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Register a new userBreakdown of Scaling and Friction Weakening in the Critical Granular Flow
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The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most dramatic manifestation are earthquakes, ultimately governed by the dynamics of rocks and debris jammed within the fault gauge. Many of the features of earthquakes, i.e. intermittency, broad times and energy scale involved, are mimicked by a very simple experimental set-up, where small beads of glass under load are slowly sheared by an elastic medium. Analyzing data from long lasting experiments, we identify a critical dynamical regime, that can be related to known theoretical models used for crackling-noise phenomena. In particular, we focus on the average shape of the slip velocity, observing a breakdown of scaling: while small slips show a self-similar shape, large does not, in a way that suggests the presence of subtle inertial effects within the granular system. In order to characterise the crossover between the two regimes, we investigate the frictional response of the system, which we trat as a stochastic quantity. Computing different averages, we evidence a weakening effect, whose Stribeck threshold velocity can be related to the aforementioned breaking of scaling.
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Cohesive granular media flowing down an inclined plane are studied by discrete element simulations. Previous work on cohesionless granular media demonstrated that within the steady flow regime where gravitational energy is balanced by dissipation arising from intergrain forces, the velocity profile in the flow direction scales with depth in a manner consistent with the predictions of Bagnold. Here we demonstrate that this Bagnold scaling does not hold for the analogous steady-flows in cohesive granular media. We develop a generalization of the Bagnold constitutive relation to account for our observation and speculate as to the underlying physical mechanisms responsible for the different constitutive laws for cohesive and noncohesive granular media.
Based on discrete element method simulations, we propose a new form of the constitution equation for granular flows independent of packing fraction. Rescaling the stress ratio $mu$ by a power of dimensionless temperature $Theta$ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number $I$. The basic power-law structure appears robust to varying particle properties (e.g. surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the Nonlocal Granular Fluidity model.
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a heat bath for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with friction, which is known to simplify in two opposite limits: at high collision frequency, it is mapped to a Fokker-Planck equation with nonlinear friction, whereas at low collision frequency, it is described by a sequence of independent random kicks followed by friction-induced relaxations. Comparison between theory and experiment in these two limits shows good agreement. Deviations are observed at very small velocities, where the real bearings are not well modeled by Coulomb friction.
Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical stability and entropy, with the latters effect increasing with friction. We show that a parameter-free maximum-entropy argument alone predicts an exponential cell order distribution, with excellent agreement with the experimental observation. We show that friction only tunes the mean cell order and, consequently, the exponential decay rate and the packing fraction. We further show that cells, which can be very large in such systems, are short-lived, implying that our systems are liquid-like rather than glassy.
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram in the volume fraction/stress plane $(phi,F)$: at low $phi$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $phi$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented.
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