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Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition. 

Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over [Formula: see text] particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for [Formula: see text], the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering and planar order, and we determine that particles are packed into hexagonal crystal layers (with numerous defects) that slide past each other. By computing local [Formula: see text] and [Formula: see text] order parameters, we determine that the defects correspond to chains of particles in a squarelike lattice. We compute the individual particle contributions to the stress tensor and discover that the largest contributors to the shear stress are primarily located in these lower density, defect regions. The defect structure enables the formation of compressed chains of particles to resist the shear, but these chains are transient and short-lived. The inclusion of a contact friction force allows the stress-bearing structures to grow into a system-spanning network, thereby disrupting the order and drastically increasing the suspension viscosity. 

Soft particulate gels can reversibly yield when sufficient deformation is applied, and the characteristics of this transition can be enhanced or limited by designing hybrid hydrogel composites. While the microscopic dynamics and macroscopic rheology of these systems have been studied separately in detail, the development of direct connections between the two has been difficult, particularly with regard to the nonlinear rheology. To bridge this gap, we perform a series of large amplitude oscillatory shear (LAOS) numerical measurements on model soft particulate gels at different volume fractions using coarse-grained molecular dynamics simulations. We first study a particulate network with local bending stiffness and then we combine it with a second component that can provide additional cross-linking to obtain two-component networks. Through the sequence of physical processes (SPP) framework, we define time-resolved dynamic moduli, and by tracking the changes in these moduli through the period, we can distinguish transitions in the material behavior as a function of time. This approach helps us establish the microscopic origin of the nonlinear rheology by connecting the changes in dynamic moduli to the corresponding microstructural changes during the deformation including the nonaffine displacement of particles, and the breakage, formation, and orientation of bonds. 

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.