Wavemaker and endogeneity of gravitationally stretched weakly viscoelastic jets

TL;DR

This paper develops a unified one-dimensional model for gravitationally stretched viscoelastic jets, analyzing their stability and the influence of elasticity on jet behavior, with implications for drop formation and micro-thread dynamics.

Contribution

It introduces a comprehensive model combining full curvature and Giesekus stress closure, and analyzes how elasticity affects jet stability and oscillation characteristics.

Findings

Elasticity shifts the critical Weber number for jet stability.

Viscoelasticity broadens the downstream sensitivity region.

Elastic stresses influence oscillation frequency and jetting transition.

Abstract

Highly stretched capillary jets produced by gravity are central to drop generation, micro-thread formation, and extensional-rheometry concepts. For Newtonian fluids, the transition from steady jetting to self-excited oscillations in a gravitationally stretched jet is predicted accurately by one-dimensional slender-jet equations that retain the exact interfacial curvature and admit a global eigenvalue analysis Rubio-Rubio et al. 2013. Separately, weakly viscoelastic jets governed by Oldroyd--B/Giesekus constitutive laws exhibit elastocapillary regimes and beads-on-a-string dynamics that are well captured by one-dimensional free-surface models Ardekani et al. 2010. Here we formulate a unified one-dimensional model for gravitationally stretched viscoelastic jets, combining full-curvature capillarity with a Giesekus stress closure, and we analyse its global linear stability on spatially developing base states. We first benchmark the Newtonian limit, reproducing marginal spectra and base-flow profiles, and then quantify how elasticity shifts the critical jetting--dripping boundary by tracking the leading global Hopf eigenpair across the rheological parametric space. For experimentally relevant moderate elasticity, characterised by order-unity Deborah numbers, polymeric tension modifies both the critical Weber number and the selected oscillation frequency, and endogeneity decompositions reveal that marginality results from a balance between capillary/kinematic contributions and an additional elastic-stress feedback pathway. To interpret and predict the onset mechanism, we compute wavemakers and receptivity/structural-sensitivity fields from direct--adjoint eigenfunctions, showing that viscoelasticity broadens the sensitivity region downstream while the adjoint remains strongly localized near the inlet, thereby identifying the near-nozzle region as the dominant receptive location.