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Global stability of axisymmetric flow focusing

Published online by Cambridge University Press:  26 October 2017

F. Cruz-Mazo Open the ORCID record for F. Cruz-Mazo [Opens in a new window] ,
M. A. Herrada ,
A. M. Gañán-Calvo  and
J. M. Montanero Open the ORCID record for J. M. Montanero [Opens in a new window]
F. Cruz-Mazo
Affiliation:
Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, E-41092 Sevilla, Spain
M. A. Herrada
Affiliation:
Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, E-41092 Sevilla, Spain
A. M. Gañán-Calvo
Affiliation:
Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, E-41092 Sevilla, 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-06071 Badajoz, Spain
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we analyse numerically the stability of the steady jetting regime of gaseous flow focusing. The base flows are calculated by solving the full Navier–Stokes equations and boundary conditions for a wide range of liquid viscosities and gas speeds. The axisymmetric modes characterizing the asymptotic stability of those flows are obtained from the linearized Navier–Stokes equations and boundary conditions. We determine the flow rates leading to marginally stable states, and compare them with the experimental values at the jetting-to-dripping transition. The theoretical predictions satisfactorily agree with the experimental results for large gas speeds. However, they do not capture the trend of the jetting-to-dripping transition curve for small gas velocities, and considerably underestimate the minimum flow rate in this case. To explain this discrepancy, the Navier–Stokes equations are integrated over time after introducing a small perturbation in the tapering liquid meniscus. There is a transient growth of the perturbation before the asymptotic exponential regime is reached, which leads to dripping. Our work shows that flow focusing stability can be explained in terms of the combination of asymptotic global stability and the system short-term response for large and small gas velocities, respectively.

JFM classification

Interfacial Flows (free surface): Capillary flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 329 - 344
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Copyright
© 2017 Cambridge University Press 

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