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For a pseudofluid consisting of a particle assembly, particle stress is transmitted through mutual contact between particles. When the particles are densely agglomerated, contacts are usually of long duration and frictional, and this part of the stress is the frictional stress. When the particles are sparsely spaced, on the other hand, contacts are temporary and collisional, and this part of the stress consists of kinetic and collisional stresses. In many cases the particle contact lies between these two extremes in a gas−solid fluidized bed, and all of these three parts of the stresskinetic, collisional, and frictional stressesplay important roles in particle-phase transport. However, the existing kinetic theory for granular flow (KTGF) only involves the kinetic and collisional parts of transport. In this paper, a frictional particle pressure was introduced for correction of KTGF in the case of highly dense flow, and the solid shear stress was corrected to be consistent with Einstein's effective viscosity equation for dilute suspensions. This modified KTGF model may account for the stress over the entire range between two extremes of a densely packed state and a sparsely spaced state. As verification in the dense gas−solid flow, the time-averaged total pressure drop and the particle pressure predicted by this modified KTGF model were found to be in agreement with the measurements in a cylindrical fluidized bed. The inflection point on the particle pressure curve, implying competition among the three transport mechanisms, was also predicted. Moreover, instantaneous formation of slugs starting from a homogeneous inflow condition was reproduced through simulation and the quantitative comparison of the slug velocity with empirical correlation was approving. For dilute gas−solid flow in a circulating fluidized-bed riser, the model predictions agree with the time-averaged solid viscosity in order of magnitude. Further modeling may require a better understanding of the drag force and turbulence.

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