Oldroyd's model and the foundation of modern rheology of yield stress fluids

Abstract

• Oldroyd's 1946 paper was ahead of its time. • Pre- and post-yielded regimes are described in a tensorial manner with a von Mises yield criterion. • Modern formulations of yield stress fluids are still heavily influenced by Oldroyd's paper. • Many experimental studies have probed the assumptions and implications of Oldroyd's model. Oldroyd's 1946 formulation of the constitutive equation of yield stress fluids laid the foundation of modern rheology of yield stress fluids, by considering not just the simple shear behavior of yield-stress fluids in the plastic regime, but also by prescribing a simple expression for how they behave prior to yielding and a 3D expression for how they behave beyond yielding. We discuss the implications of Oldroyd's model, and the ways in which researchers have tested and refined his ideas. We also review the experimental methods that have been employed to test these implications, and to determine the rheological parameters it lays out. We finally discuss the impact of Oldroyd's model, and the future of investigations into what happens prior to yielding.