Investigation On Dynamic Behaviors Of Low-dimension Non-uniform Granular System

Granular-material system here is two-phase systems composed of macroscopical particles with different sizes (e.g. coffee, powders, and detritus, etc.). Problems in granular systems are roughly divided into quasi-static (sand piles, distribution of static forces, compaction, and fracture propagation, etc.) and dynamical ones (all kinds of flows, convection, and segregation, pattern formation, and fluidized beds, etc.) [1]. Aiming at the latter, basing on fractal theory the research has been made for the non-uniform granular system.The research of the dynamic behaviors of the granular system in the far from equilibrium regime is very important in the filed of granular system. The increasing power of computer awakens advantage for this research, especially in the simulation of the dynamic behaviors evolvement. The computer simulation can mostly replace real experiments, reflecting the dynamic process of the system [2-5]. Comparing with the hydrokinetics theory the simulation method runs in broader filed, for example non-Gaussian velocity distribution of the system,the anisotropy of special density etc.On base of the identical granularity and mass or not the granular system can be classified as uniform system and non-uniform one. Mean-filed theory is often used when investigating the non-uniform system, which introduces the concept of mean mass and mean granularity. Apparently that method has some shortcoming. By reason of some difficulty in arithmetic only two-component system has been studied up to now. Experiments showed that, for many materials, the geometrical and mathematical characteristics exhibited the self-similarity [6-7]. On the base of the fractal theory we present fractal model for non-uniform granular system [8-14], studying the multi-mixture system. In this model the granularity distribution has fractal characteristic. The thermal conductivity has been investigated in the mixed system [11]. In one-dimensional case some thermodynamic characters of steady state has been researched [14].On base of the studies of non-uniform granular system [8-13], we post one-dimension and two-dimension fractal model. In one-dimensional case Langvin equation is the nucleus and in two-dimendional case particles undergo random walk. We study the noneqilibrium properties of the system by means of Monte Carlo simulation. In one-dimensional case the influence is investigated, which is of the inhomogeneity and the inelasticity on the dynamic actions: velocity distribution and special clusterization. In two-dimendional case the system is heated by means of uniform and boundary heating. We demonstrate the influence of the inhomogeneity and the inelasticity and the heating mechanism on the velocity distribution and special clusterization.The results of our simulation indicate that in one-dimensional system the fractal dimension D of size distribution (signing the granularity inhomogeneity) and the restitution coefficient e has great influences on the dynamics behaviors. The velocity distribution deviates more obviously from the Gaussian distribution and the particles cluster becomes more pronounced with the larger value of D (the inhomogeneity aggravating) or the smaller value of e (the inelasticity aggravating) in the system. In two-dimendional granular system the spatial distribution of the particles is symmetrical with uniform heating. Clusters occur when the system is drivened by boundary heating and with the larger value of D or the smaller value of e the clusterization is more evident. We also find that the form of the observed velocity distribution is governed primarily by the coefficient of restitution e and q ( q = N H NC), the ratio between the average number of heatings N H and the average number of collisions N C in the system. When q > 1, heating dominates dissipation so velocity distributions exhibit Gaussian distribution. And in this case the value of D and e can hardly effect the velocity distribution. When q < 1, the dynamics of the system is dominated by the dissipative collisions between particles so the velocity distributions are non-Gaussian. In this case the deviations are more prominent with the large value of D or the smaller value ofe .