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Reopening modes of a collapsed elasto-rigid channel

Published online by Cambridge University Press:  18 April 2017

Lucie Ducloué Open the ORCID record for Lucie Ducloué [Opens in a new window] ,
Andrew L. Hazel Open the ORCID record for Andrew L. Hazel [Opens in a new window] ,
Alice B. Thompson  and
Anne Juel Open the ORCID record for Anne Juel [Opens in a new window]
Lucie Ducloué*
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy – University of Manchester, Oxford Road, Manchester M13 9PL, UK
Andrew L. Hazel
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics – University of Manchester, Oxford Road, Manchester M13 9PL, UK
Alice B. Thompson
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics – University of Manchester, Oxford Road, Manchester M13 9PL, UK
Anne Juel
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy – University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
†Present address: Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636, PSL – ESPCI Paris, Sorbonne Université – UPMC – Univ. Paris 06, Sorbonne Paris Cité – UPD – Univ. Paris 07, 10 rue Vauquelin, 75005 Paris, France. Email address for correspondence: [email protected]
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Abstract

Motivated by the reopening mechanics of strongly collapsed airways, we study the steady propagation of an air finger through a collapsed oil-filled channel with a single compliant wall. In a previous study using fully compliant elastic tubes, a ‘pointed’ air finger was found to propagate at high speed and low pressure, which, if clinically accessible, offers the potential for rapid reopening of highly collapsed airways with minimal tissue damage (Heap & Juel Phys. Fluids, vol. 20 (8), 2008, 081702). The mechanism underlying the selection of that pointed finger, however, remained unexplained. In this paper, we identify the required selection mechanism by conducting an experimental study in a simpler geometry: a rigid rectangular Hele-Shaw channel with an elastic top boundary. The constitutive behaviour of this elasto-rigid channel is nonlinear and broadly similar to that of an elastic tube, but unlike the tube, the channel’s cross-section adopts self-similar shapes from the undeformed state to the point of first near wall contact. The ensuing simplification of the vessel geometry enables the systematic investigation of the reopening dynamics in terms of increasing initial collapse. We find that for low levels of initial collapse, a single centred symmetric finger propagates in the channel and its shape is set by the tip curvature. As the level of collapse increases, the channel cross-section develops a central region of near opposite wall contact, and the finger shape evolves smoothly towards a ‘flat-tipped’ finger whose geometry is set by the strong depth gradient near the channel walls. We show that the flat-tipped mode of reopening is analogous to the pointed finger observed in tubes. Its propagation is sustained by the vessel’s extreme cross-sectional profile at high collapse, while vessel compliance is necessary to stabilise it. A simple scaling argument based on the dissipated power reveals that this reopening mode is preferred at higher propagation speeds when it becomes favourable to displace the elastic channel wall rather than the viscous fluid.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Interfacial Flows (free surface): Interfacial Flows (free surface) Biological Fluid Dynamics: Pulmonary fluid mechanics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 121 - 146
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Copyright
© 2017 Cambridge University Press 

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