An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions

The relationship between particle size distribution and viscosity of concentrated dispersions is of great industrial importance, since it is the key to get high solids dispersions or suspensions. The problem is treated here experimentally as well as theoretically for the special case of strongly interacting colloidal particles. An empirical model based on a generalized Quemada equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} is used to describe η as a function of volume fraction for mono- as well as multimodal dispersions. The pre-factor η˜ accounts for the shear rate dependence of η and does not affect the shape of the η vs φ curves. It is shown here for the first time that colloidal interactions do not show up in the maximum packing parameter and φmax can be calculated from the particle size distribution without further knowledge of the interactions among the suspended particles. On the other hand, the exponent ɛ is controlled by the interactions among the particles. Starting from a limiting value of 2 for non-interacting either colloidal or non-colloidal particles, ɛ generally increases strongly with decreasing particle size. For a given particle system it then can be expressed as a function of the number average particle diameter. As a consequence, the viscosity of bimodal dispersions varies not only with the size ratio of large to small particles, but also depends on the absolute particle size going through a minimum as the size ratio increases. Furthermore, the well-known viscosity minimum for bimodal dispersions with volumetric mixing ratios of around 30/70 of small to large particles is shown to vanish if colloidal interactions contribute significantly.