Granular flows, radial

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. 

The wort entering the whirlpool tank initially rotates about the vertical axis. This rotational movement in the upper layers of liquid tends to throw particles radially outwards. As the tank fills up, the wort at the bottom of the vessel will, because of friction with the base of the tank, lose this rotation. A pressure gradient builds up which causes the wort to flow radially inwards at the base where the particles tend to be carried inwards to the centre. The drag of the vessel base reduces the velocity of the wort stream and so the particles tend to be deposited at the centre. From the centre, the wort rises. The circulatory currents appear to assist in the flocculation of hot trub particles because, compared with simple sedimentation, the particles are larger and more granular. 

In separation processes and chemical reactors, flow through cylindrical ducts filled with granular materials is important. In such systems conduction, convection, and radiation all contribute to the heat flow, and thermal conduction in axial ke x and radial ke r directions may be quite different, leading to highly anisotropic thermal conductivity. For a bed of uniform spheres, the axial and radial elements are approximated by... 

The Geilikman et al. model relates yield front velocity to the volumetric rate of solids production by mass balance. A front between yielded and intact zones moves radially away from the wellbore as solids production continues. Mass balance analysis allows determination of the position of the moving front. Fluid production enhancement is dependent on the instantaneous solids flux, as well as the radius of the yielded zone around the wellbore (i.e., the solids production history). Viscous resistance to oil flow is reduced when the granular matrix is also flowing. The volumetric fluid production, Qf(t), is given as... 

Whereas the longitudinal heat flow methods are most suitable for slab specimens, the radial heat flow techniques are used for loose, unconsolidated powder or granular materials. The methods can be classified as follows ... 

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