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Global stability analysis of axisymmetric liquid–liquid flow focusing

Published online by Cambridge University Press:  21 December 2020

M. G. Cabezas Open the ORCID record for M. G. Cabezas [Opens in a new window] ,
N. Rebollo-Muñoz Open the ORCID record for N. Rebollo-Muñoz [Opens in a new window] ,
M. Rubio Open the ORCID record for M. Rubio [Opens in a new window] ,
M. A. Herrada Open the ORCID record for M. A. Herrada [Opens in a new window]  and
J. M. Montanero Open the ORCID record for J. M. Montanero [Opens in a new window]
M. G. Cabezas*
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
N. Rebollo-Muñoz
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
M. Rubio
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
M. A. Herrada
Affiliation:
Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, E-41092Sevilla, Spain
J. M. Montanero
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
*
†Email address for correspondence: [email protected]
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Abstract

We analyse both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate the global eigenmodes characterizing the response of this configuration to small-amplitude perturbations. In this way, the critical conditions leading to the instability of the steady jetting tip streaming are determined. The unstable perturbations are classified according to their oscillatory character and to the region where they originate (convective and absolute instability). We derive and explain in terms of the velocity field a simple scaling law to predict the diameter of the emitted jet. The numerical stability limits are compared with experimental results, finding reasonable agreement. The experiments confirm the existence of the two instability mechanisms predicted by the global stability analysis.

JFM classification

Interfacial Flows (free surface): Capillary flows Micro-/Nano-fluid dynamics: Microfluidics Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A10
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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