Understanding dense granular flow from first principles

Abstract

Preventing natural disasters like avalanches or landsides, optimising powder-based industrial processes or predicting the flow of sand on planetary surface, are exemplary applications that would benefit from a universal model for a better understanding of granular rheology. Due to the high densities and shear rates involved, the derivation of constitutive equations from first principles is notoriously difficult. Here, we will present such a theoretical approach, the Granular Integration Through Transients (GITT) formalism. Starting from the microscopic equations of motion, GITT yields quantitative predictions for the flow curves of granular fluids at high density and shear rate. GITT predicts Newtonian, shear thinning, and shear thickening regimes depending on density and shear rate. We will present experiments in a fluidized bed rheometer that confirm the rheological regimes and can be evaluated quantitatively in terms of GITT. We will discuss a phenomenological version of GITT that makes the qualitative behaviour understandable in terms of dimensionless numbers. With this we can derive the mu(I)-rheology that has been proposed as an empirical law for granular flow and show that it is a special case of GITT for specific flow conditions.