Session X53: Focus Session: Common Features of Soft Materials: Polymers, Colloids and Granular Media II

Shear thickening and jamming in suspensions of different particle shapes

We investigated the role of particle shape on shear thickening and jamming in densely packed suspensions. Various particle shapes were fabricated including rods of different aspect ratios and non-convex hooked rods. A rheometer was used to measure shear stress vs. shear rate for a wide range of packing fractions for each shape. Each suspensions exhibits qualitatively similar Discontinuous Shear Thickening, in which the logarithmic slope of the stress vs. shear rate has the same scaling for each convex shape and diverges at a critical packing fraction $\phi_c$. The value of $\phi_c$ varies with particle shape, and coincides with the onset of a yield stress, a.k.a. the jamming transition. This suggests the jamming transition controls shear thickening, and the only effect of particle shape on steady state bulk rheology of convex particles is a shift of $\phi_c$. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. Qualitative shape dependence was only found in steady state rheology when the system was confined to small gaps where large aspect ratio particle are forced to order.   

Fluctuations and Avalanche Statistics in Sheared Systems of Elliptical Particles

We have performed a series of 2D Couette shear experiment on a system of granular particles near jamming. In these experiments, the particles, which are photoelastic ellipses with aspect ratio 2, are confined between an inner rotating wheel and a fixed outer ring. The inner wheel rotation rate was varied between 0.01 and 0.1 rpm. Using photoelastic properties of the particles and two synchronized cameras, we are able to track the position, orientation and contact forces of each particle through the entire experiment. We determined the local mean, fluctuations, and correlations for various system properties, such as density (Voronoi volume), pressure, orientational order parameter and shear rate. A striking finding of this study is the fact that near jamming, the system can exist in an effectively shear jammed metastable state for very long times before relaxing to an unjammed state. We have also studied the dynamics of avalanches by analyzing the time series of global stress. This study gives us insight to the nature of failure in sheared systems of asymmetrical particles.   

Mapping From Soft to Hard-Core Disks Near the Athermal Shear Driven Jamming Transition

We examine the rheology of soft-core, bidisperse, frictionless disks in two dimensions at zero temperature with overdamped dynamics. For shear driven flow at a uniform strain rate $\dot\gamma$, we find a simple expression for an effective hard-core packing fraction, $\phi_{\mathrm{eff}}$, such that the pressure equivalent to the shear viscosity, $p/\dot\gamma$, for different shear rates, packing fractions, and different contact interactions all collapse onto a common curve when plotted as a function of $\phi_{\mathrm{eff}}$. This function is a characteristic of the hard-core limit as it describes the system in the limit of vanishing particle overlaps. This mapping recovers all the critical behavior found in earlier scaling analyses. We use this mapping to derive a duality relation that gives the exponent of the non-linear Herschel-Bulkley rheology \emph{above} jamming in terms of the exponent of the diverging viscosity \emph{below} jamming.   

Hot spots in an athermal system

We study experimentally the dynamical heterogeneities occuring at slow shear, in a model amorphous glassy material i.e. a 3D granular packing. The deformation field is resolved spatially using a Diffusive Wave Spectroscopy technique. The heterogeneities show up as localized regions of strong deformations spanning a mesoscopic size of about $10$ grains and called the 'hot spots'. The spatial clustering of hot-spots is linked to the subsequent emergence of shear bands. Quantitively, their apparition is associated with the macroscopic plastic deformation and their rate of occurence gives a physical meaning to the concept of ``fluidity,'' recently used to describe the local and non-local rheology of soft glassy materials.   

Effect of Inertial Mass on Velocity Correlations of Shear Driven Soft-Core Disks Approaching the Athermal Jamming Transition

It was found numerically that overdamped, frictionless, soft-core disks undergoing uniform shear driven flow, show differences in behavior depending on how the viscous dissipation is introduced into the numerical simulation. When dissipation is with respect to a sheared external reservoir (the so-called ``mean-field'' approximation), velocity correlations are found to determine a finite length scale $\xi$ that diverges as the jamming transition is approached[1]. However, when dissipation is modeled by inter-particle inelastic collisions, the velocity correlations show no characteristic length other than the length of the system[2]. To study the relation between these two models of dissipation, we remove the overdamped constraint and consider particles with finite inertial mass $m$, and study how velocity correlations behave as the overdamped limit $m\to 0$ is approached. \newline [1] P. Olsson and S. Teitel, Phys.\ Rev.\ Lett.\ {\bf 99}, 178001 (2007). \newline [2] B. P. Tighe et al.\ Phys.\ Rev.\ Lett.\ {\bf 105}, 088303 (2010).   

Stretching dense colloidal suspensions: from flow to fracture

Concentrated suspensions of particles are commonly used in the pharmaceutical, cosmetic and food industries. Manufacture of these products often involves flow geometries that are substantially different from those studied by conventional shear rheology. Using a capillary break-up extensional rheometer we stretch fluids of different volume fraction at strain rates just below, at and above the critical rate required to induce jamming. We show that the jamming of a stretched colloidal column is closely related to that observed during shear rheology. However, fascinating additional effects due to the geometry are also observed. High speed photography of the filament shows evidence of dilatancy and granulation, leading finally to fracture at a critical strain rate. We also investigate an intriguing aspect of thin fluid filaments of the colloidal suspension, when stretched below the critical strain rate required to produce jamming. These filaments are observed to thin to a critical diameter before rupturing and displaying visco-elastic recoil. Finally, using fluorescent particles we visualise the flow fields inside these filaments to understand the dynamics.   

Fluctuations for Hopper Flow with Circular and Elliptical Particles

Recent studies have shown the importance of particle-scale fluctuations in granular flow, e.g. ``stick-slip'' and jamming. In this talk, we consider 2-D hopper flow, where we investigate how the mean and fluctuations of stress, velocity and density fields depend on hopper geometry (e.g. opening size and wall angle) and material properties (e.g. particle shape and initial filling height of materials). A particularly interesting observation is that the mean stress is a decreasing function of the filling height, even though the flux is nearly constant over the same range of material heights. We also find strong negative correlations between stress and velocity fluctuations. Also of interest is the effect of the particle orientation in the flow of elliptical particles. Related MD/DEM studies (supported by IFPRI and NSF) by Shattuck, Kondic and McCarthy et al. have found that good agreement between models and experiments for these flows.   

Rheology and Jamming in Soft Colloidal System

Recent simulations have proposed that the jamming transition can be understood in the framework of critical phenomena, and thus can be described by various asymptotic scaling laws. We use thermosensitive colloidal suspensions and a commercially available rheometer to study the shear response of soft colloidal glass across the jamming transition. We carry out steady-state (viscometry) and time-dependent (oscillatory) rheology experiments in the vicinity of the jamming transition. Both viscometry and oscillatory stress data exhibit asymptotic scaling and presence of critical exponents reminiscent of second-order phase transition, as reported in recent simulations. Critical scaling of frequency indicates the presence of a diverging time-scale associated with the jamming transition. We attempt to understand these critical exponents based on the microscopic interactions of the colloidal systems.   

Local interactions and global rheology in disordered media

We generalize our scaling model for the rheology of soft, frictionless repulsive spheres to include general local viscous and elastic interactions and come to a prediction of the effect on the global behavior of these local interactions. As our scaling model combines elastic and geometric ingredients and a power balance that depends on the local viscous law, we predict that the global rheology of disordered media depends on the details of the local interactions in a universal but non-trivial manner. We compare our predictions for the effect of different {\em elastic} interactions to recent experimental results on the interactions and rheology of NIPA particles.   

Jammed by shear: a new perspective of the jamming transition in frictional granular materials

In the jamming diagram (\emph{Nature} \textbf{396} 21 (1998)) for athermal systems jamming is induced only through compression, and jammed states exist above a packing fraction $\phi_J$. Recent experiments in frictional disks clearly show shear induced jamming (D. Bi et al, \emph{Nature} doi:10.1038/nature10667 (2011)). A minimum shear stress, $\tau_0$, is needed to create robust, shear-jammed (SJ) states with a strong force network percolating along both the compressive and dilational directions. This percolation transition is controlled by the fraction of force-bearing grains, a parameter not previously discussed in the context of jamming. The minimum anisotropy of SJ states vanishes as $\phi\to\phi_J$ from below in a manner reminiscent of an order-disorder transition. To shed light on the origin of shear jamming we have constructed a lattice gas model of force-bearing grains with nematic interactions between the force tiles (objects that reflect force balance on each grain). We will show that there are clear signatures of nematic ordering in SJ states, and present analysis of the nature of the shear-induced jamming transitions as a function of $\phi$. We will also present numerical simulation results of sheared frictional particles.   

Deformation of inherent structures to detect short- and long-range correlations in supercooled liquids

We use deformation of inherent structures as a tool for detecting structural changes and the onset of cooperativity in supercooled liquids. The non-affine displacement (NAD) field resulting from the applied deformation shows characteristic differences between the high temperature liquid and supercooled state, that are typically observed in dynamic quantities and correlated to normal mode structure. The average magnitude of the NAD is very sensitive to temperature changes in the supercooled regime and is found to be strongly correlated with the inherent structure energy. We can rationalize such changes in terms of a crossover from a viscous liquid to a regime dominated by elastic effects. In addition, the NAD field is characterized by a correlation length that increases upon lowering the temperature towards the supercooled regime. By analysing different measures of correlations in the direction of the NAD field, we discuss their analogies with observations in the cooperative dynamics.   

Experiments on ordering transitions in mechanically stable structures of granular rods

We investigated the evolution of granular rods from mechanically stable disordered to crystalline states in response to vibrations. We obtained positions and orientations of the rods in three dimensions using micro-focus X-ray Computed Tomography. Above a critical aspect ratio, we find that rods align vertically in layers with hexagonal order within a layer, independent of the shape of the container and details of the form of vibration. We also quantitatively study the evolution of local and global ordering using density pair correlation function $g(r)$ and orientational order parameter $q_{6}$ as a function of aspect ratio. As the system compacts, local structures emerge and grow, their size and orientation being dependent on volume fraction. Although the initial nucleation of order occurs along the boundaries, we show that the geometry of boundaries have little overall effect on the observed ordering transition. Finally we show that configuration entropy arguments do not play a significant role in the observed ordering, and the system evolves towards increasing stability under small perturbations.   

Elasticity of floppy amorphous systems

Simple amorphous solids made of repulsive particles display curious properties when they are barely mechanically stable, in particular near the unjamming transition where pressure vanishes. Here we focus on another class of materials, including granular flows, covalent glasses or gels of semi-flexible polymers. In such materials the coordination associated with the dominant interaction is too weak to guarantee mechanical stability. This fact implies the presence of floppy modes, collective motions of particles that have no or very little restoring force, and that strongly affect the properties of these materials. We use analytical methods to derive the response of these systems, their length scale and frequency dependence, and test these numerically. If time permits our results will be compared with numerical observations in simplified suspension flows.   

Granular Matter, Foams, and Beyond: Applications of the Granocentric Model

We present a local stochastic model that predicts the statistical fluctuations in jammed packings of monodisperse and polydisperse spheres revealed by confocal microscopy. Moreover, we find that this model can account for the properties of looser and denser random packings that result from depletion attraction between the particles or compression by an applied load, respectively. Finally, we extend the model to space-filling packings of cells in tissues and biliquid foams by testing analytic predictions for the dependence of the number of neighbors of a given cell on its volume. Interestingly, the model distinguishes between scenarios in which size or positional disorder in the packing dominate, in good agreement with experimental data. This versatile model can be put into the statistical mechanics framework proposed by Edwards in order to compute the entropy and compactivity of each packing.   

Force landscape for particulate systems

We discuss the properties of force landscape for isotropically compressed particulate systems characterized by a wide range of packing fractions. The computational methods used are based on persistence diagrams which allow for clear identification of mathematical properties of force landscapes and help their physical interpretation. We find that using this technique which previously has not been applied to particulate matter, a significant new information can be extracted, going much beyond separation into `strong' and `weak' force networks. One result of this analysis is clear indication that for small packing fractions, polydispersity is a crucial parameter that defines the landscape, while for large packing fractions, friction, if present, becomes dominant. Preliminary results for dynamical features of force networks obtained from time-dependent analysis of force landscapes will be presented as well.   

Rearrangements in flow of foam

The nonaffine deformation of amorphous solids has attracted considerable attention. Recent simulations and experiments have shown that the non-affine particle rearrangements under an applied stress are localised, and they generate a long-ranged quadrupolar strain field. Here we have investigated the particle rearrangements in flows of soft, viscous spheres near the jamming point. The characteristics of the particle rearrangements are extremely different as we move away from the jamming point.