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...