Bead-spring model of dilute polymer solutions: Continuum modifications and an explicit constitutive equation

A continuum modification of the bead‐spring (elastic dumbbell) theory of dilute solutions of linear macromolecules, recently introduced by Gordon and Schowalter, is used to obtain explicit constitutive equations for the stress and polarizability tensors. The stress constitutive equation, closely related to a semiempirical result obtained earlier by Spriggs, is superior in predictive capability to the constitutive equation obtained from the elastic dumbbell theory. Results are presented for steady shearing flow, large‐amplitude oscillatory shearing, and stress relaxation following cessation of steady shearing and are compared with the results of the elastic and rigid dumbbell theories. In general, predictions are similar to those of the rigid dumbbell and thus are in qualitative agreement with experiment.