Modified bead spring theory of dilute polymer solutions. III. Inclusion of multiple relaxation times



A previously derived constitutive equation, representing a blending of the molecular dumbbell theory and a continuum theory of anisotropic fluids, has been extended to the multidumbbell (Rouse-Zimm) case. The equation thus derived yields predictions equivalent to the Rouse-Zimm theory in small-amplitude dynamic shearing, with the exception that the introduction of an “effective molecular weight” as the concentration of polymer is increased is no longer required. In simple shearing flow, the theory predictions are far superior to those of the Rouse-Zimm model, yielding realistic non-Newtonian viscosity behavior, a positive primary normal stress difference, and a negative secondary normal stress difference. In stress relaxation following the cessation of steady shearing flow, the rate of relaxation is found to depend to the initial velocity gradient, but the effect is predicted to be too small to be observed experimentally in typical dilute polymer solutions. The effects of molecular weight, molecular weight distribution, and polymer–solvent interaction are explicitly accounted for, and in all cases the theory predictions are in excellent qualitative agreement with accepted experimental behavior.