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Dynamics of thin liquid films on vertical cylindrical fibres

Published online by Cambridge University Press:  19 February 2019

H. Ji Open the ORCID record for H. Ji [Opens in a new window] ,
C. Falcon Open the ORCID record for C. Falcon [Opens in a new window] ,
A. Sadeghpour ,
Z. Zeng ,
Y. S. Ju Open the ORCID record for Y. S. Ju [Opens in a new window]  and
A. L. Bertozzi Open the ORCID record for A. L. Bertozzi [Opens in a new window]
H. Ji*
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA
C. Falcon
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA
A. Sadeghpour
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
Z. Zeng
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
Y. S. Ju
Affiliation:
Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
A. L. Bertozzi
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA
*
†Email address for correspondence: hangjie@math.ucla.edu
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Abstract

Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.

JFM classification

Instability: Instability Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 303 - 327
Copyright
© 2019 Cambridge University Press 

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