Molecular Dynamics Simulation of Size Segregation in ThreeDimensionsJason

We report the rst three-dimensional molecular dynamics simulation of particle segregation by shaking. Two diierent containers are considered: one cylindrical and another with periodic boundary conditions. The dependence of the time evolution of a test particle inside the material is studied as a function of the shaking frequency and amplitude, damping coeecients and dispersivity. 1 Dynamical properties of mesoscopic materials such as grains and powders have been subjects of recent research, both theoretically and experimentally 1]. In spite of much work, relatively little is known about the basic physical processes involved in the dynamics of granular media and many puzzles remain to be solved in this eld. Apart from posing numerous fundamental and diicult questions from a theoretical point of view, knowledge of granular dynamics is needed for many industrial applications involving the preparation of food, drugs, detergents, cosmetics, cements, etc 2]. Granular dynamics appears also during industrial processes such as the homogenization of plastic \pills" before melting them into, for example, a Compact Disc, or in the development of new strategic materials such as transparent ceramics, a process which involves careful powder compaction before sintering 3]. A common feature of all these processes is the dynamical interplay of polydisperse gran-ular particles. >From the plethora of complex behaviors present in cohesionless polydisperse granular materials, this Letter presents results of a full 3D Molecular Dynamics simulation of size segregation by shaking, the so-called \Brazil nuts" eeect, the eeect by which large particles move to the top when shaken or jostled 4]. Size segregation has been discussed recently 5{7] but diiculties with its theoretical description using variants of the sequential algorithm originally proposed by Visscher and Bolsterli 8] has led to some controversy 9]. Using Molecular Dynamics, the present Letter reports results of the rst 3D simulation of the problem. A basic result presented in this Letter is the qualitative reproduction of an eeect that is easily observed in experiments: the up-and-down movement of large test particles immersed in the granular media. As far as we know, our simulation is the rst one able to reproduce this important eeect. Several models describing inelastic collisions between non-cohesive grains exist in the literature 10{12]. Here we use the same expressions discussed by Walton 10] and Haa and Werner 11]. We have previously applied similar expressions to simulate a few diierent experiments 13], always then in two dimensions. In the framework deened in Refs. 10,11], …