Ongoing relevance of Oldroyd 8-constant fluids

Jeffrey Giacomin

Queens University, Canada

Abstract

Of the many seminal contributions by Oldroyd to science and engineering, his weightiest embodies his 1958 general vision of the expected and allowable constitutive behaviors of elastic liquids. This remarkable vision is reflected in his constitutive framework which incorporates all possible tensorial products of the extra stress and rate-of-deformation tensors, along with all possible terms that are quadratic in the rate[1]of-deformation tensor. This framework involves exactly 8 constants, the most fundamental of which are the zero-shear viscosity, and the relaxation and retardation times. Oldroyd gives the general solution for the complex viscosity for all special cases of his framework in terms of the latter three constants. Further, Oldroyd gives the general solution for the steady shear viscosity for all special cases of his framework in terms of all eight constants. Since 1958, the framework has embraced many new constitutive equations as its special cases, and in this sense, its relevance continues to this day. Many of these special cases have led to exact analytical solutions for polymer processing problems, allowing continuing exploration of the role of melt elasticity. Moreover, when the Oldroyd framework is bridged to the macromolecular theory, the role of molecular structure in polymer processing is uncovered, and this exciting use for the framework continues to this day.

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