Recent advances in the continuum mechanics of viscoelastic liquids

The kinematics of viscoelastic fluid flows, the development of constitutive relations and their use in viscometric and nonviscometric flows is given. Experimental data in viscometric flows, extensional flows and the eccentric rotating disk motion along with oscillatory shear flows are presented and compared with theoretical predictions. The flow classification scheme for the selection of the appropriate constitutive equation, the perturbation schemes applicable to fixed and variable domains are described. These are applied to review the literature on particle motions, lubrication problems and rotating flows. Stability of the flows is discussed along with some recent work on existence, uniqueness and the use of dynamical system and hyperbolic theory in connection with propagating singular surfaces.