Convective and absolute instability of falling viscoelastic liquid jets surrounded by a gas

A. Alhushaybari*, J. Uddin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We examine the convective and absolute instability of a 2D axisymmetric viscoelastic liquid jet falling vertically in a medium of an inviscid gas under the influence of gravity. We use the upper-convected Maxwell model to describe the viscoelastic liquid jet and together with an asymptotic approach, based on the slenderness of the jet, we obtain steady-state solutions. By considering travelling wave modes, and using linear instability analysis, the dispersion relation, relating the frequency to wavenumber of disturbances, is derived. We solve this dispersion relation numerically using the Newton-Raphson method and explore regions of instability in parameter space. In particular, we investigate the influence of gravity, the effect of changing the gas-to-liquid density ratio, the Weber number and the Deborah number on convective and absolute instability. In this paper, we utilize a mapping technique developed by Afzaal (2014, Breakup and instability analysis of compound liquid jets. Doctoral Dissertation, University of Birmingham) to find the cusp point in the complex frequency plane and its corresponding first-order saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes along the axial length of the jet.

Original languageEnglish
Pages (from-to)58-75
Number of pages18
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume86
Issue number1
Early online date14 Oct 2020
DOIs
Publication statusPublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 2020 The Author(s) 2020.

Keywords

  • Absolute instability
  • Free surface
  • Liquid jet
  • Viscoelastic

ASJC Scopus subject areas

  • Applied Mathematics

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