Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids. Part II: Suspensions at finite concentration

The steady shear rheology of nondilute suspensions of noncolloidal, rigid spheres in highly elastic, constant viscosity fluids is studied via numerical simulation using three-dimensional, finite-volume methods and via experiments using cone-and-plate measurements. In the numerical study, we use an immersed boundary method to simulate an ensemble of particles as a function of time until they achieve steady average bulk properties, and the simulations include fully resolved particle-scale hydrodynamics and fluid stresses. The simulations show that for low volume fraction, nondilute suspensions, the viscosity thickens at high shear and this effect can be fully determined by considering a single particle’s interactions with the suspending fluid. In fact, we show that experimentally measured viscosities of suspensions up to ϕ∼0.25, where ϕ is the volume fraction of particles, can be characterized by a shift factor that determines the zero-shear viscosity and a master curve that describes the viscosity thickening. The master curve is determined by single particle–fluid interactions that depend critically on the extensional properties of the suspending fluid. Thus, the “per particle” thickening contribution to the viscosity, at large values of the Weissenberg number, is not dependent on particle–particle interactions when plotted versus the suspension stress. This “master curve” for the thickening of the shear viscosity is not only demonstrated in the simulations, but also we show that it is consistent with all available experimental data including our own. We show that the first normal stress difference coefficient can be described similarly by a shift factor and a master curve. Our numerical simulations do not quantitatively reproduce the experimental data and in general underpredict the experimentally measured shear-thickening of the rheological properties. We suggest, and provide supporting evidence, that this can be explained by the inability of the constitutive model employed in the simulations to adequately describe the extensional properties of the suspending fluid.