No Arabic abstract
Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional $mu(I)$-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakening, shear thinning, a discontinuous thinning transition, and gaseous shear thickening. The employed setup gives access to dynamic fluctuations, which exhibit a broad range of timescales. In the slow dense regime the frequency of cage-opening increases with stress and enhances, with respect to $mu(I)$-rheology, the decrease of viscosity. Diffusivity is exponential in the shear stress in both thinning and thickening regimes, with a huge growth near the transition.
By shaking a sand box the grains on the top start to jump giving the picture of evaporating a sand bulk, and a gaseous transition starts at the surface granular matter (GM) bed. Moreover the mixture of the grains in the whole bed starts to move in a cooperative way which is far away from a Brownian description. In a previous work we have shown that the key element to describe the statistics of this behavior is the exclusion of volume principle, whereby the system obeys a Fermi configurational approach. Even though the experiment involves an archetypal non-equilibrium system, we succeeded in defining a global temperature, as the quantity associated to the Lagrange parameter in a maximum entropic statistical description. In fact in order to close our approach we had to generalize the equipartition theorem for dissipative systems. Therefore we postulated, found and measured a fundamental dissipative parameter, written in terms of pumping and gravitational energies, linking the configurational entropy to the collective response for the expansion of the centre of mass (c.m.) of the granular bed. Here we present a kinetic approach to describe the experimental velocity distribution function (VDF) of this non-Maxwellian gas of macroscopic Fermi-like particles (mFp). The evaporation transition occurs mainly by jumping balls governed by the excluded volume principle. Surprisingly in the whole range of low temperatures that we measured this description reveals a lattice-gas, leading to a packing factor, which is independent of the external parameters. In addition we measure the mean free path, as a function of the driving frequency, and corroborate our prediction from the present kinetic theory.
Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect model parameters, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for measurements of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are well-fit by nonlocal rheology, with each particle having a distinct triad of the local, nonlocal, and frictional parameters. While the local parameter b is always approximately unity, the nonlocal parameter A depends sensitively on both the particle shape and material. The critical stress ratio mu_s, above which Coulomb failure occurs, varies for particles with the same material but different shapes, indicating that geometric friction can dominate over material friction.
Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we are able to track how a dense suspension approaches its shear jammed state dynamically, and can quantitatively map out the onset stress for solidification in a state diagram.
We analyze the capabilities of various recently developed techniques, namely Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheel--dry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Results show that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding that of traditional terramechanics methodology in several circumstances. Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.
A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. (Phys. Rev. Lett., 106 (2011) 108301): a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by (Phys. Rev. Lett., 111 (2013) 238301) and derived from a gradient expansion of the rheology $mu[I]$. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed.