Slip and flow of hard-sphere colloidal glasses

Interplay between wall slip and shear banding in a thixotropic yield stress fluid

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Structure and short-time diffusion of concentrated suspensions consisting of silicone-stabilised PMMA particles: a quantitative analysis taking polydispersity effects into account

We characterise structure and dynamics of concentrated suspensions of silicone-stabilised PMMA particles immersed in index-matching decalin-tetralin mixtures by means of static and quasielastic light scattering experiments. These particles can reproducibly be prepared via a comparatively easy route and are thus promising model systems with hard-sphere interaction. We demonstrate the hard-sphere behaviour of dense suspensions of these systems rigorously taking polydispersity effects into account. Structure factors S(Q) can in the entire range of volume fractions with liquid-like structure quantitatively be modelled using a multi-component Percus-Yevick ansatz regarding the particle size distribution and the form factor assuming a core-shell model with a scattering length density gradient in the PMMA core. Herewith, hydrodynamic functions H(Q) are in the whole accessible Q-range beyond the second maximum of H(Q) quantitatively modelled using a rescaled δγ-approach for all investigated volume fractions. With these data, previously provided characterisation of dilute systems is extended: the excellent agreement of structural and dynamic properties with theoretical predictions for hard spheres demonstrates the suitability of these particles as a model system for hard spheres.

Parallel-Disk Viscometry of a Viscoplastic Hydrogel: Yield Stress and Other Parameters of Shear Viscosity and Wall Slip

The rheology, i.e., the flow and deformation properties, of hydrogels is generally a very important consideration for their functionality. However, the accurate characterization of their rheological material functions is handicapped by their ubiquitous viscoplasticity and associated wall slip behavior. Here a parallel-disk viscometer was used to characterize the shear viscosity and wall slip behavior of a crosslinked poly(acrylic acid) (PAA) carbomer hydrogel (specifically Carbopol^® at 0.12% by weight in water). It was demonstrated that parallel-disk viscometry, i.e., the steady torsional flow in between two parallel disks, can be used to unambiguously determine the yield stress and other parameters of viscoplastic constitutive equations and wall slip behavior. It was specifically shown that torque versus rotational speed information, obtained from parallel-disk viscometry, was sufficient to determine the yield stress of a viscoplastic hydrogel. Additional gap-dependent data from parallel-disk viscometry could then be used to characterize the other parameters of the shear viscosity and wall slip behavior of the hydrogel. To investigate the accuracy of the parameters of shear viscosity and apparent wall slip that were determined, the data were used to calculate the torque values and the velocity distributions (using the lubrication assumption and parallel plate analogy) under different flow conditions. The calculated torques and velocity distributions of the hydrogel agreed very well with experimental data collected by Medina-Bañuelos et al., 2021, suggesting that the methodologies demonstrated here provide the means necessary to understand in detail the steady flow and deformation behavior of hydrogels. Such a detailed understanding of the viscoplastic nature and wall slip behavior of hydrogels can then be used to design and develop novel hydrogels with a wider range of applications in the medical and other industrial areas, and for finding optimum conditions for their processing and manufacturing.

Viscoplastic Couette Flow in the Presence of Wall Slip with Non-Zero Slip Yield Stress

The steady-state Couette flow of a yield-stress material obeying the Bingham-plastic constitutive equation is analyzed assuming that slip occurs when the wall shear stress exceeds a threshold value, the slip (or sliding) yield stress. The case of Navier slip (zero slip yield stress) is studied first in order to facilitate the analysis and the discussion of the results. The different flow regimes that arise depending on the relative values of the yield stress and the slip yield stress are identified and the various critical angular velocities defining those regimes are determined. Analytical solutions for all the regimes are presented and the implications for this important rheometric flow are discussed.

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.

Wall slip for complex liquids - Phenomenon and its causes

In this review, we tried to qualify different types and mechanisms of wall slip phenomenon, paying particular attention to the most recent publications and issues. The review covers all type of fluids - homogeneous low molecular weight liquids, polymer solution, multi-component dispersed media, and polymer melts. We focused on two basic concepts - fluid-solid wall interaction and shear-induced fluid-to-solid transitions - which are the dominant mechanisms of wall slip. In the first part of the review, the theoretical and numerical studies of correlation of wetting properties and wall slip of low molecular weight liquids and polymeric fluids are reviewed along with some basic experimental results. The influence of nanobubbles and microcavities on the effectiveness of wall slip is illuminated with regard to the bubble dynamics, as well as their stability at smooth and rough interfaces, including superhydrophobic surfaces. Flow of multi-component matter (microgel pastes, concentrated suspensions of solid particles, compressed emulsions, and colloidal systems) is accompanied by wall slip in two cases. The first one is typical of viscoplastic media which can exist in two different physical states, as solid-like below the yield point and liquid-like at the applied stresses exceeding this threshold. Slip takes place at low stresses. The second case is related to the transition from fluid to solid states at high deformation rates or large deformations caused by the strain-induced glass transition of concentrated dispersions. In the latter case, the wall effects consist of apparent slip due to the formation of a low viscous thin layer of fluid at the wall. The liquid-to-solid transition is also a dominant mechanism in wall slip of polymer melts because liquid polymers are elastic fluids which can be in two relaxation states depending on the strain rate. The realization of these mechanisms is determined by polymer melt interaction with the solid wall.

Wall Slip of Soft-Jammed Systems: A Generic Simple Shear Process

From well-controlled long creep tests, we show that the residual apparent yield stress observed with soft-jammed systems along smooth surfaces is an artifact due to edge effects. By removing these effects, we can determine the stress solely associated with steady-state wall slip below the material yield stress. This stress is found to vary linearly with the slip velocity for a wide range of materials whatever the structure, the interaction types between the elements and with the wall, and the concentration. Thus, wall slip results from the laminar flow of some given free liquid volume remaining between the (rough) jammed structure formed by the elements and the smooth wall. This phenomenon may be described by the simple shear flow in a Newtonian liquid layer of uniform thickness. For various systems, this equivalent thickness varies in a narrow range (35±15  nm).

Particle-wall tribology of slippery hydrogel particle suspensions

Slip is an important phenomenon that occurs during the flow of yield stress fluids like soft materials and pastes. Densely packed suspensions of hydrogel microparticles are used to show that slip is governed by the tribological interactions occurring between the samples and shearing surfaces. Both attractive/repulsive interactions between the dispersed particles and surface, as well as the viscoelasticity of the suspension, are found to play key roles in slip occurring within rheometric flows. We specifically discover that for two completely different sets of microgels, the sliding stress at which slip occurs scales with both the modulus of the particles and the bulk suspension modulus. This suggests that hysteresis losses within the viscoelastic particles contribute to friction forces and thus slip at the particle-surface tribo-contact. It is also found that slip during large amplitude oscillatory shear and steady shear flows share the same generic features.

Shear thickening regimes of dense non-Brownian suspensions

We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mechanisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrodynamic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface properties under certain flow conditions. Microstructural transitions associated with frictional shear thickening are presented. We find very distinctive divergences of both microstructural and dynamic variables with respect to volume fraction in the thickened and non-thickened states.

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.

Colloidal binary mixtures at fluid-fluid interfaces under steady shear: structural, dynamical and mechanical response

We experimentally study the link between structure, dynamics and mechanical response of two-dimensional (2D) binary mixtures of colloidal microparticles spread at water/oil interfaces. The particles are driven into steady shear by a microdisk forced to rotate at a controlled angular velocity. The flow causes particles to layer into alternating concentric rings of small and big colloids. The formation of such layers is linked to the local, position-dependent shear rate, which triggers two distinct dynamical regimes: particles either move continuously ("Flowing") close to the microdisk, or exhibit intermittent "Hopping" between local energy minima farther away. The shear-rate-dependent surface viscosity of the monolayers can be extracted from a local interfacial stress balance, giving "macroscopic" flow curves whose behavior corresponds to the distinct microscopic regimes of particle motion. Hopping regions reveal a higher resistance to flow compared to the flowing regions, where spatial organization into layers reduces dissipation.

Model of heap formation in vibrated gravitational suspensions

In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.

Slip mechanisms in complex fluid flows

The classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of several classes of complex fluids including polymer melts, their blends, polymer solutions, microgels, glasses, suspensions and pastes. In fact, it appears that slip effect in these systems is the rule and not the exemption. The occurrence of slip complicates the analysis of rheological data, although it provides new opportunities to understand their behavior in restricted environments delineating additional molecular mechanisms i.e. entropic restrictions due to limitations in the number of molecular conformations. This article discusses these complexities and provides future research opportunities.

Tuning colloidal gels by shear

Using a powerful combination of experiments and simulations we demonstrate how the microstructure and its time evolution are linked with mechanical properties in a frustrated, out-of-equilibrium, particle gel under shear. An intermediate volume fraction colloid-polymer gel is used as a model system, allowing quantification of the interplay between interparticle attractions and shear forces. Rheometry, confocal microscopy and Brownian dynamics reveal that high shear rates, fully breaking the structure, lead after shear cessation to more homogeneous and stronger gels, whereas preshear at low rates creates largely heterogeneous weaker gels with reduced elasticity. We find that in comparison, thermal quenching cannot produce structural inhomogeneities under shear. We argue that external shear has strong implications on routes towards metastable equilibrium, and therefore gelation scenarios. Moreover, these results have strong implications for material design and industrial applications, such as mixing, processing and transport protocols coupled to the properties of the final material.

Apparent wall slip in non-Brownian hard-sphere suspensions

We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates.

Role of shear-induced dynamical heterogeneity in the nonlinear rheology of colloidal gels

We report the effect of flow-induced dynamical heterogeneity on the nonlinear elastic modulus of weakly aggregated colloidal gels that have undergone yielding by an imposed step strain deformation. The gels are comprised of sterically stabilized poly(methyl methacrylate) colloids interacting through short-ranged depletion attractions. When a step strain of magnitude varying from γ = 0.1 to 80.0 is applied to the quiescent gels, we observe the development of a bimodal distribution in the single-particle van Hove self-correlation function. This distribution is consistent with the existence of a fast and slow subpopulation of colloids within sheared gels. We evaluate the effect of incorporating the properties of the slow, rigid subpopulation of the colloids into a recent mode coupling theory for the nonlinear elasticity of colloidal gels.

Nonlinear elasticity of microsphere heaps

Thermal fluctuations, geometric exclusion, and external driving all govern the mechanical response of dense particulate suspensions. Here, we measure the stress-strain response of quasi-two-dimensional flow-stabilized microsphere heaps in a regime in which all three effects are present using a microfluidic device. We observe that the elastic modulus and the mean interparticle separation of the heaps are tunable via the confining stress provided by the fluid flow. Furthermore, the measured stress-strain curves exhibit a universal nonlinear shape, which can be predicted from a thermal van der Waals equation of state with excluded volume. This analysis indicates that many-body interactions contribute a significant fraction of the stress supported by the heap.

Confocal imaging of confined quiescent and flowing colloid-polymer mixtures

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed assembly(1-3), drug delivery(4), improved hydrocarbon recovery(5-7), and flowable electrodes for energy storage(8). Suspensions containing fluorescent colloids and non-adsorbing polymers are appealing model systems, as the ratio of the polymer radius of gyration to the particle radius and concentration of polymer control the range and strength of the interparticle attraction, respectively. By tuning the polymer properties and the volume fraction of the colloids, colloid fluids, fluids of clusters, gels, crystals, and glasses can be obtained(9). Confocal microscopy, a variant of fluorescence microscopy, allows an optically transparent and fluorescent sample to be imaged with high spatial and temporal resolution in three dimensions. In this technique, a small pinhole or slit blocks the emitted fluorescent light from regions of the sample that are outside the focal volume of the microscope optical system. As a result, only a thin section of the sample in the focal plane is imaged. This technique is particularly well suited to probe the structure and dynamics in dense colloidal suspensions at the single-particle scale: the particles are large enough to be resolved using visible light and diffuse slowly enough to be captured at typical scan speeds of commercial confocal systems(10). Improvements in scan speeds and analysis algorithms have also enabled quantitative confocal imaging of flowing suspensions(11-16,37). In this paper, we demonstrate confocal microscopy experiments to probe the confined phase behavior and flow properties of colloid-polymer mixtures. We first prepare colloid-polymer mixtures that are density- and refractive-index matched. Next, we report a standard protocol for imaging quiescent dense colloid-polymer mixtures under varying confinement in thin wedge-shaped cells. Finally, we demonstrate a protocol for imaging colloid-polymer mixtures during microchannel flow.

A multi-axis confocal rheoscope for studying shear flow of structured fluids

We present a new design for a confocal rheoscope that enables uniform uniaxial or biaxial shear. The design consists of two precisely positioned parallel plates with a gap that can be adjusted down to 2 ±0.1 μm, allowing for the exploration of confinement effects. By using our shear cell in conjunction with a biaxial force measurement device and a high-speed confocal microscope, we are able to measure the real-time biaxial stress while simultaneously imaging the material three-dimensional structure. We illustrate the importance of the instrument capabilities by discussing the applications of this instrument in current and future research topics in colloidal suspensions.

Complex oscillatory yielding of model hard-sphere glasses

The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.

A mesoscopic model for the rheology of soft amorphous solids, with application to microchannel flows

We have studied a mesoscopic model for the flow of amorphous solids. The model is based on key features identified at the microscopic level, namely periods of elastic deformation interspersed with localised rearrangements of particles that induce long-range elastic deformations. These long-range deformations are derived following a continuum mechanics approach, in the presence of solid boundaries, and are included in full in the model. Indeed, they mediate spatial cooperativity in the flow, whereby a localised rearrangement may lead a distant region to yield. In particular, we have simulated a channel flow and found manifestations of spatial cooperativity that are consistent with published experimental observations for concentrated emulsions in microchannels. Two categories of effects are distinguished. On the one hand, the coupling of regions subject to different shear rates, for instance, leads to finite shear rate fluctuations in the seemingly unsheared "plug" in the centre of the channel. On the other hand, there is convincing experimental evidence of a specific rheology near rough walls. We discuss the diverse possible physical origins for this effect, and we suggest that it may be associated with the bumps of particles into surface asperities as they slide along the wall.

Transient dynamics in dense colloidal suspensions under shear: shear rate dependence

A combination of confocal microscopy and rheology experiments, Brownian dynamics (BD) and molecular dynamics (MD) simulations and mode coupling theory (MCT) have been applied in order to investigate the effect of shear rate on the transient dynamics and stress-strain relations in supercooled and glassy systems under shear. Immediately after shear is switched on, the microscopic dynamics display super-diffusion and the macroscopic rheology a stress overshoot, which become more pronounced with increasing shear rate. MCT relates both to negative sections of the generalized shear modulus, which grow with increasing shear rate. When the inverse shear rate becomes much smaller than the structural relaxation time of the quiescent system, relaxation through Brownian motion becomes less important. In this regime, larger stresses are accumulated before the system yields and the transition from localization to flow occurs earlier and more abruptly.

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.

Yielding of hard-sphere glasses during start-up shear

Concentrated hard-sphere suspensions and glasses are investigated with rheometry, confocal microscopy, and Brownian dynamics simulations during start-up shear, providing a link between microstructure, dynamics, and rheology. The microstructural anisotropy is manifested in the extension axis where the maximum of the pair-distribution function exhibits a minimum at the stress overshoot. The interplay between Brownian relaxation and shear advection as well as the available free volume determine the structural anisotropy and the magnitude of the stress overshoot. Shear-induced cage deformation induces local constriction, reducing in-cage diffusion. Finally, a superdiffusive response at the steady state, with a minimum of the time-dependent effective diffusivity, reflects a continuous cage breakup and reformation.

Jamming phase diagram for frictional particles

We investigate the jamming transition of frictional particulate systems via discrete element simulations, reporting the existence of new regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be "fragile" as speculated. In particular, we find a regime, characterized by extremely long processes, with a diverging time scale, whereby a suspension first flows but then suddenly jams. We link this sudden jamming transition to the presence of impeded dilatancy.

Microfluidics and complex fluids

In this paper, we describe four experimental studies we carried out over the last four years in the MMN lab, regarding the dynamical behaviour of complex fluids in microfluidic systems. The topics are: (1) Polymer breakup in microfluidic systems. (2) Flows of polymer solutions in microchannels close to a smooth wall. (3) Shear banding flows in microchannels (rheology, instabilities). (4) Flows of concentrated solutions of microgel particles through microchannels. Depending on the situation, we exploit the duality low Reynolds numbers/high Weissenberg numbers (for instance, by working at high shear rates without generating turbulence), use visualization windows naturally offered by the microfluidic environment or take advantage of the integration of various functionalities on the chip. In all cases, new information, hardly accessible to non-miniaturized approaches, could be obtained by using microfluidic technology.

Stochastic transitions and jamming in granular pipe flow

We study a model granular suspension driven down a channel by an embedding fluid via computer simulations. We characterize the different system flow regimes and the stochastic nature of the transitions between them. For packing fractions below a threshold ϕ{m}, granular flow is disordered and exhibits an Ostwald-de Waele-type power-law shear-stress constitutive relation. Above ϕ{m}, two asymptotic states exist; disordered flow can persist indefinitely, yet, in a fraction of samples, the system self-organizes in an ordered form of flow where grains move in parallel ordered layers. In the latter regime, the Ostwald-de Waele relationship breaks down and a nearly solid plug appears in the center, with linear shear regions at the boundaries. Above a higher threshold ϕ{g}, an abrupt jamming transition is observed if ordering is avoided.

Shear banding and flow-concentration coupling in colloidal glasses

We report experiments on hard-sphere colloidal glasses that show a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability due to shear-concentration coupling, a mechanism previously thought unimportant in these materials. Below a characteristic shear rate γ(c) we observe increasingly nonlinear and localized velocity profiles. We attribute this to very slight concentration gradients in the unstable flow regime. A simple model accounts for both the observed increase of γ(c) with concentration, and the fluctuations in the flow.

Nonlinear rheology of colloidal dispersions

Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.