The Cox–Merz rule extended: A rheological model for concentrated suspensions and other materials with a yield stress

Abstract

A nonlinear rheological model combining elastic, viscous, and yielding phenomena is developed in order to describe the rheological behavior of materials which exhibit a yield stress. A key feature of the formulation is the incorporation of a recoverable strain; it has a maximum value equal to the critical strain at which the transition from an elastic solid-like response to a viscous shear thinning response occurs. An analysis is presented to enable determination of all the model parameters solely from dynamic measurements which are easily accessible experimentally. A rigorous correlation, analogous in form to the Cox–Merz rule, is shown to exist between the steady shear viscosity and the complex dynamic viscosity in terms of a newly defined ‘‘effective shear rate.’’ Experimental data obtained for a 70 vol % suspension of silicon particles in polyethylene indicate agreement with theoretical predictions for both the dynamic and steady shear behavior.