Powder Processing: Models and Simulations

Granular materials, which can be either wet or dry and range in size from nanometers to centimeters, are widely encountered as particles or powder in industries and in nature. As with solids, they can withstand deformation and form heaps; as with liquids, they can flow; as with gases, they exhibit compressibility. Corresponding to the fluid- and solid-like modes, they show different flow regimes: quasi-static regime, rapid flow regime, and a transitional regime that lies in between. These features give rise to another state of matter that is poorly understood. The development of a general theory to describe the packing (statics) and flow (dynamics) of granular materials has been a problem challenging the scientific community for years. Essentially, the existing approaches to modeling granular materials can be classified into two categories: the continuum approach at a macroscopic level and the discrete approach at a microscopic level. In the continuum approach, the macroscopic behavior is described by balance equations, for example, mass and momentum as used in the two fluid model (TFM), closed with constitutive relations together with initial and boundary conditions. This approach is preferred in process modeling and applied research because of its computational convenience. However, its effective use depends heavily on constitutive or closure relations and the momentum exchange between particles of different type. In the past, different theories have been devised for different materials and for different flow regimes. For example, models have been proposed to derive the constitutive equations for the rate-independent deformation of granular materials based....