DYNAMIC-MODEL FOR GRANULAR ASSEMBLY

In this paper, we investigate in detail the complex dynamics and flow patterns of granular materials based on two simple yet quite realistic models: the diffusing void model and the nonlinear dynamic model. We first show how the diffusing void model describes some of the unusual and unique features of granular flows in a confined geometry such as t he deformation of the free surface, the formation of dead zones, the f low around obstacles, the shock front with its companion void regions, and the front profile of the propagating density waves. We then provi de theoretical framework for the diffusing void model by deriving it f rom the continuity equation and the microscopic force balance equation . This approach shows how the nonlinear term arises naturally, leading to the nonlinear dynamic equation, whose numerical solutions do exhib it the features shown by the diffusing void model and the experiment. When nonlocal interaction between grains is taken into account, the ma ss term appears in the dynamic equation in the thermodynamic limit, le ading to exponential decay of the granular pile. This might account fo r the different behaviors for large and small granular piles. We also present exact results of the stress distribution of a hexagonally pack ed granular pile in two dimensions and show that the load acting on ea ch grain at the bottom layer is identical. We also present the results of molecular dynamics simulations which show that the speed of the ou tgoing grains in a hopper is independent of the depth. We then outline a few outstanding problems that are technologically important, yet ca n be handled by the models proposed and developed in this paper.