Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

Abdullah Alhushaybari*, Jamal Uddin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
337 Downloads (Pure)

Abstract

The convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady state solutions. By considering traveling wave modes, we derive a dispersion relation relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the Froude number, on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer, Bers, and Ram ["The cusp map in the complex-frequency plane for absolute instabilities," Phys. Fluids 30, 3075-3082 (1987)] to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

Original languageEnglish
Article number044106
JournalPhysics of Fluids
Volume31
Issue number4
DOIs
Publication statusPublished - 26 Apr 2019

Bibliographical note

Funding Information:
A.A. would like to thank the Saudi Embassy for the financial support. We would also like to thank one of the anonymous referees whose comments helped to improve the paper.

Publisher Copyright:
© 2019 Author(s).

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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