Wavemaker and endogeneity of gravitationally stretched weakly viscoelastic jets

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, J. Fluid Mech. , vol. 729, pp. 471–483). 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 J. Fluid Mech. , vol. 665, pp. 46–56). Here, we study the global linear stability of a one-dimensional full-curvature model for gravitationally stretched viscoelastic jets in the Oldroyd-B limit. 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, i.e. the local contribution of the unperturbed flow dynamics to the selected global eigenvalue, reveals 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 localised near the inlet, thereby identifying the near-nozzle region as the dominant receptive location.