The rheology of concentrated suspensions of arbitrarily-shaped particles

We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the intrinsic viscosity is known in the dilute limit and the particles are not too elongated. The procedure allows to construct a continuum-medium model in which correlations between the particles are introduced through an effective volume fraction. We have tested the procedure using spheres, ellipsoids, cylinders, dumbells, and other complex shapes. In the case of hard spherical particles, our expression improves considerably previous models like the widely used Krieger–Dougherty relation. The final expressions obtained for the viscosity scale with the effective volume fraction and show remarkable agreement with experiments and numerical simulations at a large variety of situations.

Graphical abstractLeft panel: relative viscosity η(ϕ)/η0η(ϕ)/η0 as predicted by our model for isotropic rods with different aspect ratios and intrinsic viscosities as given by Table 3. Silica rods (solid line), schizophylian (dashed line), xanthan (dotted line), and PMMA fibre (dash-dotted line). Right panel: the same as left panel but assuming orientational order and using ϕmax≃0.9069ϕmax≃0.9069. The fitted values of [ηη] were 90 for silica rods (solid line), 50 for schizophylian (dashed line), 40 for xanthan (dotted line), and 13 for PMMA fibre (dash-dotted line). The data sets were taken from Ref. [9].Figure optionsDownload full-size imageDownload high-quality image (94 K)Download as PowerPoint slide