Microscopic Origin of Frictional Rheology in Dense Suspensions: Correlations in Force Space

摘要

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (sigma(xy)) and packing fraction (phi). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, mu = sigma(xy)/P. We find that mu decreases (i) as phi is increased and (ii) as sigma(xy) is increased. Using a new constitutive relation between mu and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a discontinuous shear thickening flow diagram that is in good agreement with numerical simulations, and the qualitative features of mu that lead to the generic flow diagram of a discontinuous shear thickening fluid observed in experiments.