Capillary-elastic Instabilities of Liquid-lined Lung Airways

[+] Author and Article Information
J. Rosenzweig

Centre for Computational Science, Queen Mary & Westfield College, Mile End Road, London E1 4NS, UKe-mail: J.Rosenzweig@qmul.ac.uk

O. E. Jensen

Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UKe-mail: Oliver.Jensen@nottingham.ac.uk

J Biomech Eng 124(6), 650-655 (Dec 27, 2002) (6 pages) doi:10.1115/1.1516811 History: Received March 01, 2001; Revised July 01, 2002; Online December 27, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Lambert,  R. K., 1991, “Role of Bronchial Basement Membrane in Airway Collapse,” J. Appl. Physiol., 81, pp. 666–673.
Kamm,  R. D., 1999, “Airway Wall Mechanics,” Annual Review of Biomedical Engineering, 1, pp. 47–72.
Lambert,  R. K., Codd,  S. L., Alley,  M. R., and Pack,  R. J., 1994, “Physical Determinants of Bronchial Mucosal Folding,” J. Appl. Physiol., 77, pp. 1206–1216.
Seo,  C. Y., Wang,  L., and Paré,  P. D., 2000, “Airway Narrowing and Internal Structural Constraints,” J. Appl. Physiol., 88, pp. 527–533.
Wiggs,  B. R., Hrousis,  C. A., Drazen,  J. M., and Kamm,  R. D., 1997, “On the Mechanism of Mucosal Folding in Normal and Asthmatic Airways,” J. Appl. Physiol., 83, pp. 1814–1821.
Yager,  D., Butler,  J. P., Bastacky,  J., Israel,  E., Smith,  G., and Drazen,  J. M., 1989, “Amplification of Airway Constriction due to Liquid Filling of Airway Interstices,” J. Appl. Physiol., 66, pp. 2873–2884.
Hill,  M. J., Wilson,  T. E., and Lambert,  R. K., 1997, “Effects of Surface Tension and Intraluminal Fluid on Mechanics of Small Airways,” J. Appl. Physiol., 18, pp. 233–239.
Grotberg,  J. B., 1994, “Pulmonary Flow and Transport Phenomena,” Annu. Rev. Fluid Mech., 26, pp. 529–571.
Johnson,  M., Kamm,  R. D., Ho,  L. W., Shapiro,  A., and Pedley,  T. J., 1991, “The Nonlinear Growth of Surface-tension-driven Instabilities of a Thin Annular Film,” J. Fluid Mech., 233, pp. 141–156.
Kamm,  R. D., and Schroter,  R. C., 1983, “Is Airway Closure caused by a Liquid Film Instability?” Respir. Physiol., 75, pp. 141–156.
Halpern,  D., and Grotberg,  J. B., 1992, “Fluid-elastic Instabilities of Liquid-lined Flexible Tubes,” J. Fluid Mech., 244, pp. 615–632.
Halpern,  D., and Grotberg,  J. B., 1993, “Surfactant Effects on Fluid-elastic Instabilities of Liquid-lined Flexible Tubes: a Model of Airway Closure” ASME J. Biomech. Eng., 119, pp. 271–277.
Heil,  M., 1998, “Minimal Liquid Bridges in Non-axisymmetrically Buckled Elastic Tubes,” J. Fluid Mech., 380, pp. 309–337.
Heil,  M., 1999, “Airway Closure: Occluding Liquid Bridges in Strongly Buckled Elastic Tubes,” ASME J. Biomech. Eng., 121, pp. 487–493.
Okazawa,  M., Paré,  P. D., and Lambert,  R. K., 2000, “Compliance of Peripheral Airways Deduced from Morphometry,” J. Appl. Physiol., 89, pp. 2373–2381.
Wang,  C. Y., Watson,  L. T., and Kamat,  M. P., 1983, “Buckling, Postbuckling, and the Flow through a Tethered Elastic Cylinder under External Pressure,” J. Appl. Mech., 50, pp. 13–18.
Heil,  M., and White,  J. P., 2002, “Airway Closure: Surface-tension-driven Non-axisymmetric Instabilities of Liquid-lined Elastic Rings,” J. Fluid Mech., 462, pp. 79–109.
Flaherty,  J. E., Keller,  J. B., and Rubinow,  S. I., 1972, “Post-buckling Behavior of Elastic Tubes and Rings with Opposite Sides in Contact,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 23, pp. 446–455.
Tadjbakhsh,  I., and Odeh,  F., 1967, “Equilibrium States of Elastic Rings,” J. Math. Anal. Appl., 18, pp. 59–74.
Lambert,  R. K., Paré,  P. D., and Okazawa,  M., 2001, “Stiffness of Peripheral Airway Folding Membrane in Rabbits,” J. Appl. Physiol., 90, pp. 2041–2047.
Rosenzweig, J., 2000, “Capillary-elastic Instabilities and Draining Flows in Buckled Lung Airways,” Ph.D. thesis, University of Cambridge.
Gaver,  D. P. , Halpern,  D., Jensen,  O. E., and Grotberg,  J. B., 1996, “The Steady Motion of a Semi-infinite Bubble through a Flexible-walled Channel,” J. Fluid Mech., 319, pp. 25–65.
Jensen,  O. E., Horsburgh,  M. K., Halpern,  D., and Gaver,  D. P. , 2002, “The Steady Propagation of a Bubble in a Flexible-walled Channel: Asymptotic and Computational Models,” Phys. Fluids, 14, pp. 443–457.


Grahic Jump Location
The tube is initially circular and is lined with a film of uniform thickness; (a) As p is increased, the tube buckles (here into two lobes), and the film ruptures (b, c, d) to form a capillary meniscus, leaving part of the wall effectively dry. Opposite wall contact at s=π/2 is illustrated in (d).
Grahic Jump Location
Pressure-volume curves for n=2,Vl=π/5 and σ=0, 0.4, 0.6, 1. Film rupture is denoted by * and opposite wall contact by ○. Stable (unstable) solution branches are shown solid (dotted).
Grahic Jump Location
Pressure-volume curves for n=2,Vl=3π/5 and σ/σcrit=0, 1/2, 1,[[ellipsis]]7/2. Stable (unstable) solution branches are shown solid (dashed). The dash-dotted line shows the p–V curve for σ=0,Vfl=0.
Grahic Jump Location
(σ,Vl) parameter space, n=2. Insets show typical p–V curves for regions (i)–(v) of parameter space. Circles denote computed points, accurate to Vl±0.01; they are connected by straight lines.
Grahic Jump Location
Pressure-volume curves for n=4,Vl/π=0.15 and σ=0, 1, 2, 3, with σ increasing from right to left. Film rupture and reattachment are labeled by *. Stable (unstable) solution branches are shown solid (dashed). The centerlines of the pictures of half-lobes at various degrees of collapse correspond to their respective values of V.
Grahic Jump Location
(σ,Vl) parameter space, n=4. The typical p–V curves for regions (i)–(v) are as illustrated in Fig. 4. Circles denote computed points, accurate to Vl±0.01; they are connected by straight lines.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In