ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 17, 2009

The viscosity of particle suspensions depend on the volume fraction of particles. This was demonstrated by Einstein1,2 for dilute suspensions and later extended to less dilute systems by Batchelor3 and Batchelor and Green4. Krieger and Dougherty5 followed a different approach to analyse concentrated suspensions. They combined the result of Einstein with a self-consistent field approach and obtained a very useful expression for the viscosity as a function of the solvent viscosity (ηs) and the volume fraction of particles (φ) as well as a maximum packing parameter (φm). The maximum packing parameter φm, though physically sound, was introduced in a very heuristic way. In recent work by Hansen and Szabo6,7 a model was developed for the viscosity of particle suspensions which takes into account finite size effects. Data reported by de Kruiff et al.8 were compared to predictions by the new model as well as to other models from the literature (e.g. Krieger and Dougherty5). We found that the inclusion of finite size effects improved the model prediction of the viscosity. The idea of a discrete spectrum of particles was also presented in Hansen and Szabo6,7. Here we shall explore the model consequences as the particles in suspension are no longer identical