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 to all modern filament thinning techniques, which aim to measure the extensional properties of low-viscosity polymer solutions. Examples are the slow retraction method (SRM) for capillary breakup extensional rheometry (CaBER), or the dripping method, in which a drop detaches from a nozzle. As part of these techniques, a stable liquid bridge is brought slowly to its stability threshold, where capillary-driven thinning starts. This thinning slows down dramatically at a critical radius, marking the onset of the elasto-capillary regime, characterised by a filament of nearly uniform radius. While a theoretical scaling exists for this transition in the case of the classical step-strain CaBER protocol, where polymer chains stretch without relaxing during the fast plate separation, we show that this theory is not necessarily valid for a slow protocol such as the SRM. In that case, polymer chains start stretching (beyond their equilibrium coiled configuration) only when the bridge thinning rate becomes comparable to the inverse of their relaxation time. We derive a universal scaling for, valid for both low- and high-viscosity polymer solutions. This scaling is validated by CaBER experiments with a slow plate separation protocol using different polymer solutions, plate diameters and sample volumes, as well as by numerical simulations using the FENE-P model.