Granular rheology: A tale of three time scales.

Abstract

We adapt statistical models of the physics of complex fluids to study the rheology of granular liquids. This allows us to provide laws of granular rheology based on first principles, which compare well with previously established phenomenological laws. In particular, the very successful law of μ(I) rheology can be understood within our model as the lowest order nontrivial Padé approximant of the macroscopic laws of rheology if one takes into account processes taking place at three distinct types of time scales: Collisions occurring at microscopic scales, collective motions like cage effect taking place at intermediate, mesoscopic scales, and finally advection that takes place at the macroscopic time scale. Our model's ability to describe granular physics outside of the Bagnold scaling regime allows for a natural extension to the rheology of granular suspensions.