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The effect of viscous relaxation on the spatiotemporal stability of capillary jets

Published online by Cambridge University Press:  02 September 2011

Alejandro Sevilla
Alejandro Sevilla*
Affiliation:
Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, 28911 Leganés, Spain
*
†Email address for correspondence: alejandro.sevilla@uc3m.es
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Abstract

The linear spatiotemporal stability properties of axisymmetric laminar capillary jets with fully developed initial velocity profiles are studied for large values of both the Reynolds number, , and the Froude number, , where is the injector radius, the volume flow rate, the kinematic viscosity and the gravitational acceleration. The downstream development of the basic flow and its stability are addressed with an approximate formulation that takes advantage of the jet slenderness. The base flow is seen to depend on two parameters, namely a Stokes number, , and a Weber number, , where is the surface tension coefficient, while its linear stability depends also on the Reynolds number. When non-parallel terms are retained in the local stability problem, the analysis predicts a critical value of the Weber number, , below which a pocket of local absolute instability exists within the near field of the jet. The function is computed for the buoyancy-free jet, showing marked differences with the results previously obtained with uniform velocity profiles. It is seen that, in accounting for gravity effects, it is more convenient to express the parametric dependence of the critical Weber number with use made of the Morton and Bond numbers, and , as replacements for and . This alternative formulation is advantageous to describe jets of a given liquid for a known value of , in that the resulting Morton number becomes constant, thereby leaving as the only relevant parameter. The computed function for a water jet under Earth gravity is shown to be consistent with the experimental results of Clanet and Lasheras for the transition from jetting to dripping of water jets discharging into air from long injection needles, which cannot be properly described with a uniform velocity profile assumed at the jet exit.

JFM classification

Instability: Absolute/convective instability Interfacial Flows (free surface): Interfacial Flows (free surface) Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 204 - 226
Copyright
Copyright © Cambridge University Press 2011

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