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Trapping and displacement of liquid collars and plugs in rough-walled tubes

Feng Xu*

Oliver E. Jensen†

  • School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom

  • School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

  • *f.xu.2@bham.ac.uk
  • †oliver.jensen@manchester.ac.uk
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Phys. Rev. Fluids 2, 094004 – Published 18 September, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.094004

Abstract

A liquid film wetting the interior of a long circular cylinder redistributes under the action of surface tension to form annular collars or occlusive plugs. These equilibrium structures are invariant under axial translation within a perfectly smooth uniform tube and therefore can be displaced axially by very weak external forcing. We consider how this degeneracy is disrupted when the tube wall is rough, and determine threshold conditions under which collars or plugs resist displacement under forcing. Wall roughness is modeled as a nonaxisymmetric Gaussian random field of prescribed correlation length and small variance, mimicking some of the geometric irregularities inherent in applications such as lung airways. The thin film coating this surface is modeled using lubrication theory. When the roughness is weak, we show how the locations of equilibrium collars and plugs can be identified in terms of the azimuthally averaged tube radius; we derive conditions specifying equilibrium collar locations under an externally imposed shear flow, and plug locations under an imposed pressure gradient. We use these results to determine the probability of external forcing being sufficient to displace a collar or plug from a rough-walled tube, when the tube roughness is defined only in statistical terms.

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Phys. Rev. Fluids 2, 094004– Published 18 September, 2017
  • Received 2 May 2017
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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