Viscosity of concentrated suspensions: influence of cluster formation

Dispersed particles can form clusters even at low concentrations. Colloidal and hydrodynamic forces are responsible for this phenomenon and these forces determine both structure and size of clusters. We assume that the viscosity of a concentrated suspension is completely determined by cluster size distribution, regardless if clusters form under the action of colloidal, hydrodynamic interactions or applied shear rates. Based on this assumption an equation, which describes dependency of viscosity on a concentration of dispersed particles taking into account cluster formation, is deduced. Under special restrictions the deduced dependency coincides with the well-known Dougherty-Krieger's equation except for a clear physical meaning of parameters entered. Our consideration shows that Dougherty-Krieger's equation has deeper physical background than it has been supposed earlier. Experimental verification of the suggested model shows a good agreement with the theory predictions and proves a presence of clusters even at low concentrations of dispersed particles.