Spatiotemporal linear instability of viscoelastic slender jets

Abstract: We revisit the problem of the two-dimensional spatiotemporal linear stability of viscoelastic slender jets obeying linear Phan-Thien-Tanner (PTT) stress constitutive equation, and investigate the role of finite stresses on the elasto-capilliary stability of the Beads-on-a-String (BOAS) structure (structures which include the formation of very thin filament between drops) and identify the regions of topological transition of the advancing jet interface, in the limit of low to moderate Ohnesorge number ($Oh$) and high values of Weissenberg number ($We$). The Briggs idea of analytic continuation {previously elucidated in the nonaffine response regime [Bansal, Ghosh and Sircar, ``Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime'', Phys. Fluids {\bf 33}, 054106 (2021)]} is deployed to classify regions of temporal stability and absolute and convective instabilities, as well as evanescent modes, and the results are compared with previously conducted experiments for viscoelastic filaments. The impact of the finite stresses are evident in the form of strain-hardening ensuing in lower absolute growth rates, relatively rapid drainage and finite-time pinch-off. The phase diagrams reveal the influence of (a) capillary force stabilization at infinitesimally small values of $Oh$, and (b) inertial stabilization at significantly larger values of $Oh$.