us to capture the interactions between the cilia and the surrounding fluid. Using our gLSM-LBM hybrid model we determine the factors that govern the bending and beating of individual cilium and also their collective dynamic behavior. Our findings provide guidelines for designing ciliated surfaces that can exhibit biomimetic functionality.   

Designing active cilial sensors

We employ a hybrid lattice Boltzmann / lattice spring computational model to simulate the three-dimensional hydrodynamic interactions among actuated and sensory elastic cilia tethered to a wall of a microfluidic channel. These actuated and sensory cilia are arranged a chessboard pattern on the channel wall. The actuated cilia are driven by a sinusoidal force applied to their free ends and induce periodic oscillations of a viscous fluid filling the microchannel. The passive, sensory cilia are used to measure the force arising due to fluid oscillations. We show that the combination of sensory and actuated cilia allows us to evaluate distances to solid objects located in a fluid-filled microchannel, thereby yielding a useful active sensor for microfluidic and biomedical applications.   

Nonlinear dynamics of flagellar bundling

Flagella are long thin appendages of microscopic organisms used for propulsion in low-Reynolds environments. In many bacterial species, helical-shaped flagella driven by a molecular motor will bundle up. This bundling process is poorly understood, and the exact roles of hydrodynamic interactions, helix elasticity, and mechanical contact are unclear. To investigate the bundling, we consider two flexible helices next to each other, as well as several flagella attached to a spherical body. Each helix is modeled as several prolate spheroids connected by springs. For HI, we consider the flagella to made up of point forces, while the finite size of the body is incorporated via Fax\'{e}n's laws. Before flagella can bundle, they must synchronize. Synchronization occurs fast relative to the bundling process. For flagella next to each other, the initial stage of bundling is governed by rotlet interactions generated by the rotating helices. At longer times, once bundling has occurred, we find that a sharp distinction can be made between ``tight'' and ``loose'' bundles, indicated by the local distance between the flagella. As function of the anchor point distance, a sharp transition from tight to loose is found when starting from the completely unbundled state. Incremental steps from stationary situations give multiple stationary for a single anchor distance. We show that the balance between elasticity and strong non-linear hydrodynamic interactions is responsible for this bifurcation behavior.   

Spontaneous transitions in the synchronisation states of a Chlamydomonas mutant

The mechanisms by which eukaryotic flagella are found to synchronise is poorly understood; the origins being dependent upon the hydrodynamics, as well as the underlying molecular biochemistry. Exemplifying how available phenotypic variations in a species may be exploited to extend our mathematical models for flagellar coupling, we turn to ptx1 - a non-phototactic mutant strain of the biflagellated alga \textit{Chlamydomonas} with seemingly intact flagellar apparatus, which does not exhibit any gross motility defects. Intriguingly however, our high-speed imaging analysis of flagellar dynamics in ptx1 have revealed that rather unlike their wildtype predecessors, which beat mostly in synchrony interrupted by brief periods of drifts or slip [1], the two flagella of ptx1 are observed to consistently revert from synchrony to a state of stable, coupled, anti-phase beating dynamics. Incorporating the interpretation of the flagella pair as coupled noisy oscillators, we show how such behaviour corroborates readily with a secondary contribution to the coupling, which is further conjectured to be inherent in the wildtype. \newline [1] Polin M et al. \textit{Science}, 487-490, \textbf{2009}.   

Emergence of synchronisation in flagella of variable length

{\it Chlamydomonas reinhardtii} is a unicellular green alga that can swim by the concerted breaststroke-like beating of its two flagella. When the flagella are synchronised the organism moves along a straight helical path, while a large difference in the two beating frequencies induces sharp turns. Even in the synchronous state, however, the two flagella have slightly different intrinsic frequencies, and synchrony is guaranteed only by the presence of a sufficiently strong interflagellar coupling. Although the magnitude of this coupling is consistent with the value derived from a rough hydrodynamic estimate, no direct experimental test for the role of hydrodynamic in interflagellar coupling is available. In order to better understand the origin of interflagellar coupling, we employ high- speed imaging to study the dynamics of the two flagella of \textit{Chlamydomonas} as they regrow after mechanically induced deflagellation. Our results show that the duration of synchronised motion is strongly dependent on flagellar length. We discuss this dependence in light of hydrodynamic models of flagellar synchronisation.   

Fluid dynamics and noise in bacterial scattering

Bacterial communication through chemical and physical channels is permanently challenged by internal and external noise. While the role of stochastic fluctuations in quorum sensing has been widely studied both theoretically and experimentally, our understanding of hydrodynamic interactions between bacteria is limited by the absence of empirical data. Here, we report the first direct measurement of the fluid flow generated by an individual bacterium far away from and near to a wall. The experiments show that the micro-hydrodynamics of E. coli are considerably different from that of more complex eucaryotes as, for example, Chlamydomonas algae. We discuss the implications of our results for bacterial cell-cell and cell-wall interactions.