To win, a model must thin: Capillary thinning as a benchmark complex flow for constitutive models of viscoelastic polymer solutions

Abstract

Capillary thinning of a liquid bridge is an exemplar of complex flow, where the macroscopic geometry couples tightly to the microscopic evolution of polymer conformations. Since its inception, capillary-breakup rheometry (CBR) has been viewed as a tool for measuring a single relaxation time. Yet experiments show that the apparent relaxation time depends systematically on polymer concentration, device geometry, and the preparation protocol. We argue that this variability is not a flaw, but evidence that thinning should be treated as a benchmark complex flow for testing constitutive models. We recast the output of a CBR experiment as the self-selected elastic strain rate, expressed through the elastic Weissenberg number Wi_e, rather than an apparent relaxation time, and organize it in an elastocapillary Pipkin diagram -- Wi_e against a geometry-controlled Deborah number. A single-mode, mid-filament stress balance yields a family of Pipkin curves with universal features -- a low-De_0 plateau and a finite-extensibility-constrained rise -- that a scaling analysis collapses onto a master curve, with an elastic-onset-referenced Deborah number absorbing the unmeasured initial prestretch. The Conformation- and Concentration-Dependent Drag (C2D2) model, acting through coil-stretch hysteresis, lowers the plateau below the Entov-Hinch value and organizes data spanning decades in molecular weight and concentration, across a range of devices, where the classical FENE-P model cannot. The Pipkin diagram framework offers a path toward master plots for classes of polymer solutions, clarifying what is universal in extension-dominated flows.