Soft particle glasses form a broad family of materials made of deformable particles, as diverse as microgels, emulsion droplets, star polymers, block copolymer micelles and proteins, which are jammed at volume fractions where they are in contact and interact via soft elastic repulsions. Despite a great variety of particle elasticity, soft glasses have many generic features in common. They behave like weak elastic solids at rest but flow very much like liquids above the yield stress. This unique feature is exploited to process high-performance coatings, solid inks, ceramic pastes, textured food and personal care products. Much of the understanding of these materials at volume fractions relevant in applications is empirical, and a theory connecting macroscopic flow behaviour to microstructure and particle properties remains a formidable challenge. Here we propose a micromechanical three-dimensional model that quantitatively predicts the nonlinear rheology of soft particle glasses. The shear stress and the normal stress differences depend on both the dynamic pair distribution function and the solvent-mediated EHD interactions among the deformed particles. The predictions, which have no adjustable parameters, are successfully validated with experiments on concentrated emulsions and polyelectrolyte microgel pastes, highlighting the universality of the flow properties of soft glasses. These results provide a framework for designing new soft additives with a desired rheological response.

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We perform experiments on jammed suspensions of microgels with different constituent properties to determine their stress relaxation behavior on flow cessation. We observe that the stress relaxes through a two-step process: A rapid initial relaxation where internal stresses are trapped followed by a much slower decay. Trapped internal stresses are related to the solvent viscosity, particle elasticity, and volume fraction through a universal scaling. The second slower relaxation of the internal stress is characterized by a single exponential decay, which is independent of the preshear stress and relatively insensitive to the material properties of the microgel suspension. Particle-scale simulations are used to understand the microscopic mechanisms which drive the amplitude and the kinetics of the stress relaxation as well as the local particle dynamics in each regime. The rapid initial relaxation occurs through ballistic particle motion, where the number of contacts and average compression return to their static values but the asymmetry of the pair distribution function remains as a signature of the internal stress.

Summary. A rigid-plastic Cosserat model has been used to study dense, fully developed flow of granular materials through a vertical channel. Frictional models based on the classical continuum do not predict the occurrence of shear layers, at variance with experimental observations. This feature has been attributed to the absence of a material length scale in their constitutive equations. The present model incorporates such a material length scale by treating the granular material as a Cosserat continuum. Thus localised couple stresses exist and the stress tensor is asymmetric. The velocity profiles predicted by the model are in close agreement with available experimental data. The predicted dependence of the shear layer thickness on the width of the channel is in reasonable agreement with data. In the limit of small ǫ (ratio of the particle diameter to the half-width of the channel), the model predicts that the shear layer thickness scaled by the particle diameter grows as ǫ −1/3 .

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