(87g) Particle Velocity Distribution Function and the Non-Equilibrium Characteristics of Gas-Solid Flows

Particle velocity distribution function (PVDF) is the cornerstone of kinetic theory of granular flow and the PVDFs in gas-solid flow can be Maxwellian, bimodal and/or non-Maxwellian with an overpopulated high-energy tail, depending on the physical nature of gas-solid flow. Here we theoretically show that different PVDFs can be unified under the umbrella of a recently proposed kinetic theory framework (Wang et al., AIChE Journal, 2016, 62: 2649-2657) and the root of different PVDFs lies in the different characteristics of mesoscale structures, moreover, mathematical analysis shows that both of the Maxwellian distribution and the non-Maxwellian with an overpopulated high-energy tail are special cases of bimodal distribution. Validation of theoretical analysis was then carried out by comparing the theoretical prediction with experimental and DNS data available in literature. Finally, according to the mathematical relation, we infer that those PVDFs represent the extent of non-equilibrium of the studied gas-solid flows: Maxwellian distribution representing equilibrium flow, bimodal distribution representing flows far away from equilibrium and non-Maxwellian distribution with an overpopulated high-energy tail representing something in between. The findings of present study offer a possibility of developing a unified kinetic theory for gas-solid flows.