Analysis of a frictional–kinetic model for gas–particle flow

A frictional–kinetic rheological model for dense assemblies of solids in a gas–particle mixture is described. This model treats the kinetic and frictional stresses additively. The former is modeled using the kinetic theory of granular materials. For the latter, we begin with the model described by Schaeffer [J. Differ. Equ. 66 (1987) 19] and modify it to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. Results of simulations of two model problems, namely, the gravity discharge of particles from a bin and the rise of a bubble in a fluidized bed, are presented. The simulations capture the height-independent rate of discharge of particles from the bin, the dilation of particle assembly near the exit orifice, the significant effect of the interstitial air on the discharge behavior of fine particles and the occurrence of pressure deficit above the orifice. However, the stagnant shoulder at the bottom corners of the bin is not captured; instead, one obtains a region of slow flow at the corners. The bubble rise example shows the significant effect of frictional stresses on the bubble shape. In both examples, a simplified version of the rheological model obtained by invoking a critical state hypothesis is found to be adequate.