Effect of configuration-dependent intramolecular hydrodynamic interaction on elastocapillary thinning and breakup of filaments of dilute polymer solutions

Abstract

We use a new constitutive model for the polymer stress in a dilute polymer solution to predict elastocapillary thinning and breakup of a thin filament of the solution. The constitutive model accounts for the effects of finite chain extensibility and configuration-dependent intramolecular hydrodynamic interaction, and is used in the simple stress balance equation proposed by Entov and Hinch [Entov, V. M., and E. J. Hinch, J. Non-Newtonian Fluid Mech. 72, 31–53 (1997)] for situations where inertial effects are negligible. In their seminal study, Entov and Hinch showed that during the period where the elastic polymer stresses are dominant, the filament radius decreases exponentially with time. We find that configuration-dependent hydrodynamic interactions cause the time constant in this exponential decay to depend on concentration, as observed in recent experiments. Moreover, the phenomenon of coil-stretch hysteresis permits a large polymer stress even though the transient Weissenberg number during elastocapillary thinning decreases below the critical value of 1∕2 for the coil-to-stretch transition of a dilute polymer solution in an extensional flow. As a consequence, the Weissenberg number does not have a lower bound of 2∕3 as predicted originally by Entov and Hinch using a simpler constitutive model that does not account for configuration-dependent hydrodynamic interactions.