Three-dimensional airway reopening: The steady propagation of a semi-infinite bubble into a buckled elastic tube

Journal of Fluid Mechanics

Volumn 478, Issue , 2003, Pages 47-70

  Hazel, Andrew L ^a   Heil, Matthias ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLES (IN FLUIDS); ELASTICITY; FINITE ELEMENT METHOD; SURFACE TENSION; TUBES (COMPONENTS); VISCOUS FLOW;

ELASTIC TUBES;

FLUID DYNAMICS;

AIRFLOW; BUBBLE; MEDICAL APPLICATION; THREE-DIMENSIONAL FLOW;

EID: 0037430132     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112002003452     Document Type: Article

References (27)

1. BOGNER, F. K., FOX, R. L. & SCHMIT, L. A. 1967 A cylindrical shell discrete element. AIAA J. 5, 745-750.
2. BRETHERTON, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166-188.
3. CASSIDY, K. J., GAVRIELY, N. & GROTBERG, J. B. 2001 Liquid plug flow in straight and bifurcating tubes. Trans. ASME: J. Biomech. Engng 123, 580-589.
4. COX, B. G. 1962 On driving a viscous fluid out of a tube. J. Fluid Mech. 14, 81-96.
5. DUFF, I. S. & SCOTT, J. A. 1996 The design of a new frontal code for solving sparse, unsymmetric linear systems. ACM Trans. Math. Software 22, 30-45.
6. FLAHERTY, J. E., KELLER, J. B. & RUBINOW, S. I. 1972 Post buckling behavior of elastic tubes and rings with opposite sides in contact. SIAM J. Appl. Maths. 23, 446-455.
7. FRY, D. L. 1968 Acute vascular endothelial changes associated with increased blood velocity gradients. Circ. Res. 22, 165-197.
8. 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, 25-56.
9. GAVER, D. P. III, SAMSEL, R. W. & SOLWAY, J. 1990 Effects of surface tension and viscosity on airway reopening. J. Appl. Physiol. 369, 74-85.
10. GHADIALI, S. N., HALPERN, D. & GAVER, D. P. III 2001 A dual-reciprocity boundary element method for evaluating bulk convective transport of surfactant in free-surface flows. J. Comput. Phys. 171, 534-559.
11. GIAVEDONI, M. D. & SAITA, F. A. 1997 The axisymmetric and plane cases of a gas phase steadily displacing a Newtonian liquid - a simultaneous solution of the governing equations. Phys. Fluids 9, 2420-2428.
12. HALPERN, D. & GROTBERG, J. B. 1992 Fluid-elastic instabilities of liquid-lined flexible tubes. J. Fluid Mech. 244, 615-632.
13. 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.
14. HEIL, M. 1997 Stokes flow in collapsible tubes: computation and experiment. J. Fluid Mech. 353, 285-312.
15. HEIL, M. 2000 Finite Reynolds number effects in the propagation of an air finger into a liquid-filled flexible-walled tube. J. Fluid Mech. 424, 21-44.
16. HEIL, M. 2001 The Bretherton problem in elastic-walled channels: Finite Reynolds number effects. In IUTAM Symp. on Free Surface Flows (ed. Y. Shikmurzaev), pp. 113-120. Kluwer.
17. HORSBURGH, M. 2000 Bubble propagation in flexible and permeable channels. PhD thesis, Cambridge University.
18. HUGHES, J. M. B., ROSENZWEIG, D. Y. & KIVITZ, P. B. 1970 Site of airway closure in excised dog lungs: histologic demonstration. J. Appl. Physiol. 29, 340-344.
19. 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.
20. KISTLER, S. F. & SCRIVEN, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (ed. J. R. A. Pearson & S. M. Richardson), pp. 243-299. London: Applied Science Publishers.
21. MACKLEM, P. T., PROCTOR, D. F. & HOGG, J. C. 1970 The stability of the peripheral airways. Respir. Physiol. 8, 191-203.
22. PRIDE, N. B. & MACKLEM, P.T. 1986 Lung mechanics in disease. In Handbook of Physiology. Section 3: The Respiratory System, Vol III, Part 2, pp. 659-692. American Physiological Society.
23. REINELT, D. A. & SAFFMAN, P. G. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Statist. Comput. 6, 542-561.
24. TAYLOR, C. & HOOD, P. 1973 A numerical solution of the Navier-Stokes equations using the finite element technique. Computers Fluids 1, 73-100.
25. WEATHERBURN, C. E. 1955 Differential Geometry of Three Dimensions, Volume 1, 1st edn. Cambridge University Press.
26. YAMAKI, N. 1984 Elastic Stability of Circular Cylindrical Shells. North-Holland.
27. YAP, D. Y. K. & GAVER, D. P. III 1998 The influence of surfactant on two-phase flow in a flexible-walled channel under bulk equilibrium conditions. Phys. Fluids 10, 1846-1863.