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In fact, the kinetic theory approach for granular flow allows the determination of, for example, particle phase stress, pressure, and viscosity in place of the empirical equations.
After this developmental stage of granular theory, there have been several modifications to the constitutive equations such as extension of the kinetic theory for granular flow for mixtures of multi-type particles.
The second group of models is based on the kinetic theory of granular flow.
In dense granular flows, in addition to the kinetic and collisional stresses (described by the kinetic theory), the model should account for the frictional stresses as well, which is dominant in flow regimes denser than the bubbling regime.
Although in some granular flows the restitution coefficient is restrained to values close to unity, its deviation from unity results in a significant variation in the properties of granular flow.
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