Carried Along on a Path Line in Modelling Constitutive Equations of Viscoelastic Fluids

Abstract

A retrospect is given on the “path line” whereon the author was carried along in search for structural constitutive models which predict viscoelastic properties. In the first section of this path an analysis was carried out of a dilute solution of rigid dumbbells, and subsequenty of linear-elastic dumbbells with finite equilibrium length. In doing so, the associated constitutive equation for the special case of Hookean dumbbells could be identified with that of an Oldroyd B fluid. The second section was devoted to the indication of conditions under which second normal-stress differences would appear. This was shown to be the case for solutions of rigid dumbbells with spheroidal beads without and with inclusion of hydrodynamic interaction and also for solutions of rigid spheroids. In a third section of this path line attention was focused on the dependence of rheological properties of suspensions with rigid particles of different shape on orientation and motion subject to different types of flow. Eventually, in a last section an approach was attempted to comprehend more concentrated solutions in these investigations. This was based on the concept of configuration-dependent tensorial mobility as a function of the mean configuration tensor. Already a linear relation between these tensors resulted in a model which predicted most features of polymer fluids. When substituting instead a slightly more complicated relation of relaxation type, these predictions could be substantially improved. Finally, inclusion of a quadratic and an exponential term, respectively, in the first mentioned linear relation allowed for a description of flow hardening phenomena.