The absolute instability of an inviscid compound jet

Document Type

Article

Publication Date

1-1-2006

Abstract

This paper examines the emergence of the absolute instability from convectively unstable states of an inviscid compound jet. A compound jet is composed of a cylindrical jet of one fluid surrounded by a concentric annulus of a second, immiscible fluid. For all jet velocities v, there are two convectively unstable modes. As in the single-fluid jet, the compound jet becomes absolutely unstable below a critical dimensionless velocity or Weber number V (:=√v2ρ1 R1/σ1 where ρ1, R1 are the core density, radius and core-annular interfacial tension), which is a function of the annular/core ratios of densities β, surface tensions γ and radii a. At V=0, the absolutely unstable modes and growth recover the fastest growing temporal waves. We focus specifically on the effect of γ at a=2 and β = 1 and find that when the outer tension is significantly less than the inner (0.1< γ<0.3), the critical Weber number Vcrit decreases with γ, whereas for higher ratios (0.3<γ<3) it increases. The values (1.2-2.3) of Vcrit for the compound jet include the parameter-independent critical value of 1.77 for the single jet. Therefore, increasing the outer tension can access the absolute instability at higher dimensional velocities than for a single jet with the same radius and density as the core and a surface tension equal to the compound jet's liquid-liquid tension. We argue that this potentially facilitates distinguishing experimentally between absolute and convective instabilities because higher velocities and surface tension ratios higher than 1 extend the breakup length of the convective instability. In addition, for 0.3 < γ <1.16, the wavelength for the absolute instability is roughly half that of the fastest growing convectively unstable wave. Thus choosing γ in this range exaggerates its distinction from the convective instability and further aids the potential observation of absolute instability. © 2006 Cambridge University Press.

Identifier

33645808946 (Scopus)

Publication Title

Journal of Fluid Mechanics

External Full Text Location

https://doi.org/10.1017/S0022112005007056

e-ISSN

14697645

ISSN

00221120

First Page

81

Last Page

98

Volume

549

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