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Dynamics of a liquid plug in a capillary tube under cyclic forcing: memory effects and airway reopening

Published online by Cambridge University Press:  12 January 2018

S. Signe Mamba Open the ORCID record for S. Signe Mamba [Opens in a new window] ,
J. C. Magniez ,
F. Zoueshtiagh  and
M. Baudoin
S. Signe Mamba
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520 - IEMN, International laboratory LIA/LICS, F-59000 Lille, France
J. C. Magniez
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520 - IEMN, International laboratory LIA/LICS, F-59000 Lille, France
F. Zoueshtiagh
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520 - IEMN, International laboratory LIA/LICS, F-59000 Lille, France
M. Baudoin*
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520 - IEMN, International laboratory LIA/LICS, F-59000 Lille, France
*
†Email address for correspondence: michael.baudoin@univ-lille1.fr
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Abstract

In this paper, we investigate both experimentally and theoretically the dynamics of a liquid plug driven by a cyclic periodic forcing inside a cylindrical rigid capillary tube. First, it is shown that, depending on the type of forcing (flow rate or pressure cycle), the dynamics of the liquid plug can either be stable and periodic, or conversely accelerative and eventually leading to plug rupture. In the latter case, we identify the sources of the instability as: (i) the cyclic diminution of the plug viscous resistance to motion due to the decrease in the plug length and (ii) a cyclic reduction of the plug interfacial resistance due to a lubrication effect. Since the flow is quasi-static and the forcing periodic, this cyclic evolution of the resistances relies on the existence of flow memories stored in the length of the plug and the thickness of the trailing film. Second, we show that, contrary to unidirectional pressure forcing, cyclic forcing enables breaking of large plugs in a confined space although it requires longer times. All the experimentally observed tendencies are quantitatively recovered from an analytical model. This study not only reveals the underlying physics but also opens up the prospect for the simulation of ‘breathing’ of liquid plugs in complex geometries and the determination of optimal cycles for obstructed airways reopening.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 165 - 191
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Copyright
© 2018 Cambridge University Press 

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Signe Mamba et al. supplementary movie 1

Movie showing the temporal evolution of a single liquid plug of initial length $L_0=1.05mm $ pushed with the cyclic flow rate forcing in a cylindrical capillary tube of radius $R_c = 0.47mm$. The movie was shot with a Photron SA3 high speed camera mounted on a Z16 Leica Microscope at a frame rate of $125$ images per second, a trigger time of $1/3000 s$ and a resolution of $1024 \times 64$ pixels. a. Initial state b. Final state.

Download Signe Mamba et al. supplementary movie 1(Video)
Video 2.7 MB
Supplementary material: PDF

Signe Mamba et al. supplementary material

Supplementary captions

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PDF 163.3 KB

Signe Mamba et al. supplementary movie 2

Movie showing the temporal evolution of a single liquid plug of initial length $L_0 = 3.39mm $ pushed with the pressure cyclic forcing in a cylindrical capillary tube of radius $R_c = 0.47mm$. The movie was shot with a Photron SA3 high speed camera mounted on a Z16 Leica Microscope at a frame rate of $125$ images per second, a trigger time of $1/3000 s$ and a resolution of $1024 \times 64$ pixels a. Initial state b. End of the cycle there is no more plug and only liquid remains on the walls of the capillary tube.

Download Signe Mamba et al. supplementary movie 2(Video)
Video 1.2 MB

Signe Mamba et al. supplementary movie 3

Movie showing the temporal evolutions of a single liquid plug of initial length $L1=2.5mm$ pushed with the pressure cyclic forcing in a cylindrical capillary tube of radius $R_c = 0.47mm$. The movie was shot with a Photron SA3 high speed camera mounted on a Z16 Leica Microscope at a frame rate of $125$ images per second, a trigger time of $1/3000 s$ and a resolution of $1024 \times 64$ pixels a. Initial state b. Final state.

Download Signe Mamba et al. supplementary movie 3(Video)
Video 938.5 KB

Signe Mamba et al. supplementary movie 4

Movie showing the temporal evolutions of a single liquid plug of initial length $L2=2.85mm$ pushed with the pressure cyclic forcing in a cylindrical capillary tube of radius $R_c = 0.47mm$. In the same cycle, the rupture length of the smaller plug in movie S3 is higher that the one for the bigger plug. The movie was shot with a Photron SA3 high speed camera mounted on a Z16 Leica Microscope at a frame rate of $125$ images per second, a trigger time of $1/3000 s$ and a resolution of $1024 imes 64$ pixels a. Initial state b. Final state.

Download Signe Mamba et al. supplementary movie 4(Video)
Video 1.2 MB