Stress Jump at the Inception of Shear and Elongational Flows of Dilute Polymer Solutions due to Internal Viscosity

Abstract

All versions of the internal viscosity (IV) model for polymer chain dynamics lead to the prediction that the inception of flow from a rest state is accompanied by a stress jump at t=0. For the general case of long chains (large number of submolecules, N), the jump is predicted here for the onsets of simple shear flow and elongational flow at constant deformational rate. The exact model formulation (i.e., following Booij and van Wiechen) is used, without the need to approximate deformational velocities in the Cerf/Peterlin sense, and rigorous closed‐form solutions are presented. This is apparently the only rheological prediction now available for the large N IV model using the rigorous formulation. Intermediate steps in the analysis demonstrate the extent to which the motions of beads are correlated with those of neighbors at various distances in the linear sequence; the effect is small and depends slightly on φ/f. Final results show that viscosity jumps are independent of deformational rate and depend on both φ and φ/f, where φ is the IV coefficient and f the bead/solvent friction coefficient. Experiments on stress jumps and subsequent transients are thus potentially able to evaluate φ alone, unlike steady‐state experiments which respond only to φ/f. Predictions for shear flow are also compared with those made using the Cerf/Peterlin linearization approximation, showing that the two diverge severely at high values of φ/f.