Temporal instability analysis of inviscid compound jets falling under gravity

Muhammad Mohsin*, Jamal Uddin, Stephen P. Decent, Muhammad F. Afzaal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Compound liquid jets can be used in a variety of industrial applications ranging from capsule production in pharmaceutics to enhance printing methods in ink-jet printing. An appreciation of how instability along compound jets can lead to breakup and droplet formation is thus critical in many fields in science and engineering. In this paper, we perform a theoretical analysis to examine the instability of an axisymmetric inviscid compound liquid jet which falls vertically under the influence of gravity. We use a long-wavelength, slender-jet asymptotic expansion to reduce the governing equations of the problem into a set of one-dimensional partial differential equations, which describe the evolution of the leading-order axial velocity of the jet as well as the radii of both the inner and the outer interfaces. We first determine the steady-state solutions of the one-dimensional model equations and then we perform a linear temporal instability analysis to obtain a dispersion relation, which gives us useful information about the maximum growth rate and the maximum wavenumber of the imposed wave-like disturbance. We use our results to estimate the location and qualitative nature of breakup and then compare our results with numerical simulations.
Original languageEnglish
Article number012103
JournalPhysics of Fluids
Issue number1
Publication statusPublished - 18 Jan 2013
Externally publishedYes


  • liquid jet
  • compound jet
  • droplet
  • gravity

ASJC Scopus subject areas

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


Dive into the research topics of 'Temporal instability analysis of inviscid compound jets falling under gravity'. Together they form a unique fingerprint.

Cite this