Eddy viscosity in dense granular flows.

We present a seminal set of experiments on dense granular flows in the stadium shear geometry. The advantage of this geometry is that it produces steady shear flow over large deformations, in which the shear stress is constant. The striking result is that the velocity profiles exhibit an S shape, and are not linear as local constitutive laws would predict. We propose a model that suggests this is a result of wall perturbations which span through the system due to the nonlocal behavior of the material. The model is analogous to that of eddy viscosity in turbulent boundary layers, in which the distance to the wall is introduced to predict velocity profiles. Our findings appear pivotal in a number of experimental and practical situations involving dense granular flows next to a boundary. They could further be adapted to other similar materials such as dense suspensions, foams, or emulsions.

Rapid Plateau border size variations expected in three simple experiments on 2D liquid foams.

Up to a global scaling, the geometry of foams squeezed between two solid plates (2D GG foams) essentially depends on two independent parameters: the liquid volume fraction and the degree of squeezing (bubble thickness to diameter ratio). We describe it in two main asymptotic regimes: fully dry floor tiles, where the Plateau border radius is smaller than the distance between the solid plates, and dry pancakes, where it is larger. We predict a rapid variation of the Plateau border radius in one part of the pancake regime, namely when the Plateau border radius is larger than the inter-plate distance but smaller than the geometric mean of that distance and the bubble perimeter. This rapid variation is not related to any topological change in the foam: in all the regimes we consider, the bubbles remain in mutual lateral contact through films located at mid-height between both plates. We provide asymptotic predictions in different types of experiments on such 2D GG foams: when foam is being progressively dried or wetted, when it is being squeezed further or stretched, when it coarsens through film breakage or through inter-bubble gas diffusion. Our analysis is restricted to configurations close to equilibrium, as we do not include stresses resulting from bulk viscous flow or from non-homogeneous surfactant concentrations. We also assume that the inter-plate distance is sufficiently small for gravity to be negligible. The present work does not provide a method for measuring small Plateau border radii experimentally, but it indicates that large (and easily observable) Plateau borders should appear or disappear rather suddenly in some types of experiments with small inter-plate gaps. It also gives expected orders of magnitude that should be helpful for designing experiments on 2D GG foams.

Internal relaxation time in immersed particulate materials.

We study the dynamics of the static-to-flow transition in a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they get closer than a tuned steric length, and their elastic deflection induced by those two forces. We use soft dynamics to simulate the dynamics of this material when it experiences a step increase in the shear stress and a constant normal stress. We observe a long creep phase before a substantial flow eventually establishes. We measure the change in volume (dilatancy) and find that during the creep phase, it does not change significantly. We find that the typical creep time relies on an internal relaxation process, namely, the separation of two particles driven by the applied stress and resisted by the viscous friction. The present mechanism should be relevant for granular pastes, living cells, emulsions, and wet foams.

Thermal transients and convective particle motion in dense granular materials.

The mechanism of dry granular convection within dense granular flows is mostly neglected by current analytical heat equations describing such materials, for example, in geophysical analyses of shear gouge layers of earthquake and landslide rupture planes. In dry granular materials, the common assumption is that conduction by contact overtakes any other mode of heat transfer. Conversely, we discover that transient correlated motion of heated grains can result in a convective heat flux normal to the shear direction up to 3-4 orders magnitude larger than by contact conduction. Such a thermal efficiency, much higher than that of water, is appealing and might be common to other microscopically structured fluids such as granular pastes, emulsions, and living cells.

Soft Dynamics simulation. 2. Elastic spheres undergoing a T(1) process in a viscous fluid.

Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T(1) process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T(1) process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.

Soft Dynamics simulation. 1. Normal approach of two deformable particles in a viscous fluid and optimal-approach strategy.

Discrete simulation methods are efficient tools to investigate the behaviors of complex fluids such as dry granular materials or dilute suspensions of hard particles. By contrast, materials made of soft and/or concentrated units (emulsions, foams, vesicles, dense suspensions) can exhibit both significant elastic particle deflections (Hertz-like response) and strong viscous forces (squeezed liquid). We point out that the gap between two particles is then not determined solely by the positions of their centers, but rather exhibits its own dynamics. We provide the first ingredients of a new discrete numerical method, named Soft Dynamics, to simulate the combined dynamics of particles and contacts. As an illustration, we present the results for the approach of two particles. We recover the scaling behaviors expected in three limits: the Stokes limit for very large gaps, the Poiseuille-lubricated limit for small gaps and even smaller surface deflections, and the Hertz limit for significant surface deflections. We find that for each gap value, an optimal force achieves the fastest approach velocity. The principle of larger-scale simulations with this new method is provided. They will consitute a promising tool for investigating the collective behaviors of many complex materials.