Shear-induced diffusion in non-local granular flows

We investigate the properties of self-diffusion in heterogeneous dense granular flows involving a gradient of stress and inertial number. The study is based on simulated plane shear with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield. Below the yield, diffusivity is no longer governed by velocity fluctuations, and we evidenced a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit a caging dynamics developing in zones below the yield. We finally introduce an explicit scaling for the profile of local inertial number in these zones, which leads to a straightforward expression of the diffusivity as a function of the stress and position in non-local flows.Comment: 7 pages, 5 figure

Dense granular flows: interpolating between grain inertia and fluid viscosity based constitutive laws

A scalar constitutive law was recently obtained for dense granular flows from a two-grain argument, both in the inertial regime (grain inertia) and in the viscous regime. As the resulting law is not exactly the same in both regimes, we here provide an expression for the crossover between both regimes.Comment: 3 page

Dense granular flows: two-particle argument accounts for friction-like constitutive law with threshold

A scalar constitutive law is obtained for dense granular flows, both in the inertial regime where the grain inertia dominates, and in the viscous regime. Considering a pair of grains rather than a single grain, the classical arguments yield a constitutive law that exhibits a flow threshold expressed as a finite effective friction at flow onset. The value of the threshold is not predicted. The resulting law seems to be compatible with existing data, provided the saturation at high velocity (collisional regime) is added empirically. The law is not exactly the same in both regimes, which seems to indicate that there is no "universal" law.Comment: 4 page

Note and calculations concerning elastic dilatancy in 2D glass-glass liquid foams

When deformed, liquid foams tend to raise their liquid contents like immersed granular materials, a phenomenon called dilatancy. We have aready described a geometrical interpretation of elastic dilatancy in 3D foams and in very dry foams squeezed between two solid plates (2D GG foams). Here, we complement this work in the regime of less dry 2D GG foams. In particular, we highlight the relatively strong dilatancy effects expected in the regime where we have predicted rapid Plateau border variations.Comment: 12 pages, 3 tables, 5 figure