Crossover from intermittent to continuum dynamics for locally driven colloids

CM, Martínez Fernández R, Betterelli Giuliano C, Zhang R, Valeriani C, Wilson LG. The carnivorous plant Genlisea harnesses active particle dynamics to prey on microfauna

Carnivory in plants is an unusual trait that has arisen multiple times, independently, throughout evolutionary history. Plants in the genus Genlisea are carnivorous and feed on microorganisms that live in soil using modified subterranean leaf structures (rhizophylls). A surprisingly broad array of microfauna has been observed in the plants' digestive chambers, including ciliates, amoebae, and soil mites. Here, we show, through experiments and simulations, that Genlisea exploit active matter physics to "rectify" bacterial swimming and establish a local flux of bacteria through the structured environment of the rhizophyll toward the plant's digestion vesicle. In contrast, macromolecular digestion products are free to diffuse away from the digestion vesicle and establish a concentration gradient of carbon sources to draw larger microorganisms further inside the plant. Our experiments and simulations show that this mechanism is likely to be a localized one and that no large-scale efflux of digested matter is present.

Yield stress fluids and fundamental particle statistics

Yield stress in complex fluids is described by resorting to fundamental statistical mechanics for clusters with different particle occupancy numbers. Probability distribution functions are determined for canonical ensembles of volumes displaced at the incipient motion in three representative states (single, double, and multiple occupancies). The statistical average points out an effective solid fraction by which the yield stress behavior is satisfactorily described in a number of aqueous (Si3N4, Ca3(PO4)2, ZrO2, and TiO2) and non-aqueous (Al2O3/decalin and MWCNT/PC) disperse systems. Interestingly, the only two model coefficients (maximum packing fraction and stiffness parameter) turn out to be correlated with the relevant suspension quantities. The latter relates linearly with (Young's and bulk) mechanical moduli, whereas the former, once represented versus the Hamaker constant of two particles in a medium, returns a good linear extrapolation of the packing fraction for the simple cubic cell, here recovered within a relative error ≈ 1.3%.

Colloidal particles driven across periodic optical-potential-energy landscapes

We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. First, the average particle velocity is found as a function of the driving velocity and the wavelength of the optical potential energy landscape. The relationship between average particle velocity and driving velocity is found to be well described by a theoretical model treating the landscape as sinusoidal, but only at small trap spacings. At larger trap spacings, a nonsinusoidal model for the landscape must be used. Subsequently, the critical velocity required for a particle to move across the landscape is determined as a function of the wavelength of the landscape. Finally, the velocity of a particle driven at a velocity far exceeding the critical driving velocity is examined. Both of these results are again well described by the two theoretical routes for small and large trap spacings, respectively. Brownian motion is found to have a significant effect on the critical driving velocity but a negligible effect when the driving velocity is high.

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Colloidal lattice shearing and rupturing with a driven line of particles

We examine the dynamics of two-dimensional colloidal systems using numerical simulations of a system with a drive applied to a thin region in the middle of the sample to produce a local shear. For a monodisperse colloidal assembly, we find a well-defined decoupling transition separating a regime of elastic motion from a plastic phase where the driven particles break away or decouple from the bulk particles and produce a shear band. For a bidisperse assembly, the onset of a bulk disordering transition coincides with the broadening of the shear band. We identify several distinct dynamical regimes that are correlated with features in the velocity-force curves. As a function of bidispersity, the decoupling force shows a nonmonotonic behavior associated with features in the noise fluctuations, power spectra, and bulk velocity profiles. When pinning is added in the bulk, we find that the shear band regions can become more localized, causing a decoupling of the driven particles from the bulk particles. For a system with thermal noise and no pinning, the shear band region becomes more extended and the average velocity of the driven particles drops at the thermal disordering transition of the bulk system.

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Micro-rheology on (polymer-grafted) colloids using optical tweezers

Optical tweezers are experimental tools with extraordinary resolution in positioning (± 1 nm) a micron-sized colloid and in the measurement of forces (± 50 fN) acting on it-without any mechanical contact. This enables one to carry out a multitude of novel experiments in nano- and microfluidics, of which the following will be presented in this review: (i) forces within single pairs of colloids in media of varying concentration and valency of the surrounding ionic solution, (ii) measurements of the electrophoretic mobility of single colloids in different solvents (concentration, valency of the ionic solution and pH), (iii) similar experiments as in (i) with DNA-grafted colloids, (iv) the nonlinear response of single DNA-grafted colloids in shear flow and (v) the drag force on single colloids pulled through a polymer solution. The experiments will be described in detail and their analysis discussed.

Fluctuations, jamming, and yielding for a driven probe particle in disordered disk assemblies

Using numerical simulations we examine the velocity fluctuations and velocity-force curve characteristics of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of ϕJ=0.843. As ϕ increases toward ϕJ, the average velocity of the probe particle decreases and the velocity fluctuations show an increasingly intermittent or avalanchelike behavior. When ϕ is within a few percent of the jamming density, the velocity distributions are exponential, while when ϕ is less than 1% away from jamming, the velocity distributions have a power-law character with exponents in agreement with recent experiments. The velocity power spectra exhibit a crossover from a Lorentzian form to a 1/f shape near jamming. We extract a correlation length exponent ν which is in good agreement with recent shear simulations. For ϕ>ϕJ, there is a critical threshold force F(c) that must be applied for the probe particle to move through the sample which increases with increasing ϕ. The velocity-force curves are linear below jamming, while at jamming they have a power-law form. The onset of the probe motion above ϕJ occurs via a local yielding of the particles around the probe particle which we term a local shear banding effect.

Diffusion in two-dimensional colloidal systems on periodic substrates

We study the diffusive behavior of two-dimensional charged colloidal suspensions subjected to a sinusoidal substrate by means of Brownian dynamics simulations. We mainly focus on the dependence of the mean-square displacement on the substrate strength. Our findings show a variation in the particle diffusion due to a substrate-induced distortion of the dynamic cage of nearest-neighbor colloids. This mechanism leads to a transition from normal diffusion at short times to subdiffusion on intermediate time scales. However, at long times normal diffusion is recovered. We also show that the variation in the long-time self-diffusion coefficient may be associated with the freezing and re-entrant melting transitions.

Colloids dragged through a polymer solution: Experiment, theory, and simulation

We present microrheological measurements of the drag force on colloids pulled through a solution of lambda-DNA (used here as a monodisperse model polymer) with an optical tweezer. The experiments show a drag force that is larger than expected from the Stokes formula and the independently measured viscosity of the DNA solution. We attribute this to the accumulation of DNA in front of the colloid and the reduced DNA density behind the colloid. This hypothesis is corroborated by a simple drift-diffusion model for the DNA molecules, which reproduces the experimental data surprisingly well, as well as by corresponding Brownian dynamics simulations.

Dressing of driven colloidal particles in a subcritical liquid suspension

At equilibrium, colloidal particles in a subcritical liquid suspension are surrounded by a drying layer if the colloid has solvophobic interaction. Using Brownian dynamics computer simulations, we investigate the nonequilibrium response of this layer to a strong external driving force. We find that the driven colloidal particle dresses itself with more particles than in the equilibrium drying layer. The effective interaction between two such dressed particles exhibits a deep drive-induced attraction due to a stretched joint gas bubble.

Viscous decoupling transitions for individually dragged particles in systems with quenched disorder

We show that when an individual particle is dragged through an assembly of other particles in the presence of quenched disorder, a viscous decoupling transition occurs between the dragged particle and the surrounding particles which is controlled by the quenched disorder. A counterintuitive consequence of this transition is that the velocity of the dragged particle can be increased by increasing the strength or density of the quenched disorder. The decoupling transition can also occur when the external drive on the dragged particle is increased and is observable as a clear signature in the velocity-force response.

Rhythmic cluster generation in strongly driven colloidal dispersions

We study the response of a nematic colloidal dispersion of rods to a driven probe particle which is dragged with high speed through the dispersion perpendicular to the nematic director. In front of the dragged particle, clusters of rods are generated which rhythmically grow and dissolve by rotational motion. We find evidence for a mesoscopic cluster-cluster correlation length, independent of the imposed drag speed. Our results are based on nonequilibrium Brownian dynamics computer simulations and in line with a dynamical scaling theory.

Cooperative behavior and pattern formation in mixtures of driven and nondriven colloidal assemblies

We simulate a disordered assembly of particles interacting through a repulsive Yukawa potential with a small fraction of the particles coupled to an external drive. Distortions in the arrangement of the nondriven particles produce a dynamically induced effective attraction between the driven particles, giving rise to intermittent one-dimensional stringlike structures. The velocity of a moving string increases with the number of driven particles in the string. We identify the average stable string length as a function of driving force, background particle density, and particle charge. This model represents a type of collective transport system composed of interacting particles moving through deformable disorder.