When does the elastic regime begin in viscoelastic pinch-off?

Abstract: In this experimental and numerical study, we revisit the question of the onset of the elastic regime in viscoelastic pinch-off. This is relevant for all modern filament thinning techniques which aim at measuring the extensional properties of low-viscosity polymer solutions such as the Slow Retraction Method (SRM) in Capillary Breakup Extensional Rheometry (CaBER) as well as the dripping method where a drop detaches from a nozzle. In these techniques, a stable liquid bridge is slowly brought to its stability threshold where capillary-driven thinning starts, slowing down dramatically at a critical radius $h_1$ marking the onset of the elastic regime where the bridge becomes a filament with elasto-capillary thinning dynamics. While a theoretical scaling for this transition radius exists for the classical step-strain CaBER protocol, where polymer chains stretch without relaxing during the fast plate separation, we show that it is not necessarily valid for a slow protocol such as in SRM since polymer chains only start stretching (beyond their equilibrium coiled configuration) when the bridge thinning rate becomes comparable to the inverse of their relaxation time. We derive a universal scaling for $h_1$ valid for both low and high-viscosity polymer solution which is validated by both CaBER (SRM) experiments with different polymer solutions, plate diameters and sample volumes and by numerical simulations using the FENE-P model.