Class of dilute granular Couette flows with uniform heat flux

In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad's moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad's method, the agreement being only qualitative in the case of the kinetic model.Comment: 15 pages, 10 figures; v2: change of title plus some other minor change

A note on Stokes' problem in dense granular media using the μ(I)\mu(I)--rheology

The classical Stokes' problem describing the fluid motion due to a steadily moving infinite wall is revisited in the context of dense granular flows of mono-dispersed beads using the recently proposed $\mu(I)$--rheology. In Newtonian fluids, molecular diffusion brings about a self-similar velocity profile and the boundary layer in which the fluid motion takes place increases indefinitely with time $t$ as $\sqrt{\nu t}$, where $\nu$ is the kinematic viscosity. For a dense granular visco-plastic liquid, it is shown that the local shear stress, when properly rescaled, exhibits self-similar behaviour at short-time scales and it then rapidly evolves towards a steady-state solution. The resulting shear layer increases in thickness as $\sqrt{\nu_g t}$ analogous to a Newtonian fluid where $\nu_g$ is an equivalent granular kinematic viscosity depending not only on the intrinsic properties of the granular media such as grain diameter $d$, density $\rho$ and friction coefficients but also on the applied pressure $p_w$ at the moving wall and the solid fraction $\phi$ (constant). In addition, the $\mu(I)$--rheology indicates that this growth continues until reaching the steady-state boundary layer thickness $\delta_s = \beta_w (p_w/\phi \rho g )$, independent of the grain size, at about a finite time proportional to $\beta_w^2 (p_w/\rho g d)^{3/2} \sqrt{d/g}$, where $g$ is the acceleration due to gravity and $\beta_w = (\tau_w - \tau_s)/\tau_s$ is the relative surplus of the steady-state wall shear-stress $\tau_w$ over the critical wall shear stress $\tau_s$ (yield stress) that is needed to bring the granular media into motion... (see article for a complete abstract).Comment: in press (Journal of Fluid Mechanics

Interparticle friction leads to non-monotonic flow curves and hysteresis in viscous suspensions

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular flows is still debated. However, most mechanisms put forward so far rely on the presence of inertia at the particle level. In this paper, we study the avalanche dynamics of non-Brownian suspensions in slowly rotating drums and reveal large hysteresis of the avalanche angle even in the absence of inertia. By using micro-silica particles whose interparticle friction coefficient can be turned off, we show that microscopic friction, conversely to inertia, is key to triggering hysteresis in granular suspensions. To understand this link between friction and hysteresis, we use the rotating drum as a rheometer to extract the suspension rheology close to the flow onset for both frictional and frictionless suspensions. This analysis shows that the flow rule for frictionless particles is monotonous and follows a power law of exponent $\alpha \!= \! 0.37 \pm 0.05$, in close agreement with the previous theoretical prediction, $\alpha\!=\! 0.35$. By contrast, the flow rule for frictional particles suggests a velocity-weakening behavior, thereby explaining the flow instability and the emergence of hysteresis. These findings show that hysteresis can also occur in particulate media without inertia, questioning the intimate nature of this phenomenon. By highlighting the role of microscopic friction, our results may be of interest in the geophysical context to understand the failure mechanism at the origin of undersea landslides.Comment: 10 pages, 8 figure

Astex microgravity experiment: simulated asteroid regoliths

AstEx is a microgravity experiment selected to fly on ESA's 51st Microgravity Research Campaign in November 2009. The experiment will investigate the dynamics of regolith on asteroid surfaces. Despite their very low surface gravities, asteroids exhibit a number of different geological processes involving granular matter. Understanding the mechanical response of this granular material subject to external forces in microgravity conditions is vital to the design of a successful asteroid sub-surface sampling mechanism, and in the interpretation of the fascinating geology on an asteroid. The AstEx experiment uses a microgravity modified Taylor-Couette shear cell to investigate granular flow caused by shear forces under the conditions of parabolic flight microgravity. It is intended to determine how a steady state granular flow is achieved in microgravity conditions, and what effect prior shear history has on the timescales involved in initiating a steady state flow in a granular material. Presented are the technical details of the AstEx experimental design with particular emphasis on how the team have designed the equipment specifically for the parabolic flight microgravity environment

A general constitutive model for dense, fine particle suspensions validated in many geometries

Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in simple flow geometries suggests inter-granular repulsion is central to this effect --- for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas, when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to two-dimensional, steady, simple shearing flows. In this work, we introduce a predictive and general, three-dimensional continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a micro-structural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, non-uniform flow configurations where it is shown to accurately capture a variety of key behaviors: (i) the continuous shear thickening (CST) and discontinuous shear thickening (DST) behavior observed in steady flows, (ii) the time-dependent propagation of `shear jamming fronts', (iii) the time-dependent propagation of `impact activated jamming fronts', and (iv) the non-Newtonian, `running on oobleck' effect wherein fast locomotors stay afloat while slow ones sink

Jamming phase diagram for frictional particles

The non-equilibrium transition from a fluid-like state to a disordered solid-like state, known as the jamming transition, occurs in a wide variety of physical systems, such as colloidal suspensions and molecular fluids, when the temperature is lowered or the density increased. Shear stress, as temperature, favors the fluid-like state, and must be also considered to define the system 'jamming phase diagram' [1-4]. Frictionless athermal systems [1], for instance, can be described by the zero temperature plane of the jamming diagram in the temperature, density, stress space. Here we consider the jamming of athermal frictional systems [8-13] such as granular materials, which are important to a number of applications from geophysics to industry. At constant volume and applied shear stress[1, 2], we show that while in absence of friction a system is either fluid-like or jammed, in the presence of friction a new region in the density shear-stress plane appears, where new dynamical regimes are found. In this region a system may slip, or even flow with a steady velocity for a long time in response to an applied stress, but then eventually jams. Jamming in non-thermal frictional systems is described here by a phase diagram in the density, shear-stress and friction space

Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N < 16), we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady-state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.Comment: 18 pages, 23 figures, 5 table