New origin of a convective motion: Elastically induced convection in granular materials

Abstract

Convection and fluidization in a vibrated bed of powder are reproduced in a numerical simulation. In the simulation, each particle of the powder, during a collision, has a viscoelastic interaction with the other colliding particle. Because of the discreteness of the particles, this elasticity causes convection. The critical values of fluidization and convection agree with experiments. PACS numbers: 46.10,+z, 02.60.+y, 47.25.Qv Recently, many physicists [1,2] have studied the dynamics of granular materials, because these materials behave differently from continuous media like rigid, elastic, or viscous bodies. This difference is because granular materials behave in two distinct ways: as a set of particles and as continuous media. For example, granular materials under gravity can have a slope with nonzero angle (angle of repose) in the quasistationary state. Avalanches are also characteristic features in the dynamics of granular materials.One of the stranger phenomena is convection in a fluidized bed under vertical vibration [3][4][5][6][7]. A schematic figure of a typical experimental setup is shown in Fig. 1. When a vessel containing a large number of small particles is shaken strongly, heaping of the surface starts spontaneously. At the same time, convection of particles starts. Experimentalists claim that these phenomena are dynamical phase transitions.Moreover, convection is localized near the surface (surface fluidization). The depth of the convection region increases as the strength of the vibration increases. The purpose of this paper is to propose a numerical modeling to reproduce the convective motion and surface fluidization effect.Our model is a very simple one [1,8]. However, no one has pointed out that this model can reveal an instability in the fluidized bed [9]. In this model, each particle is regarded as a sphere with definite diameter d. When particles collide with one another, they penetrate into each other. During the collision, there is a viscoelastic interac-J tion between them. The equation the particles obey isx/ -xy -d X/~Xy |x/-Xy| + »/(v/-Vy) -g> where 0(x) is a step function, TV is the total number of spheres, x, is the position vector of the ith sphere, and k and 77 are the elastic constant and the viscosity coefficient, respectively, g is the acceleration of gravity and v is velocity. The step function restricts the interaction between particles to periods when the distance between two particles is less than d.In order to understand the physical meanings of the two interaction parameters k and 77, we consider the case n glass spheres • 0cm / diameter im$^6&?S&9999S8pS& 5mm io~i CPH b c 0 s CL> 0 t FIG. 1. A schematic of a typical experiment.where two spheres collide head-on with each other. In this case, they have an effective coefficient of restitution e =exp( --qn/(o). The time interval during a collision is also a function of k and 77. We call this interval the collision time, t CQ \=7t/(o [a> = (2& -77 2 ) 1/2 ]. Therefore, fixing k and 77 determines the effective coefficient of...

Numerical study of granular turbulence and the appearance of the energy spectrum without flow

“…When Γ exceeds the gravity acceleration, the convection and the surface fluidization are observed [13]. The fluidized region where the flow exists has the finite depth which increases as Γ increases and coexists with the solid region where the powder does not flow (See Fig.1).…”

“…First, the numerical behavior of the vibrated bed of powder obtained in the previous publications [13,28,29] is summarized. When Γ exceeds the gravity acceleration, the convection and the surface fluidization are observed [13].…”

Phase diagram of vertically shaken granular matter

“…Granular convection has been studied extensively at mild fluidization [23,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69], for which the convection is principally boundary-driven. However, the buoyancy-driven convection observed here occurs at high fluidization and this has been reported much more rarely in the literature.…”

Reverse Brazil Nut Problem: Competition between Percolation and Condensation

“…Since most experiments were carried out with a single large grain in a sea of smaller ones [4][5][6], it is not quite clear which of these observed mechanisms apply for the segregation of binary mixtures. For example, while the convection is responsible for the rise of the single large grain, MD simulations [8] and hydrodynamic models [9] clearly indicate that convection cells are absent in the bulk, but confined near the wall when the width of the container is much larger than the height. Recently, Shinbrot and Muzzio [10] observed a reverse buoyancy in shaken granular beds, where again a single large grain in a sea of smaller grains could segregate to the bottom if the bed was deep and the amplitude of vibration was large.…”