Continuum mechanics modeling of complex fluid systems following Oldroyd's seminal 1950 work

Abstract

We present a review of some key developments in the continuum mechanics – based macroscopic modeling of complex fluid flows, following the pioneering work of Oldroyd in the 1950s. We start by reviewing the major developments achieved by Oldroyd, namely how his work established rules for consistency in developing continuum stress constitutive models extending the material into objective time derivatives for tensor quantities, with first application the stress tensor in viscoelastic constitutive relationships. We then show how the impact of his work to viscoelastic fluid flows has been amplified from the kinetic theory work of Bird and others who established a firm macromolecular structural connection. The use of objective time derivatives was then extended to include second order conformation tensors and through them the connection was made to internal deformation energy by Marrucci. We then further demonstrate the impact of this work by analyzing the models through the microstructural descriptions offered within the non-equilibrium thermodynamics formalism. We then conclude with a brief mentioning of direct applications of the original Oldroyd-B model (through stability analyses, etc.) towards bettering our understanding of the rheological behaviour of complex fluid systems.