Micromechanics and apparent viscosities of non-Newtonian fluid suspensions

The influence on the overall shear-stress versus shear-rate relation of different volume-fraction solid-filled non-Newtonian fluid suspensions is investigated at the level of dilute concentration. The method developed is based on the approximate mean-field theory for plasticity of two-phase composites. Using the approximation approach of Berveiller and Zaoui [Berveiller, M., Zaoui, A., 1979. An extension of the self-consistent to plastically-flowing polycrystals, J. Mech. Phys. Solids. 26, 325–344.], the constraint due to the matrix phase is characterized by the apparent viscosity of the matrix, while the interaction of the solid-filled suspensions is accounted for by the Mori–Tanaka mean-field theory. It is shown that this simple, but approximate theory is capable of predicting the volume fraction dependence of the nonlinear shear-stress versus shear-rate relation. An analytic solution and a master curve of the shear-stress versus shear-rate relation are obtained. This theory of overall viscosity of solid-filled non-Newtonian fluid suspensions was checked by performing the capillary rheometer test to measure the overall viscosity of a glass bead-reinforced polyetheretherketone (PEEK) suspension. The experimental results are in very good agreement with the theoretical predictions.