Momentum Fluxes and Particulate Stresses

With the same area-averaging method and notations used in Eqs. 9.26 and 9.27, the time-averaged momentum flux pij of the particulate phase can be expressed (Sun, 1989) as 

This particulate stress represents the kinetic components of granular momentum transfer, and includes both the viscous contribution due to the small-scale random motion of individual particles as well as the macroscopic turbulence contributions due to collective random motions such as eddies and bubbles (Sun, Chen, and Chao, 1990). The complete granular stress should consist of this particulate stress component and a collisional stress component. 

FIGURE 9.15 Solids particulate stresses in a fluidized bed for 500-p.m glass particles at ujumf = 2 

FIGURE 9. 16 Variation of density-weighted, volume-averaged particulate stresses with ujum] 

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