A rheological constitutive model for semiconcentrated rod suspensions in Bingham fluids

A rheological constitutive law is developed for a suspension of rigid rods in a Bingham fluid for volume fractions ranging up to the semiconcentrated regime. Based on a cell model approach, which allows expressing the shear stress on the particle surface, the particle stress contribution is derived and involves additional yield stress terms related to an ensemble average orientation distribution of the rods. As a first approach, a von Mises criterion is used to describe the composite flow threshold, which is found to be anisotropic in the sense that it depends on the rod orientation. A rod dynamics equation is also proposed and incorporates some diffusion/perturbation due to yielded regions encountered throughout the suspension. In parallel, an equivalent kinetic theory is also developed. The model provides good agreement with shear stress experiments for kaolin pastes filled with steel fibers of two different aspect ratios.