Rheology of dilute and semidilute noncolloidal hard sphere suspensions

Abstract

The dissipative behavior of model suspensions composed of non-Brownian, inertialess, rigid spheres immersed in Newtonian and viscoelastic matrices is investigated in the range of volumetric concentrations up to 10%, thus encompassing both the dilute and semidilute regimes. Polymethylmethacrylate beads are dispersed into polyisobutylene, characterized by a Newtonian rheology, and into two viscoelastic polydimethylsiloxanes. Both steady state viscosity and oscillatory shear loss modulus measurements are performed. As expected, the presence of the filler increases both the viscosity and the loss modulus of all suspensions. Following the hydrodynamic calculations of Batchelor, the concentration dependence is described by a second order polynomial expansion in the volume fraction. For low concentrations, the linear Einstein and Palierne predictions for Newtonian and viscoelastic fluids are found to be well obeyed by both the Newtonian and the viscoelastic suspensions. In the semidilute regime, the experimental data for the Newtonian suspension show an excellent quantitative agreement with Batchelor’s calculations. Conversely we find that, out of possible experimental errors, the viscoelastic suspensions show more pronounced deviations from the linear dilute behavior, resulting in a second order polynomial coefficient substantially larger than that predicted by Batchelor for Newtonian systems.