Capillarity-driven thinning dynamics of entangled polymer solutions

Abstract: We analyze the capillarity-driven thinning dynamics of entangled polymer solutions described by the Doi-Edwards-Marrucci-Grizzuti (DEMG) model and the Rolie-Poly (RP) model. Both models capture polymer reptation, finite rates of chain retraction and finite extensibility of single polymer molecules, while differing slightly in their final form regarding to the convective constraint release. We calculate numerically the filament thinning profiles predicted by the two models with realistic entanglement densities, assuming cylindrical filament shapes and no fluid inertia. Both results reveal an early tube-reorientation regime, followed by a brief intermediate elasto-capillary regime, and finally a finite-extensibility regime close to the pinch-off singularity. The results presented in this work reveal two critical features in the transient extensional rheology of entangled polymer solutions that have been reported from previous experimental studies, but are poorly described by the widely-used FENE-P model. First, the relaxation time obtained from capillary breakup extensional rheometry is notably smaller than that from steady-shear rheometry. Their ratio can be expressed as a universal function of the entanglement state and the polymer concentration, which agrees well with the experimental data for a range of entangled polymer solutions. Second, the filament thinning dynamics at sufficiently high polymer concentrations are governed by the tube reorientation at intermediate strain-rates, and the apparent extensional viscosity shows a noticeably rate-thinning response. We finally evaluate the filament thinning dynamics of aqueous polyethylene oxide solutions (1 MDa) over dilute and entangled regimes. As the concentration increases, the profiles deviate from the well-studied exponential-thinning trends beyond the entangled threshold, becoming increasingly power-law in character.