Granular viscosity

In order to include the kinetic deviatoric pressure tensor, the mean free path theory [25,49, 67] is used to calculate the dilute granular viscosity (i.e., see (4.377)), and further the derived quantities like the granular kinetic viscosity (i.e., see (4.379)), the kinetic deviatoric pressure tensor p " (i.e., see (4.381)) are calculated through them. 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

If PVC polymer particles are mixed, at room temperature, with plasticisers the immediate product may take one of two forms. If there is insufficient plasticiser to fill all the gaps between the particle a mush will be produced. If all the voids are filled then the particles will become suspended in the plasticiser and a paste will be formed. In the case of conventional granular polymer, or with emulsion polymer cenospheres, the particles are too large to remain in suspension and will settle out. Therefore compounds used in paste-processes must use polymers with a small particle size. On the other hand there is a lower limit to this, since small particles will have a very high surface/volume ratio and measurable plasticiser absorption will occur at room temperature to give a paste whose viscosity will increase unduly with time. As a consequence paste polymers have an average particle size of about 0.2-1.5 ptm. 

It will be assumed for the present considerations that sufficient binder is present in the granulator as determined by the binder/powder ratio and that the binder is appropriately spread on enough granular surfaces so as to ensure that most random collisions between particles will occur on binder-covered areas. It will also be assumed that the particles are more or less spherical having a characteristic dimension, a. The simplified system of two colliding particles is schematically shown in Fig. 21. The thickness of the liquid layer is taken to be h, while the liquid is characterized by its surface tension yand its viscosity /x. The relative velocity U0 is taken to be only the normal component between particles while the tangential component is neglected. 

In another class of models, pioneered by Elghobashi and Abou-Arab (1983) and Chen (1985), a particle turbulent viscosity, derived by extending the concept of turbulence from the gas phase to the solid phase, has been used. This is the so-called k—s model, where the k corresponds to the granular temperature and s is a dissipation parameter for which another conservation law is required. By coupling with the gas phase k—s turbulence model, Zhou and Huang (1990) developed a k—s model for turbulent gas-particle flows. The k—s models do not... 

Starch gelatinization is the disruption of molecular orderliness within the starch granule. It results in granular swelling, crystallite melting, loss of birefringence, viscosity development, and solubilization. 

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