Numerical analysis of capillarity-driven thinning rheometry for polydisperse polymer solutions
Liquid bridges of polymer solutions that are self-thinning due to the action of capillarity undergo a transition from Newtonian-like linear thinning to exponential elastocapillary (EC) thinning when the polymer chains are stretched by the elongational flow and the resulting elastic contribution to the stress exceeds the viscous stress. As the Oldroyd-B model predicts that the EC thinning rate is set by the relaxation time ($\tau$) of the polymer, the characteristic thinning timescale extracted from the exponential decay ($\tau_{EC}$) is commonly interpreted as a direct measure of $\tau$. Here we show that for real polydisperse polymer solutions, $\tau_{EC}$ reflects only a subset of the molecular weight (MW) distribution -- those chains actively stretched by the flow. We demonstrate this using a multi-mode FENE-PM model that explicitly incorporates the molecular weight distribution, validated against the filament thinning experiments of Calabrese et al. [Phys. Rev. X 15, 021025 (2025)] on bidisperse blends of narrowly-distributed low-MW and high-MW polystyrene solutions. The model predicts that only chains with effective Weissenberg number $Wi = \dot{\varepsilon} \tau > 1/2 $ are extended by the flow and contribute elastic stress; this threshold naturally favors high molecular weight species, whose longer relaxation times allow them to remain stretched throughout the elastocapillary regime. The measured $\tau_{EC}$ is therefore set by this stress-contributing sub-ensemble rather than the full distribution. Further, our model predicts that $\tau_{EC}$ depends on both the molecular weight distribution and total polymer concentration, as well as experimental parameters including pre-stretch and initial filament diameter, confirming that it is best understood as an experiment-specific quantity rather than an intrinsic fluid property.