Flow regime transitions in dense non-Brownian suspensions: rheology, microstructural characterisation and constitutive modelling

Shear flow of dense, non-Brownian suspensions is simulated using the discrete element method, taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of solid volume fraction, shear rate, fluid viscosity and particle stiffness. Below a critical volume fraction $\phi_c$, the rheology is governed by the Stokes number, which distinguishes between viscous and inertial flow regimes. Above $\phi_c$, a quasistatic regime exists for low and moderate shear rates. At very high shear rates, the $\phi$ dependence is lost and soft particle rheology is explored. The transitions between rheological regimes are associated with the evolving contribution of lubrication to the suspension stress. Transitions in microscopic phenomena such as inter-particle force distribution, fabric and correlation length are found to correspond to those in the macroscopic flow. Motivated by the bulk rheology, a constitutive model is proposed combining a viscous pressure term with a dry granular model presented by Chialvo, Sun and Sundaresan [Phys. Rev. E. \textbf{85}, 021305 (2012)]. The model is shown to successfully capture the flow regime transitions.