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Bubble transitions in strongly collapsed elastic tubes

Published online by Cambridge University Press:  25 August 2009

ALEXANDRA HEAP  and
ANNE JUEL
ALEXANDRA HEAP
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics, The University of Manchester, Manchester M13 9PL, UK
ANNE JUEL*
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics, The University of Manchester, Manchester M13 9PL, UK
*
†E-mail address for correspondence: anne.juel@manchester.ac.uk
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Abstract

The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the usual parabolic-tipped bubble as Ca increases. We also characterize the mechanisms underlying the discontinuous transitions between asymmetric and double-tipped bubbles, and double-tipped and pointed bubbles. In particular, we find that the tube must reopen to a critical height for double-tipped bubbles to be selected. The length of the precursor fingers in the double-tipped bubble decreases with Ca, and the bubble loses stability to pointed bubbles when this length is less than the height of the tube at the point where the fingers merge. By contrast with the asymmetric and double-tipped bubbles, the pointed bubble infiltrates the most collapsed part of the tube to yield the rapid reopening of the airway at low pressure, with the potential to reduce ventilation-induced lung damage.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 485 - 507
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Bland, R. D. 1991 Fetal lung liquid and its removal near birth. In The Lung: Scientific Foundations (ed. Crystal, R. G., West, J. B., Barnes, P. J. & Weibel, E. R.). Lippincott, Williams and Wilkins.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Cohen, I. & Nagel, S. R. 2002 Scaling at the selective withdrawal transition through a tube suspended above the fluid surface. Phys. Rev. Lett. 88, 074501.CrossRefGoogle ScholarPubMed
Concus, P. & Finn, R. 1974 On capillary free surfaces in the absence of gravity. Acta Mathematica 132, 177–198.CrossRefGoogle Scholar
Courrech du Pont, S. & Eggers, J. 2006 Sink flow deforms the interface between a viscous liquid and air into a tip singularity. Phys. Rev. Lett. 96, 034501.CrossRefGoogle ScholarPubMed
Fearn, R. 1988 Perturbed motions of a bubble rising in a vertical tube. Phys. Fluids 31, 238–241.CrossRefGoogle Scholar
Flaherty, J. E., Keller, J. B. & Rubinow, S. I. 1972 Post-buckling behaviour of elastic tubes and rings with opposite sides in contact. SIAM J. Appl. Math. 23, 446–455.CrossRefGoogle Scholar
Gaver, D. P. III, Halpern, D., Jensen, O. E. & Grotberg, J. B. 1996 The steady motion of a semi-infinite bubble through a flexible-walled channel. J. Fluid Mech. 319, 25–65.CrossRefGoogle Scholar
Gaver, D. P. III, Samsel, R. W. & Solway, J. 1990 Effects of surface tension and viscosity on airway reopening. J. Appl. Physiol. 69, 74–85.CrossRefGoogle ScholarPubMed
Ghadiali, S. & Gaver, D. P. 2008 Biomechanics of liquid–epithelium interactions in pulmonary airways. Respir. Physiol. Neurobiol. 163, 232–243.CrossRefGoogle ScholarPubMed
Grotberg, J. B. 2001 Respiratory fluid mechanics and transport processes. Ann. Rev. Biomech. Engng 3, 421–457.CrossRefGoogle ScholarPubMed
Grotberg, J. B. & Jensen, O. E. 2004 Biofluid mechanics in flexible tubes. Ann. Rev. Fluid Mech. 36, 121–147.CrossRefGoogle Scholar
Hazel, A. L. & Heil, M. 2002 The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section. J. Fluid Mech. 470, 91–114.CrossRefGoogle Scholar
Hazel, A. L. & Heil, M. 2003 Three-dimensional airway reopening: the steady propagation of a semi-infinite bubble into a buckled elastic tube. J. Fluid Mech. 478, 47–70.CrossRefGoogle Scholar
Hazel, A. L. & Heil, M. 2006 Finite-Reynolds-number effects in steady, three-dimensional airway reopening. ASME J. Biomech. Engng 128, 573–578.CrossRefGoogle ScholarPubMed
Hazel, A. L. & Heil, M. In press The influence of gravity on the steady propagation of a semi-infinite bubble into a flexible channel. Phys. Fluids 20, 092109.CrossRefGoogle Scholar
Heap, A. & Juel, A. 2008 Anomalous bubble propagation in elastic tubes. Phys. Fluids 20, 081702.CrossRefGoogle Scholar
Heil, M. 1999 Minimal liquid bridges in non-axisymmetrically buckled elastic tubes. J. Fluid Mech. 380, 309–337.CrossRefGoogle Scholar
Heil, M., Hazel, A. L. & Smith, J. A. 2008 The mechanics of airway closure. Respir. Physiol. Neurobiol. 163, 214–221.CrossRefGoogle ScholarPubMed
Hong, D. 1988 Wire perturbations in the Saffman–Taylor problem. Phys. Rev. A 37, 2724–2727.CrossRefGoogle ScholarPubMed
Jensen, O. E., Horsburgh, M. K., Halpern, D. & Gaver, D. P. III 2002 The steady propagation of a bubble in a flexible-walled channel: asymptotic and computational models. Phys. Fluids 14, 443–457.CrossRefGoogle Scholar
Juel, A. & Heap, A. 2007 The reopening of a collapsed fluid-filled elastic tube. J. Fluid Mech. 572, 287–310.CrossRefGoogle Scholar
Kamm, R. D. 1999 Airway wall mechanics. Ann. Rev. Biomech. Engng 1, 47–72.CrossRefGoogle ScholarPubMed
Kuang, J., Petitjeans, P. & Maxworthy, T. 2004 Velocity fields and streamline patterns of miscible displacements in cylindrical tubes. Exp. Fluids 37, 301–308.CrossRefGoogle Scholar
Lorenceau, E., Restagno, F. & Quéré, D. 2003 Fracture of a viscous liquid. Phys. Rev. Lett. 90, 184501.CrossRefGoogle ScholarPubMed
de Lózar, A., Heap, A., Box, F., Hazel, A. L. & Juel, A. 2009 Partially-occluded tubes can force switch-like transitions in the behavior of propagating bubbles. Phys. Rev. Lett. Submitted.CrossRefGoogle Scholar
Perun, M. L. & Gaver, D. P. III 1995 An experimental model investigation of the opening of a collapsed untethered pulmonary airway. ASME J. Biomech. Engng 117, 245–253.CrossRefGoogle ScholarPubMed
Petitjeans, P. & Maxworthy, T. 1996 Miscible displacements in capillary tubes. Part I. Experiments. J. Fluid Mech. 326, 37–56.CrossRefGoogle Scholar
Tabeling, P., Zocchi, G. & Libchaber, A. 1987 An experimental study of the Saffman–Taylor instability. J. Fluid Mech. 177, 67–82.CrossRefGoogle Scholar
Taylor, G. I. 1961 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161–165.CrossRefGoogle Scholar