Structural responses of quasi-two-dimensional colloidal fluids to excitations elicited by nonequilibrium perturbations

Spatial Crossover Between Far-From-Equilibrium and Near-Equilibrium Dynamics in Locally Driven Suspensions

We examine the response of a quasi-two-dimensional colloidal suspension to a localized circular driving induced by optical tweezers. This approach allows us to resolve over 3 orders of magnitude in the Péclet number (Pe) and provide a direct observation of a sharp spatial crossover from far- to near-thermal-equilibrium regions of the suspension. In particular, particles migrate from high to low Pe regions and form strongly inhomogeneous steady-state density profiles with an emerging length scale that does not depend on the particle density and is set by Pe≈1. We show that the phenomenological two phase fluid constitutive model is in line with our results.

Complex dynamical interplay between solid particles and flow in driven granular suspensions

Granular materials immersed in a fluid are ubiquitous in daily life, industry, and nature. They include food processing, pastes, cosmetics, paints, concretes, cements, muds, wet sands, snows, landslides, and lava flow. They are known to exhibit a rich variety of complex rheological behavior, but the role of a fluid component in such behavior has remained poorly understood due to the nonlocal and many-body nature of hydrodynamic interactions between solid particles mediated by the fluid. We address this fundamental problem by comparing the microrheological response of athermal granular suspensions with and without hydrodynamic interactions to an externally driven probe particle by numerical simulations. We find that the presence of the fluid drastically increases the drag coefficient of the probe particle by more than one order of magnitude near the jamming transition. We reveal that this is a consequence of the nontrivial long-range nature of hydrodynamic interactions, which originates from unlimited cumulative transmission of near-field hydrodynamic interactions due to the incompressibility of both fluid and solid particles. Force chain formation of solid particles is dynamically coupled with hydrodynamic flow, leading to strong spatiotemporal fluctuations of flow pattern and nonlinear rheological response. Our study reveals essential roles of hydrodynamic interactions in complex rheological behavior of dense granular suspensions under an external drive.

Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex

To date investigations of the dynamics of driven colloidal systems have focused on hydrodynamic interactions and often employ optical (laser) tweezers for manipulation. However, the optical fields that provide confinement and drive also result in electrodynamic interactions that are generally neglected. We address this issue with a detailed study of interparticle dynamics in an optical ring vortex trap using 150-nm diameter Ag nanoparticles. We term the resultant electrodynamically interacting nanoparticles a driven optical matter system. We also show that a superior trap is created by using a Au nanoplate mirror in a retroreflection geometry, which increases the electric field intensity, the optical drive force, and spatial confinement. Using nanoparticles versus micron sized colloids significantly reduces the surface hydrodynamic friction allowing us to access small values of optical topological charge and drive force. We quantify a further 50% reduction of hydrodynamic friction when the nanoparticles are driven over the Au nanoplate mirrors versus over a mildly electrostatically repulsive glass surface. Further, we demonstrate through experiments and electrodynamics-Langevin dynamics simulations that the optical drive force and the interparticle interactions are not constant around the ring for linearly polarized light, resulting in a strong position-dependent variation in the nanoparticle velocity. The nonuniformity in the optical drive force is also manifest as an increase in fluctuations of interparticle separation, or effective temperature, as the optical driving force is increased. Finally, we resolve an open issue in the literature on periodic modulation of interparticle separation with comparative measurements of driven 300-nm-diameter polystyrene beads that also clearly reveal the significance of electrodynamic forces and interactions in optically driven colloidal systems. Therefore, the modulations in the optical forces and electrodynamic interactions that we demonstrate should not be neglected for dielectric particles and might give rise to some structural and dynamic features that have previously been attributed exclusively to hydrodynamic interactions.

Driven tracers in narrow channels

Steady-state properties of a driven tracer moving in a narrow two-dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one-dimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean-field theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.

Correlated two-particle diffusion in dense colloidal suspensions at early times: Theory and comparison to experiment

The spatially resolved diffusive dynamic cross correlations of a pair of colloids in dense quasi-two-dimensional monolayers of identical particles are studied experimentally and theoretically at early times where motion is Fickian. In very dense systems where strong oscillatory equilibrium packing correlations are present, we find an exponential decay of the dynamic cross correlations on small and intermediate length scales. At large separations where structure becomes random, an apparent power law decay with an exponent of approximately -2.2 is observed. For a moderately dense suspension where local structural correlations are essentially absent, this same apparent power law decay is observed over all probed interparticle separations. A microscopic nonhydrodynamic theory is constructed for the dynamic cross correlations which is based on interparticle frictional effects and effective structural forces. Hydrodynamics enters only via setting the very short-time single-particle self-diffusion constant. No-adjustable-parameter quantitative predictions of the theory for the dynamic cross correlations are in good agreement with experiment over all length scales. The origin of the long-range apparent power law is the influence of the constraint of fixed interparticle separation on the amplitude of the mean square force exerted on the two tagged particles by the surrounding fluid. The theory is extended to study high-packing-fraction 3D hard sphere fluids. The same pattern of an oscillatory exponential form of the dynamic cross correlation function is predicted in the structural regime, but the long-range tail decays faster than in monolayers with an exponent of -3.

Local-heterogeneous responses and transient dynamics of cage breaking and formation in colloidal fluids

Quantifying the interactions in dense colloidal fluids requires a properly designed order parameter. We present a modified bond-orientational order parameter, ψ̄6, to avoid problems of the original definition of bond-orientational order parameter. The original bond-orientational order parameter can change discontinuously in time but our modified order parameter is free from the discontinuity and, thus, it is a suitable measure to quantify the dynamics of the bond-orientational ordering of the local surroundings. Here we analyze ψ̄6 in a dense driven monodisperse quasi-two-dimensional colloidal fluids where a single particle is optically trapped at the center. The perturbation by the trapped and driven particle alters the structure and dynamics of the neighboring particles. This perturbation disturbs the flow and causes spatial and temporal distortion of the bond-orientational configuration surrounding each particle. We investigate spatio-temporal behavior of ψ̄6 by a Wavelet transform that provides a time-frequency representation of the time series of ψ̄6. It is found that particles that have high power in frequencies corresponding to the inverse of the timescale of perturbation undergo distortions of their packing configurations that result in cage breaking and formation dynamics. To gain insight into the dynamic structure of cage breaking and formation of bond-orientational ordering, we compare the cage breaking and formation dynamics with the underlying dynamical structure identified by Lagrangian Coherent Structures (LCSs) estimated from the finite-time Lyapunov exponent (FTLE) field. The LCSs are moving separatrices that effectively divide the flow into distinct regions with different dynamical behavior. It is shown that the spatial distribution of the FTLE field and the power of particles in the wavelet transform have positive correlation, implying that LCSs provide a dynamic structure that dominates the dynamics of cage breaking and formation of the colloidal fluids.

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.