Influence of stretching induced self-concentration and self-dilution on coil-stretch hysteresis and capillary thinning of unentangled polymer solutions

Entov and Hinch [J. Non-Newtonian Fluid Mech. 72,31-53 (1997)] predicted a Weissenberg number of 2/3 during capillary thinning of slender filaments of polymer solutions. Data from the experiments of Clasen et al. [J. Rheol. 50, 849-881 (2006)] however show that that is not the case. The Weissenberg number is observed to systematically decrease with concentration in nominally dilute solutions to values well below the critical value of 1/2 for the coil-to-stretch transition to reach a minimum around the critical-overlap concentration c*, and thereafter increase in semidilute solutions. Conformation dependence of the polymeric friction coefficient and the phenomenon of coil-stretch hysteresis are shown to play vital roles in determining capillary thinning dynamics. A key result is that when steady-state coil-stretch hysteresis exists, transient polymer conformations during capillary thinning evolve quasistatically along the unstable manifold of the hysteresis window. It is further found necessary to account for changes in polymeric friction due to intermolecular interactions as chains stretch in the flow. A new constitutive model for unentangled polymer solutions is proposed combining blob concepts to account for the effect of hydrodynamic screening on the average friction coefficient of partially stretched chains. It is shown that stretching causes intermolecular interactions to become stronger in the dilute regime and weaker in semidilute solutions. Predictions with this constitutive model agree well with the experimental data in capillary thinning. (C) 2016 The Society of Rheology.