Correlation between stresses and microstructure in concentrated suspensions of non-Brownian spheres subject to unsteady shear flows

Abstract

Stresses within unsteady simple shear flows of suspensions of non-Brownian spheres constrained to move in the velocity-gradient plane are calculated using Stokesian dynamics simulations. The unsteady flows considered include shear reversal and oscillatory flows of varying strain amplitude. The evolution of the stresses in time are reported along with the corresponding microstructural development for all flow conditions. For shear reversal, the shear stress rapidly decreases to a minimum before gradually returning to the steady state value reached in the previous direction, whereas the normal stress briefly changes sign upon reversal of shear before returning to the steady state value. For oscillatory shear flow, the shear stress increases with total strain before attaining a steady state that depends upon the applied strain amplitude, indicating irreversible behavior even at small strain amplitudes. The shear stresses show a nonmonotonic dependence on the applied strain amplitude that agrees with experimental results [Bricker and Butler, J. Rheol. 50, 711–728 (2006)]. The steady state normal stresses also depend on the strain amplitude and may change signs at low strain amplitudes.