Spatiotemporal linear instability of viscoelastic slender jets

TL;DR

This paper analyzes the linear stability of viscoelastic slender jets using the PTT model, revealing how finite stresses influence stability, filament formation, and topological transitions, with implications for understanding jet breakup.

Contribution

It introduces a detailed spatiotemporal stability analysis of viscoelastic jets with the PTT model, highlighting the effects of finite stresses on stability and jet morphology.

Findings

Finite stresses cause strain-hardening and lower growth rates.

Capillary and inertial forces stabilize the jet at different Ohnesorge numbers.

Finite stresses lead to finite-time pinch-off and altered filament dynamics.

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 $Oh$.