Flagella bending affects macroscopic properties of bacterial suspensions.

To survive in harsh conditions, motile bacteria swim in complex environments and respond to the surrounding flow. Here, we develop a mathematical model describing how flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease in the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random reorientation) as was previously done to explain the viscosity reduction. Second, we demonstrate how a bacterium escapes from wall entrapment due to the self-induced buckling of flagella. Our results shed light on the role of flexible bacterial flagella in interactions of bacteria with shear flow and walls or obstacles.

Flexibility of bacterial flagella in external shear results in complex swimming trajectories.

Many bacteria use rotating helical flagella in swimming motility. In the search for food or migration towards a new habitat, bacteria occasionally unbundle their flagellar filaments and tumble, leading to an abrupt change in direction. Flexible flagella can also be easily deformed by external shear flow, leading to complex bacterial trajectories. Here, we examine the effects of flagella flexibility on the navigation of bacteria in two fundamental shear flows: planar shear and Poiseuille flow realized in long channels. On the basis of slender body elastodynamics and numerical analysis, we discovered a variety of non-trivial effects stemming from the interplay of self-propulsion, elasticity and shear-induced flagellar bending. We show that in planar shear flow the bacteria execute periodic motion, whereas in Poiseuille flow, they migrate towards the centre of the channel or converge towards a limit cycle. We also find that even a small amount of random reorientation can induce a strong response of bacteria, leading to overall non-periodic trajectories. Our findings exemplify the sensitive role of flagellar flexibility and shed new light on the navigation of bacteria in complex shear flows.

Model of dynamic self-assembly in ferromagnetic suspensions at liquid interfaces.

Ferromagnetic microparticles suspended at the interface between immiscible liquids and energized by an external alternating magnetic field show a rich variety of self-assembled structures, from linear snakes to radial asters. In order to obtain insight into the fundamental physical mechanisms and the overall balance of forces governing self-assembly, we develop a modeling approach based on analytical solutions of the time-averaged Navier-Stokes equations. These analytical expressions for the self-consistent hydrodynamic flows are then employed to modify effective interactions between the particles, which in turn are formulated in terms of the time-averaged quantities. Our method allows effective computational verification of the mechanisms of self-assembly and leads to a testable prediction, e.g., on the transitions between various patterns versus viscosity of the solvent.

Collision of microswimmers in a viscous fluid.

We investigate the effects of boundary conditions on the surface of self-propelled spherical swimmers moving in a viscous fluid with a low Reynolds number. We first show that collisions between the swimmers are impossible under the commonly used no-slip conditions. Next we demonstrate that collisions do occur if the more general Navier boundary conditions, allowing for a finite slip on the surface that produces drag, are imposed on the boundary of swimmers. The presence of a small inertia for each swimmer does not influence whether collisions occur between swimmers.

Viscosity control of the dynamic self-assembly in ferromagnetic suspensions.

Recent studies of dynamic self-assembly in ferromagnetic colloids suspended in liquid-air or liquid-liquid interfaces revealed a rich variety of dynamic structures ranging from linear snakes to axisymmetric asters, which exhibit novel morphology of the magnetic ordering accompanied by large-scale hydrodynamic flows. Based on controlled experiments and first principles theory, we argue that the transition from snakes to asters is governed by the viscosity of the suspending liquid where less viscous liquids favor snakes and more viscous, asters. By obtaining analytic solutions of the time-averaged Navier-Stokes equations, we gain insight into the role of mean hydrodynamic flows and an overall balance of forces governing the self-assembly. Our results illustrate that the viscosity can be used to control the outcome of the dynamic self-assembly in magnetic colloidal suspensions.

Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations.

Recently, there has been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosity significantly smaller than the viscosity of the ambient fluid. This is in sharp contrast with suspensions of hard passive inclusions, whose presence always increases the viscosity. Here we present a 2D model for a suspension of microswimmers in a fluid and analyze it analytically in the dilute regime (no swimmer-swimmer interactions) and numerically using a Mimetic Finite Difference discretization. Our analysis shows that in the dilute regime (in the absence of rotational diffusion) the effective shear viscosity is not affected by self-propulsion. But at the moderate concentrations (due to swimmer-swimmer interactions) the effective viscosity decreases linearly as a function of the propulsion strength of the swimmers. These findings prove that (i) a physically observable decrease of viscosity for a suspension of self-propelled microswimmers can be explained purely by hydrodynamic interactions and (ii) self-propulsion and interaction of swimmers are both essential to the reduction of the effective shear viscosity. We also performed a number of numerical experiments analyzing the dynamics of swimmers resulting from pairwise interactions. The numerical results agree with the physically observed phenomena (e.g., attraction of swimmer to swimmer and swimmer to the wall). This is viewed as an additional validation of the model and the numerical scheme.

Model for dynamic self-assembled magnetic surface structures.

We propose a first-principles model for the dynamic self-assembly of magnetic structures at a water-air interface reported in earlier experiments. The model is based on the Navier-Stokes equation for liquids in shallow water approximation coupled to Newton equations for interacting magnetic particles suspended at a water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snakelike structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids.

Magnetically driven surface mixing.

Magnetic microparticles suspended on the surface of liquid and energized by vertical alternating magnetic field exhibit complex collective behavior. Various immobile and self-propelled self-assembled structures have been observed. Here, we report on experimental studies of mixing and surface diffusion processes in this system. We show that the pattern-induced surface flows have properties of quasi-two-dimensional turbulence. Correspondingly, the surface advection of tracer particle exhibits properties of Brownian diffusion.

Self-assembled magnetic surface swimmers.

We report studies of novel self-assembled magnetic surface swimmers (magnetic snakes) formed from a dispersion of magnetic microparticles at a liquid-air interface and energized by an alternating magnetic field. We show that under certain conditions the snakes spontaneously break the symmetry of surface flows and turn into self-propelled objects. Parameters of the driving magnetic field tune the propulsion velocity of these snakelike swimmers. We find that the symmetry of the surface flows can also be broken in a controlled fashion by attaching a large bead to a magnetic snake (bead-snake hybrid), transforming it into a self-locomoting entity. The observed phenomena have been successfully described by a phenomenological model based on the amplitude equation for surface waves coupled to a large-scale hydrodynamic mean flow equation.

Collective alignment of polar filaments by molecular motors.

We study the alignment of polar biofilaments, such as microtubules and actin, subject to the action of multiple molecular motors attached simultaneously to more than one filament. Focusing on a paradigm model of only two filaments interacting with multiple motors, we were able to investigate in detail the alignment dynamics. While almost no alignment occurs in the case of a single motor, the filaments become rapidly aligned due to the collective action of the motors. Our analysis shows that the alignment time is governed by the number of bound motors and the magnitude of the motors' stepping fluctuations. We predict that the time scale of alignment is in the order of seconds, much faster than that reported for passive crosslink-induced bundling. In vitro experiments on the alignment of microtubules by multiple-motor covered beads are in qualitative agreement. We also discuss another mode of fast alignment of filaments, namely the cooperation between motors and passive crosslinks.

Comment on "Long-lived giant number fluctuations in a swarming granular nematic".

Narayan et al. (Reports, 6 July 2007, p. 105) reported giant number fluctuations attributed to curvature-driven active currents specific for nonequilibrium nematic systems. We present data demonstrating that similar results can be found in systems of spherical particles due either to inelastic clustering or persistent density inhomogeneity, suggesting two alternative explanations for their results.

Driven magnetic particles on a fluid surface: pattern assisted surface flows.

Magnetic microparticles suspended on the liquid-air interface and subjected to an alternating magnetic field exhibit spontaneous formation of dynamic localized snake patterns. These patterns are accompanied by four large-scale hydrodynamic vortices located at the opposite ends of the snake patterns. We report detailed studies of these large-scale vortices and their relationship to the collective response of magnetic particles in the presence of an alternating magnetic field. We present a model based on the amplitude equation for surface waves coupled to the large-scale hydrodynamic mean flow equation. The model describes both the formation of the dynamic snake patterns and the induced structure of the experimentally observed hydrodynamic flows.

Dynamic self-assembly of magnetic particles on the fluid interface: surface-wave-mediated effective magnetic exchange.

We report on studies of dynamic self-assembled structures induced by a vertical alternating magnetic field in an ensemble of magnetic particles suspended on a liquid surface. We find the formation of nontrivially ordered dynamic snakelike objects in a certain range of field magnitudes and frequencies. In order to probe the properties of the "snakes," we study their magnetic response to in-plane magnetic field applied at different angles with respect to its axis. The segments of the snake exhibit long-range antiferromagnetic ordering mediated by the surface waves, while each segment is composed of ferromagnetically aligned chains of microparticles. We propose a simple phenomenological model where the effect of surface waves is replaced by an effective exchange interaction to describe the observations. In the framework of the proposed model, the effective exchange constant corresponding to different regimes of magnetic driving was extracted from the experimental data.

Surface wave assisted self-assembly of multidomain magnetic structures.

An ensemble of magnetic microparticles at the liquid surface displays novel snakelike self-assembled structures induced by an alternating magnetic field. We demonstrate that these structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. The segments of the "snake" exhibit long-range antiferromagnetic ordering, while each segment is composed of ferromagnetically aligned chains of microparticles. The structures exhibit magnetic hysteretic behavior with respect to an external in-plane magnetic field and logarithmic relaxation of the remanent magnetic moment.

Self-diffusion of particles in gas-driven granular layers with periodic flow modulation.

We study self-diffusion of particles in gas-driven granular layers by high-speed fluorescent video microscopy. We show that periodic flow modulation results in an enhancement of the particle's diffusion. The diffusion enhancement, which in turn is an indication of more efficient fluidization of the granular layer, is associated with the onset of disordered subharmonic patterns. Our measurements provide a sensitive characterization method of the fluidization properties of particulate-gas systems.

Velocity distributions of granular gases with drag and with long-range interactions.

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.

Structure formation in electromagnetically driven granular media.

We report structure formation in submonolayers of magnetic microparticles subjected to periodic electrostatic and magnetic excitations. Depending on the excitation parameters, we observe the formation of a rich variety of structures: clusters, rings, chains, and networks. The dynamics and shapes of the structures are strongly dependent on the amplitude and frequency of the external magnetic field. We find that for pure ac magnetic driving the low-frequency magnetic excitation favors compact clusters, whereas high frequency driving favors chains and netlike structures. An abrupt phase transition from chains to a network phase was observed for a high density of particles.

Far-from-equilibrium Ostwald ripening in electrostatically driven granular powders.

We report an experimental study of cluster size distributions in electrostatically driven granular submonolayers. The cluster size distribution in this far-from-equilibrium process exhibits dynamic scaling behavior characteristic of the (nearly equilibrium) Ostwald ripening, controlled by the attachment and detachment of the "gas" particles. The scaled size distribution, however, is different from the classical Wagner distribution obtained in the limit of a vanishingly small area fraction of the clusters. A much better agreement is found with the theory of Phys. Rev. E 65, 046117 (2002)] which accounts for the cluster merger.

Self-assembly and vortices formed by microparticles in weak electrolytes.

We carried out experimental studies of the self-assembly of metallic micron-size particles in poorly conducting liquid subject to a constant electric field. Depending on the experimental conditions, the particles self-assemble into long chains directed along the electric field lines and form vortices and other structures. The vortices perform Brownian-type random motion due to self-induced chaotic hydrodynamic flows. We measured the diffusivity constant of the vortices and the conductivity and mechanical stiffness of the chains.

Theory of pattern formation of metallic microparticles in poorly conducting liquids.

We develop a continuum theory of self-assembly and pattern formation in metallic microparticles immersed in a poorly conducting liquid in a dc electric field. The theory is formulated in terms of conservation laws for the densities of immobile particles (precipitate) and bouncing particles (gas) coupled to the Navier-Stokes equation for the liquid. This theory successfully reproduced the correct topology of the phase diagram and primary patterns observed in the experiment [Phys. Rev. Lett. 90, 114301 (2003)]]: static crystals, honeycombs, dynamic pulsating rings, and rotating multipetal vortices.