Granular flow inelastic particle collisions

One can see as granular densities and pressures grow very quickly near the plane of jet interaction. Thus, solids deceleration is carried out in granular shock waves. The rapid decrease in axial components of particle velocities confirms a wavy nature of the granular flow. Radial particle velocity distributions on the jet periphery demonstrate the gas influence on the particle removal from the milling zone. This influence is observed for particles, which are smaller than 10 pm. The intensity of particle chaotic motion (relative particle-particle velocities) drops quickly with decrease in the particle diameters below 15 pm. This drop is caused by particle deceleration in a viscous gas (if collisions are elastic) and additionally by chaotic particle-particle collisions (if collisions are inelastic). This collisional intensity decrease causes a maximum of the relative particle-particle chaotic velocity at some distance from the plane of symmetry that is more explicit for inelastic collisions. Partial particle nonelasticity defines considerable drop in the chaotic velocity. The formation of a maximum of the collisional capacity at some distance from the plane of symmetry means that the maximal probability of particle fragmentation has to be also there. 

To model the particle velocity fluctuation covariances caused by particle-particle collisions and particle interactions with the interstitial gas phase, the concept of kinetic theory of granular flows is adapted (see chap 4). This theory is based on an analogy between the particles and the molecules of dense gases. The particulate phase is thus represented as a population of identical, smooth and inelastic spheres. In order to predict the form of the transport equations for a granular material the classical framework from the kinetic theory of... 

The reader may be surprised not to And a Reynolds number defined speciflcally for the disperse phase. This is because the disperse-phase viscosity is well defined only for Knp 1 (i.e. the collision-dominated or hydrodynamic regime). In this limit, Vp oc oc Knp/Map so that the disperse-phase Reynolds number would be proportional to Map/Krip when Map < 1. However, in many gas-particle flows the disperse-phase Knudsen number will not be small, even for ap 0.1, because the granular temperature (and hence the collision frequency) will be strongly reduced by drag and inelastic collisions. In comparison, molecular gases at standard temperature and pressure have KUp 1 even though the volume fraction occupied by the molecules is on the order of 0.001. This fact can be... 

---