Computer simulation of shear flows of granular material

The purpose of this paper is to present results from computer simulations of Couette flows of granular materials and to examine the detailed rheological behavior inherent in these simulations. Comparison is made with the experimental results of Bagnold (1954) and Savage and Sayed (1980, 1982) as well as with the various theoretical constitutive models

Channel flows of granular materials and their rheological implications

While the flow of a dry granular material down an inclined channel may seem at first sight to be a relatively simple flow, the experiments which have been conducted up to now suggest sufficient complexity which may be present in all but the very simplest granular material flows; consequently it is important to our general understanding of granular material rheology that these experimental observations be fully understood. This review of the current knowledge of channel flows will focus on the basic mechanics of these flows and the contributions the observations have made to an understanding of the rheology. In order to make progress in this objective, it is necessary to avoid some of the complications which can occur in practice. Thus we shall focus only on those flows in which the interstitial fluid plays very little role in determining the rheology. In his classic paper, Bagnold (1954) was able to show that the regime in which the rheology was dominated by particle/particle or particle/wall interactions and in which the viscous stresses in the interstitial fluid played a negligible role could be defined by a single, Reynolds-number-like parameter. It transpires that the important component in this parameter is a number which we shall call the Bagnold number, Ba, defined by Ba = p₈d²δ/µF where p₈,µF are the particle density and interstitial fluid viscosity, d is the particle diameter and δ is the principal velocity gradient in the flow. In the shear flows explored by Bagnold δ is the shear rate. Bagnold (1954) found that when Ba was greater than about 450 the rheology was dominated by particle/particle and particle/wall collisions. On the other hand, for Ba < 40, the viscosity of the interstitial fluid played the dominant role. More recently Zeininger and Brennen (1985) showed that the same criteria were applicable to the extensional flows in hoppers provided the extensional velocity gradient was used for δ. This review will focus on the simpler flows at large Ba where the interstitial fluid effects are small. Other important ancillary effects can be caused by electrical charge separation between the particles or between the particles and the boundary walls. Such effects can be essential in some flows such as those in electrostatic copying machines. Most experimenters have observed electrical effects in granular material flows, particularly when metal components of the structure are not properly grounded. The effect of such electrical forces on the rheology of the flow is a largely unexplored area of research. The lack of discussion of these effects in this review should not be interpreted as a dismissal of their importance. Apart from electrical and interstitial fluid effects, this review will also neglect the effects caused by non-uniformities in the size and shape of the particles. Thus, for the most part, we focus on flows of particles of spherical shape and uniform size. It is clear that while an understanding of all of these effects will be necessary in the long term, there remain some important issues which need to be resolved for even the simplest granular material flows

Szemcsés anyagok sztatikus és dinamikai szerkezete = Static and dynamical structure of granular materials

Számítógépes szimulációkkal vizsgáltuk a mágneses szemcsék lavináinak tulajdonságait. A rendszert a mágneses és a gravitációs kölcsönhatás erősségének f hányadosa jellemzi. A rézsűszög és a felületi durvaság lineárisan változik f-fel. Hasonlóan a kohézív rendszerekhez, a lavinadinamika szempontjából két tartomány figyelhető meg. Tanulmányoztuk a nyírási sávok kialakulását három dimenzióban, triaxiális elrendezésben. Kidolgoztuk a nyírási sávok numerikus azonosításának technikáját. Szimmetriasértő sávokat találtunk, amennyiben a külső kényszer ezeket nem akadályozta meg. A kísérletekkel egyezésben elmozdulási keményedést azonosítottunk. A sávon belül kritikus sűrűség áll be, amelynek végtelen súrlódáshoz tartozó határértéke csak a szemcsék alakjától függ. Általánosítottuk korábbi, nyírási sávokra vonatkozó elméletünket. Az új modell a kísérletekkel kiváló egyezésben írja le a módosított Couette?cellás kísérleteket. Megjósoltuk és szimulációval igazoltuk, hogy különböző súrlódású közegek határán a fénytöréshez hasonló nyírási sáv refrakció következik be. Vizsgáltuk, hogy torlódott állapotú rendszer perturbációjának hatását. Hatványfüggvény-szerű lecsengést találtunk az elmozdulási térben, ahol az exponens a súrlódás nem triviális függvénye, hasonlóan az elmozdulást kiváltó kritikus erő nagyságához és a behatolási mélységhez. Ezt a nem-monoton kapcsolatot összefüggésbe hoztuk a korábban, a sztatikus erőhálózatokban talált fluktuációk súrlódás-függésével. | Using computer simulations we studied the properties of avalanches of magnetic grains. The system is characterized by the ratio f of the magnetic and gravitational interaction. The angle of repose and the surface roughness vary linearly with f. Similarly to cohesive systems, we could distinguish two regimes from the point of view of the avalanche dynamics. We investigated the formation of shear bands in three dimensional axisymmetric arrangement. We constructed the techniques of identifying the sear bands. We found symmetry breaking bands whenever the external constraints did not hinder them. In agreement with experiments we found strain hardening. Within the band a critical density developed, which, in the infinite friction limit, had a value depending only on the shape of the grains. We generalized our earlier theory of the shear bands. The new model describes the experiments in the modified Couette-cell excellently. We predicted and proved by simulations that on the boundary of two media with different frictions refraction of shear bands takes place, similarly to the refraction of light. We investigated the effects of perturbations of the jammed state. We found power law decay in the displacement field where the exponent is a non-trivial function of the friction, similarly to the critical force and the penetration depth. These non-monotonic dependences were related to the friction-dependence of fluctuations in the force network found earlier static packings

Hydrodynamics of dense granular systems

The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.Comment: 10 pages, 7 figure

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

Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach.

A discrete particle model of a gas-fluidised bed has been developed and in this the two-dimensional motion of the individual, spherical particles was directly calculated from the forces acting on them, accounting for the interaction between the particles and the interstitial gas phase. Our collision model is based on conservation laws for linear and angular momentum and requires, apart from geometrical factors, two empirical parameters: a restitution coefficient and a friction coefficient. A sequence of collisions is processed using techniques which find their application in hard-sphere simulations which are commonly encountered in the field of molecular dynamics. The hydrodynamic model of the gas phase is based on the volume-averaged Navier-Stokes equations. Simulations of bubble and slug formation in a small two-dimensional bed (height 0.50 m, width 0.15 m) with 2400 particles (dp = 4 mm, material: aluminium, p = 2700 kg m¿3) showed a strong dependency of the flow behaviour with respect to the restitution and friction coefficient. A preliminary experimental validation of our model was performed using a small scale "two-dimensional" gas-fluidised bed (height 0.30 m, width 0.15 m, depth 0.015 m) with 850 ¿m ballotini glass particles (p = 2930 kg m¿3) as the bed material. Results compared fairly well with the results of a simulation which was performed with 40,000 particles using realistic values for the restitution and friction coefficients which were obtained from simple independent experiment

The effects of forcing and dissipation on phase transitions in thin granular layers

Recent experimental and computational studies of vibrated thin layers of identical spheres have shown transitions to ordered phases similar to those seen in equilibrium systems. Motivated by these results, we carry out simulations of hard inelastic spheres forced by homogenous white noise. We find a transition to an ordered state of the same symmetry as that seen in the experiments, but the clear phase separation observed in the vibrated system is absent. Simulations of purely elastic spheres also show no evidence for phase separation. We show that the energy injection in the vibrated system is dramatically different in the different phases, and suggest that this creates an effective surface tension not present in the equilibrium or randomly forced systems. We do find, however, that inelasticity suppresses the onset of the ordered phase with random forcing, as is observed in the vibrating system, and that the amount of the suppression is proportional to the degree of inelasticity. The suppression depends on the details of the energy injection mechanism, but is completely eliminated when inelastic collisions are replaced by uniform system-wide energy dissipation.Comment: 10 pages, 5 figure

Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media

In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading to even stronger dissipation and thus causing the density instability. The assumption of `molecular chaos' is valid only in the homogeneous cooling regime. As soon as the density instability occurs, the impact parameter is not longer uniformly distributed. The pair-correlation and the structure functions show that the molecular chaos assumption --- together with reasonable excluded volume modeling --- is important for short distances and irrelevant on large length scales. In this study, the probability distribution of the collision frequency is examined for pipe flow and for freely cooling granular materials as well. Uncorrelated events lead to a Poisson distribution for the collision frequencies. In contrast, the fingerprint of the cooperative phenomena discussed here is a power-law decay of the probability for many collisions per unit time. Keywords: discrete element method, event driven simulations, clustering instability, arching, shock waves, power-law distribution, cooperative phenomena.Comment: 27 pages 14 figs (2 color