Grain inertia and fluid viscosity dominated granular flow rheology: a thermodynamic analysis

We analyze a combined theory of granular flow where both the particle density and the interstitial fluid viscosity play a role in the constitutive equations which describe the rheology of the particulate phase. Such a theory combines the more classical inertial-type theories of dry and aerated granular flow with the viscosity-dominated theory recently discussed by Jenkins and McTigue. We also develop a pseudo-thermodynamic theory valid for the general case, of which our recent pseudo-thermodynamic theory for the inertial case is seen to be an asymptotic limit. Finally, we discuss propagation of particulate phase pressure waves.