Three-dimensional imaging of colloidal glasses under steady shear

A double rigidity transition rules the fate of drying colloidal drops

The evaporation of drops of colloidal suspensions plays an important role in numerous contexts, such as the production of powdered dairies, the synthesis of functional supraparticles, and virus and bacteria survival in aerosols or drops on surfaces. The presence of colloidal particles in the evaporating drop eventually leads to the formation of a dense shell that may undergo a shape instability. Previous works propose that, for drops evaporating very fast, the instability occurs when the particles form a rigid porous solid, constituted of permanently aggregated particles at random close packing. To date, however, no measurements could directly test this scenario and assess whether it also applies to drops drying at lower evaporation rates, severely limiting our understanding of this phenomenon and the possibility of harnessing it in applications. Here, we combine macroscopic imaging and space- and time-resolved measurements of the microscopic dynamics of colloidal nanoparticles in drying drops sitting on a hydrophobic surface, measuring the evolution of the thickness of the shell and the spatial distribution and mobility of the nanoparticles. We find that, above a threshold evaporation rate, the drop undergoes successively two distinct shape instabilities, invagination and cracking. While permanent aggregation of nanoparticles accompanies the second instability, as hypothesized in previous works on fast-evaporating drops, we show that the first one results from a reversible glass transition of the shell, unreported so far. We rationalize our findings and discuss their implications in the framework of a unified state diagram for the drying of colloidal drops sitting on a hydrophobic surface.

Percolation of a fine particle in static granular beds

We study the percolation of a fine spherical particle under gravity in static randomly packed large-particle beds with different packing densities ϕ and large to fine particle size ratios R ranging from 4 to 7.5 using discrete element method simulations. The particle size ratio at the geometrical trapping threshold, defined by three touching large particles, R_{t}=sqrt[3]/(2-sqrt[3])=6.464, divides percolation behavior into passing and trapping regimes. However, the mean percolation velocity and diffusion of untrapped fine particles, which depend on both R and ϕ, are similar in both regimes and can be collapsed over a range of R and ϕ with the appropriate scaling. An empirical relationship for the local percolation velocity based on the local pore throat to fine particle size ratio and packing density is obtained, which is valid for the full range of size ratio and packing density we study. Similarly, in the trapping regime, the probability for a fine particle to reach a given depth is well described by a simple statistical model. Finally, the percolation velocity and fine particle diffusion are found to decrease with increasing restitution coefficient.

Origin of Two Distinct Stress Relaxation Regimes in Shear Jammed Dense Suspensions

Many dense particulate suspensions show a stress induced transformation from a liquidlike state to a solidlike shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly nonexponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and normal stress measurements confirm that such stress discontinuity originates from the localized plastic events, whereas system spanning dilation controls the slower relaxation process. We also find an intriguing correlation between the nature of transient relaxation and the steady-state shear jamming phase diagram obtained from the Wyart-Cates model.

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

The rheology of confined colloidal hard disks

Colloids may be treated as “big atoms” so that they are good models for atomic and molecular systems. Colloidal hard disks are, therefore, good models for 2d materials, and although their phase behavior is well characterized, rheology has received relatively little attention. Here, we exploit a novel, particle-resolved, experimental setup and complementary computer simulations to measure the shear rheology of quasi-hard-disk colloids in extreme confinement. In particular, we confine quasi-2d hard disks in a circular “corral” comprised of 27 particles held in optical traps. Confinement and shear suppress hexagonal ordering that would occur in the bulk and create a layered fluid. We measure the rheology of our system by balancing drag and driving forces on each layer. Given the extreme confinement, it is remarkable that our system exhibits rheological behavior very similar to unconfined 2d and 3d hard particle systems, characterized by a dynamic yield stress and shear-thinning of comparable magnitude. By quantifying particle motion perpendicular to shear, we show that particles become more tightly confined to their layers with no concomitant increase in density upon increasing the shear rate. Shear thinning is, therefore, a consequence of a reduction in dissipation due to weakening in interactions between layers as the shear rate increases. We reproduce our experiments with Brownian dynamics simulations with Hydrodynamic Interactions (HI) included at the level of the Rotne–Prager tensor. That the inclusion of HI is necessary to reproduce our experiments is evidence of their importance in transmission of momentum through the system.

Direct Imaging of Contacts and Forces in Colloidal Gels

Colloidal dispersions are prized as model systems to understand basic properties of materials, and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulation. However in amorphous materials, relating mechanical properties, and failure in particular to microscopic structure remains problematic. Here we address this challenge by studying the contacts and the forces between particles, as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load--bearing droplets, and local stress anisotropy, and investigate their connection with locally rigid packings of the droplets.

Transition in the Glassy Dynamics of Melts of Acid-Hydrolyzed Phytoglycogen Nanoparticles

The deformability, responsiveness, and tunability of soft nanoparticles (NPs) offer unique opportunities to learn about their complex properties and the interactions between particles. In the present study, we provide new insights into the physical properties of phytoglycogen (PG) NPs, which are soft, compact particles with a dendritic architecture that are produced in the kernels of sweet corn. In particular, we study PG NPs modified using acid hydrolysis, which not only reduces their diameter but also alters their stiffness, internal structure, and the interactions between particles in aqueous dispersions. We used steady shear rheology to determine the dependence of the relative zero-shear viscosity η_r of aqueous dispersions of acid-hydrolyzed PG NPs on the effective volume fraction ϕ_eff, which indicated a reduction in stiffness of the particles relative to that of native PG NPs. We quantified this difference by analyzing the nature of the colloidal glasses formed at high ϕ_eff. We measured a smaller value of the fragility index m for acid-hydrolyzed PG NP glasses than that for native PG NP glasses, indicating that acid-hydrolyzed PG NPs form stronger glasses and are therefore softer than native PG NPs. Unlike the native PG NPs, we observed a distinctive change in the character of the glass transition of the acid-hydrolyzed PG NPs as ϕ_eff was increased above ϕ_eff∼1: a crossover in the dependence of η_r on ϕ_eff from Vogel-Fulcher-Tammann behavior to a more gradual, Arrhenius-like behavior. By expressing the steady shear and oscillatory rheology data in terms of generalized Péclet numbers, we obtained collapse of the data onto master curves. We interpret this result in terms of the acid-hydrolyzed PG NPs predominantly interpenetrating neighboring particles at large ϕ_eff, for which fluctuations of the outer chains enhance the mobility of the particles and make α-relaxation times τ_α experimentally accessible.

Role of Local Structure in the Enhanced Dynamics of Deformed Glasses

External stress can accelerate molecular mobility of amorphous solids by several orders of magnitude. The changes in mobility are commonly interpreted through the Eyring model, which invokes an empirical activation volume. Here, we analyze constant-stress molecular dynamics simulations and propose a structure-dependent Eyring model, connecting activation volume to a machine-learned field, softness. We show that stress has a heterogeneous effect on the mobility that depends on local structure through softness. The barrier impeding relaxation reduces more for well-packed particles, which explains the narrower distribution of relaxation time observed under stress.

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.

Two step micro-rheological behavior in a viscoelastic fluid

We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.

Particle sizing for flowing colloidal suspensions using flow-differential dynamic microscopy

Particle size is a key variable in understanding the behaviour of the particulate products that underpin much of our modern lives. Typically obtained from suspensions at rest, measuring the particle size under flowing conditions would enable advances for in-line testing during manufacture and high-throughput testing during development. However, samples are often turbid, multiply scattering light and preventing the direct use of common sizing techniques. Differential dynamic microscopy (DDM) is a powerful technique for analysing video microscopy of such samples, measuring diffusion and hence particle size without the need to resolve individual particles while free of substantial user input. However, when applying DDM to a flowing sample, diffusive dynamics are rapidly dominated by flow effects, preventing particle sizing. Here, we develop "flow-DDM", a novel analysis scheme that combines optimised imaging conditions, a drift-velocity correction and modelling of the impact of flow. Flow-DDM allows a decoupling of flow from diffusive motion that facilitates successful particle size measurements at flow speeds an order of magnitude higher than for DDM. We demonstrate the generality of the technique by applying flow-DDM to two separate microscopy methods and flow geometries.

Wide-angle static and dynamic light scattering under shear

We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with a sub-micron characteristic length scale. The shear device consists in two parallel plates, and the optical setup allows us to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus: a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.

Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase

Colloidal particles have been extensively used to comprehend the main principles governing liquid-crystal nucleation. Multiple mechanisms and frameworks have been proposed, through either experiments or computational approaches, to rationalise the ubiquitous formation of colloidal crystals. In this work, we elucidate the nucleation scenario behind the crystallization of oppositely charged colloids. By performing molecular dynamics simulations of colloidal electrolytes in combination with the Seeding technique, we evaluate the fundamental factors, such as the nucleation rate, free energy barrier, surface tension and kinetic pre-factor, that determine the liquid-to-solid transition of several crystalline polymorphs. Our results show that at a high packing fraction, there is a cross-over between the nucleation of the CsCl structure and that of a substitutionally disordered fcc phase, despite the CuAu crystal being the most stable phase. We demonstrate that the crucial factor in determining which phase nucleates the fastest is the free energy cost of the cluster formation rather than their kinetic ability to grow from the liquid. While at a low packing fraction, the stable phase, CsCl, is the one that nucleates and subsequently grows, we show how at moderate and high packing fractions, a disordered fcc phase subsequently grows regardless of the nature of the nucleating phase, termed parasitic crystallization. Taken together, our results provide a panoramic perspective of the complex nucleation scenario of oppositely charged colloids at moderate temperature and rationalise the different thermodynamic and kinetic aspects behind it.

Microscopic origin of shear banding as a localized driven glass transition in compressed colloidal pillars

Here we report on compression experiments of colloidal pillars in which the evolution of a shear band can be followed at the particle level during deformation. Quasistatic deformation results in dilation and anisotropic changes in coordination in a localized band of material. Additionally, a transition from solid- to liquidlike mechanical response accompanies the structural change in the band, as evidenced by saturation of the packing fraction at the glass transition point, a diminishing ability to host anelastic strains, and a rapid decay in the long-range strain correlations. Overall, our results suggest that shear banding quantitatively resembles a localized, driven glass transition.

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Rheological similarities between dense self-propelled and sheared particulate systems

Different from previous modeling of self-propelled particles, we develop a method to propel particles with a constant average velocity instead of a constant force. This constant propulsion velocity (CPV) approach is validated by its agreement with the conventional constant propulsion force (CPF) approach in the flowing regime. However, the CPV approach shows its advantage of accessing quasistatic flows of yield stress fluids with a vanishing propulsion velocity, while the CPF approach is usually unable to because of finite system size. Taking this advantage, we realize cyclic self-propulsion and study the evolution of the propulsion force with the propelled particle displacement, both in the quasistatic flow regime. By mapping the shear stress and shear rate to the propulsion force and propulsion velocity, we find similar rheological behaviors of self-propelled systems to sheared systems, including the yield force gap between the CPF and CPV approaches, propulsion force overshoot, reversible-irreversible transition under cyclic propulsion, and propulsion bands in plastic flows. These similarities suggest underlying connections between self-propulsion and shear, although they act on systems in different ways.

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated β-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the "stretching exponent" β quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

Dynamical Heterogeneity near Glass Transition Temperature under Shear Conditions

We experimentally studied the shear effect on dynamical heterogeneity near glass transition temperature. X-ray photon correlation spectroscopy was utilized to study the dynamics of polyvinyl acetate with tracer particles near its glass transition temperature, to determine the local shear rate from the anisotropic behavior of the time autocorrelation function and to calculate the dynamical heterogeneity using higher-order correlation function. The obtained results show a decrease in the dynamical heterogeneity and faster dynamics with increasing shear rate. This is the first experimental result that proved the predictions of previous molecular dynamics simulations.

Droplet clustering in cyclodextrin-based emulsions mediated by methylcellulose

Rapid droplet aggregation in cyclodextrin (CD)-stabilized emulsions limits their practical use as material templates. Herein, we formulate mixtures of submicron CD-based emulsion droplets suspended in aqueous solutions of methylcellulose (MC) with various concentrations and molecular weights. We evaluate the effects of MC on the microstructure and stability of the emulsions using different techniques including optical microscopy, laser particle analysis, confocal laser scanning microscopy and multiple light scattering, explore the rheological behavior of the emulsions through large amplitude oscillatory shear experiments, and study the viscoelastic nonlinearities of the emulsions as a function of strain and strain-rate space through nondimensional elastic and viscous Lissajous-Bowditch plots. It is demonstrated that the emulsion droplets are present in the form of small clusters and their size is almost independent of MC concentration and molecular weight. The clustering pattern is also supported by the changes in viscoelastic properties of the emulsions and the intracycle nonlinear behavior of the Lissajous-Bowditch plots. We propose for the first time that glass-like dynamic arrest takes place with the formation of small equilibrium droplet clusters in the situation where the CD-based emulsion droplets are forced by depletion flocculation and kinetic trapping simultaneously exerted by MC.

Structure-Property Relationships via Recovery Rheology in Viscoelastic Materials

The recoverable strain is shown to correlate to the temporal evolution of microstructure via time-resolved small-angle neutron scattering and dynamic shear rheology. Investigating two distinct polymeric materials of wormlike micelles and fibrin network, we demonstrate that, in addition to the nonlinear structure-property relationships, the shear and normal stress evolution is dictated by the recoverable strain. A distinct sequence of physical processes under large amplitude oscillatory shear (LAOS) is identified that clearly contains information regarding both the steady-state flow curve and the linear-regime frequency sweep, contrary to most interpretations that LAOS responses are either distinct from or somehow intermediate between the two cases. This work provides a physically motivated and straightforward path to further explore the structure-property relationships of viscoelastic materials under dynamic flow conditions.

Impact of mechanical history on sludge rheological properties: Role of the organic content

The rheological behavior is known to be of great interest in sludge treatment, but the material complexity induces strong measurement difficulties. The literature highlights two characteristics deeply impacting sludge rheological properties and their characterization: Thixotropic behavior and organic matter (Seyssiecq et al., 2003; Eshtiaghi et al., 2013), both being related to each other. Indeed, by looking at how thixotropy affects elastic modulus and yield stress with different mechanical histories at different organic matter ratios, it turns out that the higher the organic matter, the higher the thixotropic behavior.

Custom flow in overdamped Brownian dynamics

When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex, and obtaining a detailed physical understanding often requires case-by-case considerations. To facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence, compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

Probing shear-induced rearrangements in Fourier space. I. Dynamic light scattering

Understanding the microscopic origin of the rheological behavior of soft matter is a long-lasting endeavour. While early efforts concentrated mainly on the relationship between rheology and structure, current research focuses on the role of microscopic dynamics. We present in two companion papers a thorough discussion of how Fourier space-based methods may be coupled to rheology to shed light on the relationship between the microscopic dynamics and the mechanical response of soft systems. In this first companion paper, we report a theoretical, numerical and experimental investigation of dynamic light scattering coupled to rheology. While in ideal solids and simple viscous fluids the displacement field under a shear deformation is purely affine, additional non-affine displacements arise in many situations of great interest, for example in elastically heterogeneous materials or due to plastic rearrangements. We show how affine and non-affine displacements can be separately resolved by dynamic light scattering, and discuss in detail the effect of several non-idealities in typical experiments.

Probing shear-induced rearrangements in Fourier space. II. Differential dynamic microscopy

We discuss in two companion papers how Fourier-space measurements may be coupled to rheological tests in order to elucidate the relationship between mechanical properties and microscopic dynamics in soft matter. In this second companion paper, we focus on Differential Dynamic Microscopy (DDM) under shear. We highlight the analogies and the differences with dynamic light scattering coupled to rheology, providing a theoretical approach and practical guidelines to separate the contributions to DDM arising from the affine and the non-affine part of the microscopic displacement field. We show that in DDM under shear the coherence of the illuminating source plays a key role, determining the effective sample thickness that is probed. Our theoretical analysis is validated by experiments on 2D samples and 3D gels.

Local elasticity in nonlinear rheology of interacting colloidal glasses revealed by neutron scattering and rheometry

The flow of colloidal suspensions is ubiquitous in nature and industry. Colloidal suspensions exhibit a wide range of rheological behavior, which should be closely related to the microscopic structure of the systems. With in situ small-angle neutron scattering complemented by rheological measurements, we investigated the deformation behavior of a charge-stabilized colloidal glass at particle level undergoing steady shear. A short-lived, localized elastic response at particle level, termed as the transient elasticity zone (TEZ), was identified from the neutron spectra. The existence of the TEZ, which could be promoted by the electrostatic interparticle potential, is a signature of deformation heterogeneity: the body of fluids under shear behaves like an elastic solid within the spatial range of the TEZ but like fluid outside the TEZ. The size of the TEZ shrinks as the shear rate increases in the shear thinning region, which shows that the shear thinning is accompanied by a diminishing deformation heterogeneity. More interestingly, the TEZ is found to be the structural unit that provides the resistance to the imposed shear, as evidenced by the quantitative agreement between the local elastic stress sustained by the TEZ and the macroscopic stress from rheological measurements at low and moderate shear rates. Our findings provide an understanding on the nonlinear rheology of interacting colloidal glasses from a micro-mechanical view.

Unusual polysaccharide rheology of aqueous dispersions of soft phytoglycogen nanoparticles

Phytoglycogen is a natural polysaccharide produced in the form of dense, 35 nm diameter nanoparticles by some varieties of plants such as sweet corn. The highly-branched, dendrimeric structure of phytoglycogen leads to interesting and useful properties such as softness and deformability of the particles, and a strong interaction with water. These properties make the particles ideal for use as unique additives in personal care, nutrition and biomedical formulations. In the present study, we describe rheology measurements of aqueous dispersions of phytoglycogen nanoparticles. The viscosity of the dispersions remained Newtonian up to large concentrations (∼20% w/w). For higher concentrations, the zero-shear viscosity increased dramatically, reaching values that exceeded that of the water solvent by six orders of magnitude at a concentration of 30% w/w and were well described by the Vogel-Fulcher-Tammann relation of glassy dynamics. The very large values of the zero-shear viscosity are coupled with significant deformation of the soft nanoparticles. We quantified the softness of the particles by performing osmotic pressure measurements on concentrated dispersions, obtaining a value of 15 kPa for the compressional modulus. For the most concentrated samples, we observed flow at stresses less than the apparent yield stress value determined by fitting the high strain rate data to the Herschel-Bulkley model. This behavior, similar to that of star polymer glasses, suggests the possibility of a hairy colloid particle geometry. Remarkably, phytoglycogen nanoparticles dispersed in water provide a very simple experimental realization of glass-forming dispersions of soft colloidal particles that can be used to validate theoretical models in detail.

Laning, thinning and thickening of sheared colloids in a two-dimensional Taylor-Couette geometry

We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.

Continuum modelling of segregating tridisperse granular chute flow

Segregation and mixing of size multidisperse granular materials remain challenging problems in many industrial applications. In this paper, we apply a continuum-based model that captures the effects of segregation, diffusion and advection for size tridisperse granular flow in quasi-two-dimensional chute flow. The model uses the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The predictions from the model are consistent with experimentally validated discrete element method (DEM) simulations over a wide range of flow conditions and particle sizes. The degree of segregation depends on the Péclet number, Pe, defined as the ratio of the segregation rate to the diffusion rate, the relative segregation strength κ_ij between particle species i and j, and a characteristic length L, which is determined by the strength of segregation between smallest and largest particles. A parametric study of particle size, κ_ij , Pe and L demonstrates how particle segregation patterns depend on the interplay of advection, segregation and diffusion. Finally, the segregation pattern is also affected by the velocity profile and the degree of basal slip at the chute surface. The model is applicable to different flow geometries, and should be easily adapted to segregation driven by other particle properties such as density and shape.

Strain heterogeneity in sheared colloids revealed by neutron scattering

Small-angle neutron scattering experiments reveal that the microscopic strain of sheared colloids is highly heterogeneous at the particle level.

Direct Observation of Percolation in the Yielding Transition of Colloidal Glasses

When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Because of the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow us to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of nonaffine deformation percolating at yielding. In agreement with percolation theory, the spanning cluster is fractal with a fractal dimension d_{f}≃2, and the correlation length diverges upon approaching the critical yield strain. These results indicate that percolation of highly nonaffine particles is the hallmark of the yielding transition in disordered glassy systems.

Predicting and assessing rupture in protein gels under oscillatory shear

Soft materials may break irreversibly upon applying sufficiently large shear oscillations, a process whose physical mechanism remains largely elusive. In this work, the rupture of protein gels made of sodium caseinate under an oscillatory stress is shown to occur in an abrupt, brittle-like manner. Upon increasing the stress amplitude, the build-up of harmonic modes in the strain response can be rescaled for all gel concentrations. This rescaling yields an empirical criterion to predict the rupture point way before the samples are significantly damaged. "Fatigue" experiments under stress oscillations of constant amplitude can be mapped onto the former results, which indicates that rupture is independent of the temporal pathway in which strain and damage accumulate. Finally, using ultrasonic imaging, we measure the local mechanical properties of the gels before, during and after breakdown, showing that the strain field remains perfectly homogeneous up to rupture but suddenly gives way to a solid-fluid phase separation upon breakdown.

Transient inhomogeneous flow patterns in supercooled liquids under shear

Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in their local dynamical properties. Using detailed molecular dynamics simulations, we find that for sufficiently low temperatures and sufficiently high shear rates supercooled liquids also show transient inhomogeneous flow patterns (shear banding) in the start-up of steady shear flow, similar to what has already been observed for many other soft glassy systems. We verify that the onset of transient shear banding coincides quite well with the appearance of a stress overshoot for temperatures in the supercooled regime. We find that the slower bands adapt less well to the imposed deformation and therefore accumulate higher shear stresses compared to the fast bands at comparable local shear rates. Our results also indicate that the shear rates of the fast and slow bands are adjusted such that the local dissipation rate is approximately the same in both bands.

Onset of shear thinning in glassy liquids: Shear-induced small reduction of effective density

We propose a simple mechanism for describing the onset of shear thinning in a high-density glassy liquid. In a shear flow, along the compression axis, the overlap between neighboring particles is more enhanced than that at equilibrium, meaning that the "effective" size is reduced along this axis. On the other hand, along the extension axis perpendicular to the compression axis, the average structural configurations are stretched, but it does not indicate the expansion of the "effective" size itself. This asymmetric shear flow effect for particles results in a small reduction of the "effective" density. Because, in glass-forming liquids, the structural relaxation time τ_{α} strongly depends on the density ρ, even a very small reduction of the effective density should lead to a significant decrease of the relaxation time under shear flow. We predict that the crossover shear rate from Newtonian to non-Newtonian flow behaviors is given by γ[over ̇]_{c}=[ρ(∂τ_{α}/∂ρ)]^{-1}, which can be much smaller than 1/τ_{α} near the glass transition point. It is shown that this prediction is consistent with the results of molecular dynamics simulations.

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system.

Long-Lived Neighbors Determine the Rheological Response of Glasses

Glasses exhibit a liquidlike structure but a solidlike rheological response with plastic deformations only occurring beyond yielding. Thus, predicting the rheological behavior from the microscopic structure is difficult, but important for materials science. Here, we consider colloidal suspensions and propose to supplement the static structural information with the local dynamics, namely, the rearrangement and breaking of the cage of neighbors. This is quantified by the mean squared nonaffine displacement and the number of particles that remain nearest neighbors for a long time, i.e., long-lived neighbors, respectively. Both quantities are followed under shear using confocal microscopy and are the basis to calculate the affine and nonaffine contributions to the elastic stress, which is complemented by the viscoelastic stress to give the total stress. During start-up of shear, the model predicts three transient regimes that result from the interplay of affine, nonaffine, and viscoelastic contributions. Our prediction quantitatively agrees with rheological data and their dependencies on volume fraction and shear rate.

A stress-controlled shear cell for small-angle light scattering and microscopy

We develop and test a stress-controlled, parallel plates shear cell that can be coupled to an optical microscope or a small angle light scattering setup, for simultaneous investigation of the rheological response and the microscopic structure of soft materials under an imposed shear stress. In order to minimize friction, the cell is based on an air bearing linear stage, the stress is applied through a contactless magnetic actuator, and the strain is measured through optical sensors. We discuss the contributions of inertia and of the small residual friction to the measured signal and demonstrate the performance of our device in both oscillating and step stress experiments on a variety of viscoelastic materials.

Relating microstructure and particle-level stress in colloidal crystals under increased confinement

The mechanical properties of crystalline materials can be substantially modified under confinement. Such modified macroscopic properties are usually governed by the altered microstructures and internal stress fields. Here, we use a parallel plate geometry to apply a quasi-static squeeze flow crushing a colloidal polycrystal while simultaneously imaging it with confocal microscopy. The confocal images are used to quantify the local structure order and, in conjunction with Stress Assessment from Local Structural Anisotropy (SALSA), determine the stress at the single-particle scale. We find that during compression, the crystalline regions break into small domains with different geometric packing. These domains are characterized by a pressure and deviatoric stress that are highly localized with correlation lengths that are half those found in bulk. Furthermore, the mean deviatoric stress almost doubles, suggesting a higher brittleness in the highly-confined samples.

Divergence of the third harmonic stress response to oscillatory strain approaching the glass transition

The leading nonlinear stress response in a periodically strained concentrated colloidal dispersion is studied experimentally and by theory. A thermosensitive microgel dispersion serves as well-characterized glass-forming model, where the stress response at the first higher harmonic frequency (3ω for strain at frequency ω) is investigated in the limit of small amplitude. The intrinsic nonlinearity at the third harmonic exhibits a scaling behavior which has a maximum in an intermediate frequency window and diverges when approaching the glass transition. It captures the (in-) stability of the transient elastic structure. Elastic stresses in-phase with the third power of the strain dominate the scaling. Our results qualitatively differ from previously derived scaling behavior in dielectric spectroscopy of supercooled molecular liquids. This might indicate a dependence of the nonlinear response on the symmetry of the external driving under time reversal.

Note: An iterative algorithm to improve colloidal particle locating

Confocal microscopy of colloids combined with digital image processing has become a powerful tool in soft matter physics and materials science. Together, these techniques enable locating and tracking of more than half a million individual colloidal particles at once. However, despite improvements in locating algorithms that improve position accuracy, it remains challenging to locate all particles in a densely packed, three dimensional colloid without erroneously identifying the same particle more than once. We present a simple iterative algorithm that mitigates both the "missed particle" and "double counting" problems while simultaneously reducing sensitivity to the specific choice of input parameters. It is also useful for analyzing images with spatially varying brightness in which a single set of input parameters is not appropriate for all particles. The algorithm is easy to implement and compatible with existing particle locating software.

Multiple yielding processes in a colloidal gel under large amplitude oscillatory stress

Fatigue refers to the changes in material properties caused by repeatedly applied loads. It has been widely studied for, e.g., construction materials, but much less has been done on soft materials. Here, we characterize the fatigue dynamics of a colloidal gel. Fatigue is induced by large amplitude oscillatory stress (LAOStress), and the local displacements of the gel are measured through high-frequency ultrasonic imaging. We show that fatigue eventually leads to rupture and fluidization. We evidence four successive steps associated with these dynamics: (i) the gel first remains solid, (ii) it then slides against the walls, (iii) the bulk of the sample becomes heterogeneous and displays solid-fluid coexistence, and (iv) it is finally fully fluidized. It is possible to homogeneously scale the duration of each step with respect to the stress oscillation amplitude σ0. The data are compatible with both exponential and power-law scalings with σ0, which hints at two possible interpretations of delayed yielding in terms of activated processes or of the Basquin law. Surprisingly, we find that the model parameters behave nonmonotonically as we change the oscillation frequency and/or the gel concentration.

Convective Cage Release in Model Colloidal Glasses

The mechanism of flow in glassy materials is interrogated using mechanical spectroscopy applied to model nearly hard sphere colloidal glasses during flow. Superimposing a small amplitude oscillatory motion orthogonal onto steady shear flow makes it possible to directly evaluate the effect of a steady state flow on the out-of-cage (α) relaxation as well as the in-cage motions. To this end, the crossover frequency deduced from the viscoelastic spectra is used as a direct measure of the inverse microstructural relaxation time, during flow. The latter is found to scale linearly with the rate of deformation. The microscopic mechanism of flow can then be identified as a convective cage release. Further insights are provided when the viscoelastic spectra at different shear rates are shifted to scale the alpha relaxation and produce a strain rate-orthogonal frequency superposition, the colloidal analogue of time temperature superposition in polymers with the flow strength playing the role of temperature. Whereas the scaling works well for the α relaxation, deviations are observed both at low and high frequencies. Brownian dynamics simulations point to the origins of these deviations; at high frequencies these are due to the deformation of the cages which slows down the short-time diffusion, while at low frequency, deviations are most probably caused by some mild hydroclustering.

Shear-induced breaking of cages in colloidal glasses: Scattering experiments and mode coupling theory

We employ x-ray scattering on sheared colloidal suspensions and mode coupling theory to study structure factor distortions of glass-forming systems under shear. We find a transition from quadrupolar elastic distortion at small strains to quadrupolar and hexadecupolar modes in the stationary state. The latter are interpreted as signatures of plastic rearrangements in homogeneous, thermalized systems. From their transient evolution with strain, we identify characteristic strain and length-scale values where these plastic rearrangements dominate. This characteristic strain coincides with the maximum of the shear stress versus strain curve, indicating the proliferation of plastic flow. The hexadecupolar modes dominate at the wavevector of the principal peak of the equilibrium structure factor that is related to the cage-effect in mode coupling theory. We hence identify the structural signature of plastic flow of glasses.

Measurement of Stress Redistribution in Flowing Emulsions

We study how local rearrangements alter droplet stresses within flowing dense quasi-two-dimensional emulsions at area fractions ϕ≥0.88. Using microscopy, we measure droplet positions while simultaneously using their deformed shape to measure droplet stresses. We find that rearrangements alter nearby stresses in a quadrupolar pattern: stresses on neighboring droplets tend to either decrease or increase depending on location. The stress redistribution is more anisotropic with increasing ϕ. The spatial character of the stress redistribution influences where subsequent rearrangements occur. Our results provide direct quantitative support for rheological theories of dense amorphous materials that connect local rearrangements to changes in nearby stress.