Developing constitutive models for particle phase rheology in gas-fluidized suspensions through rigorous statistical mechanical methods is very difficult when complex inter-particle forces are present. In the present study, we pursue a computational approach based on results obtained through Eulerian-Lagrangian simulations of the fluidized state. Simulations were performed in a periodic domain for non-cohesive and mildly cohesive (Geldart Group A) particles. Based on the simulation results, we propose modified closures for pressure, bulk viscosity, shear viscosity and the rate of dissipation of pseudo-thermal energy. For non-cohesive particles, results in the high granular temperature T regime agree well with constitutive expressions afforded by the kinetic theory of granular materials, demonstrating the validity of the methodology. The simulations reveal a low T regime, where the inter-particle collision time is determined by gravitational fall between collisions. Inter-particle cohesion has little effect in the high T regime, but changes the behaviour appreciably in the low T regime. At a given T, a cohesive particle system manifests a lower pressure at low particle volume fractions when compared to non-cohesive systems; at higher volume fractions, the cohesive assemblies attain higher coordination numbers than the non-cohesive systems, and experience greater pressures. Cohesive systems exhibit yield stress, which is weakened by particle agitation, as characterized by T. All these effects are captured through simple modifications to the kinetic theory of granular materials for non-cohesive materials.
- kinetic theory
- particle/fluid flow