Skip to main content Accessibility help
×
Home

Lagrangian transport properties of pulmonary interfacial flows

  • Bradford J. Smith (a1), Sarah Lukens (a2) (a3), Eiichiro Yamaguchi (a1) and Donald P. Gaver III (a1)

Abstract

Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame.

Copyright

Corresponding author

Email address for correspondence: dpg@tulane.edu

References

Hide All
1. Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261304.
2. Adrian, R. J. 2005 Twenty years of particle image velocimetry. Exp. Fluids 39, 159169.
3. Bilek, A. M., Dee, K. C. & Gaver, D. P. III 2003 Mechanisms of surface-tension-induced epithelial cell damage in a model of pulmonary airway reopening. J. Appl. Physiol. 94, 770783.
4. Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166188.
5. Drescher, K., Leptos, K. C., Tuval, I., Ishikawa, T., Pedley, T. J. & Goldstein, R. E. 2009 Dancing Volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102 (16).
6. 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, 2565.
7. Gaver, D. P. III, Samsel, R. W. & Solway, J. 1990 Effects of surface tension and viscosity on airway reopening. J. Appl. Physiol. 69, 7485.
8. Ghadiali, S. N. & Gaver, D. P. III 2000 An investigation of pulmonary surfactant physicochemical behaviour under airway reopening conditions. J. Appl. Physiol. 88, 493506.
9. Ghadiali, S. N. & Gaver, D. P. III 2003 The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube. J. Fluid Mech. 478, 165196.
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, 534559.
11. Glindmeyer, W. IV, Smith, B. & Gaver, D. 2011 In situ enhancement of pulmonary surfactant function using temporary flow reversal. J. Appl. Physiol. (in press).
12. Grotberg, J. B. 2001 Respiratory fluid mechanics and transport processes. Annu. Rev. Biomed. Engng 3, 421457.
13. Haber, S., Butler, J., Brenner, H., Emanuel, I. & Tsuda, A. 2000 Shear flow over a self-similar expanding pulmonary alveolus during rhythmical breathing. J. Fluid Mech. 405, 243268.
14. Haller, G. 1999 Finding finite time invariant manifolds in two-dimensional velocity fields. Chaos 10 (1), 99108.
15. Haller, G. 2001a Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149, 248277.
16. Haller, G. 2001b Lagrangian coherent structures and the rate of strain in two-dimensional turbulence. Phys. Fluids A 13, 33653385.
17. Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14 (6), 18511861.
18. Haller, G. & Poje, A. C. 1998 Finite time transport in aperiodic flows. Physica D 119, 352380.
19. Halpern, D. & Gaver, D. P. III 1994 Boundary element analysis of the time-dependent motion of a semi-infinite bubble in a channel. J. Comput. Phys. 115, 366375.
20. Halpern, D., Naire, S., Jensen, O. E. & Gaver, D. P. III 2005 Unsteady bubble propagation in a flexible channel: predictions of a viscous stick-slip instability. J. Fluid Mech. 528, 5386.
21. Heil, M. 2001 Finite Reynolds number effects in the Bretherton problem. Phys. Fluids 13, 25172521.
22. Jensen, O. E., Horsburgh, M. K., Halpern, D. & Gaver, D. P. 2002 The steady propagation of a bubble in a flexible-walled channel: asymptotic and computational models. Phys. Fluids 14 (2), 443457.
23. Kay, S. S., Bilek, A. M., Dee, K. C. & Gaver, D. P. III 2004 Pressure gradient, not exposure duration, determines the extent of epithelial cell damage in a model of pulmonary airway reopening. J. Appl. Physiol. 97, 269276.
24. Launois-Surpas, M. A., Ivanova, T., Panaiotov, I., Proust, J. E., Puisieux, F. & Georgiev, G. 1992 Behavior of pure and mixed DPPC liposomes spread or adsorbed at the air–water interface. Colloid Polym. Sci. 270 (9), 901911.
25. Lewis, D. M. & Pedley, T. J. 2000 Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations. J. Theor. Biol. 205 (3), 377408.
26. Lu, W.-Q. & Chang, H.-C. 1988 An extension of the biharmonic boundary integral method to free surface flow in channels. J. Comput. Phys. 77, 340360.
27. Mancho, A. M. & Wiggins, S. 2006 A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues. Phys. Rep. 437, 55124.
28. Matthay, M. A., Bhattacharya, S., Gaver, D. P. III, Ware, L. B., Lim, L. H. K., Syrkina, O., Eyal, F. & Hubmayr, R. 2002 Ventilator-induced lung injury: in vivo and in vitro mechanisms. Am. J. Physiol. Lung Cell Mol. Physiol. 283, L678L682.
29. Naire, S. & Jensen, O. E. 2005 Epithelial cell deformation during surfactant-mediated airway reopening: a theoretical model. J. Appl. Physiol. 99 (2), 458471.
30. Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
31. Park, C. M. & Homsy, G. W. 1984 Two-phase displacement in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291308.
32. Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
33. Pedley, T. J. & Kamm, R. D. 1988 The effect of secondary motion on axial transport in oscillatory tube flow. J. Fluid Mech. 193, 347367.
34. Pillert, J. E. & Gaver, D. P. III 2009 Physicochemical effects enhance surfactant transport in pulsatile motion of a semi-infinite bubble. Biophys. J. 96, 312327.
35. Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flows. Cambridge University Press.
36. Reinelt, D. A. & Saffman, P. G. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Stat. Comput. 6 (3), 542.
37. Reinsch, C. 1967 Smoothing by spline functions. Numer. Math. 10, 177183.
38. Rubenfeld, G. D., Caldwell, E., Peabody, E., Weaver, J., Martin, D. P., Neff, M., Stern, E. J. & Hudson, L. D. 2005 Incidence and outcomes of acute lung injury. N. Engl. J. Med. 353, 16851693.
39. Santiago, J. G., Wereley, S. T., Meinhart, C. D., Beebe, D. J. & Adrian, R. J. 1998 A particle image velocimetry system for microfluidics. Exp. Fluids 25, 316319.
40. Shadden, S. C. & Taylor, C. A. 2008 Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Engng 36 (7), 11521162.
41. Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.
42. Shadden, S. C., Lekien, F. & Marsden, J. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271304.
43. Shen, E. I. & Udell, K. S. 1985 A finite element study of low Reynolds number two-phase flow in cylindrical tubes. Trans. ASME: J. Appl. Mech. 52, 253256.
44. Smith, B. J. & Gaver, D. P. III 2008 The pulsatile propagation of a finger of air within a fluid-occluded cylindrical tube. J. Fluid Mech. 601, 123.
45. Smith, B. J., Yamaguchi, E. & Gaver, D. P. III 2010 A translating stage system for -PIV measurements surrounding the tip of a migrating semi-infinite bubble. Meas. Sci. Technol. 21 (1), 015401.
46. Stebe, K. J. & Barthes-Biesel, D. 1995 Marangoni effects of adsorption–desorption controlled surfactants on the leading edge of an infinitely long bubble in a capillary. J. Fluid Mech. 286, 2548.
47. Yamaguchi, E., Smith, B. J. & Gaver, D. P. III 2009 Micro-PIV measurements of the flow field surrounding a migrating semi-infinite bubble. Exp. Fluids 47 (2), 309320.
48. 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 (8), 18461863.
49. Zambon, M. & Vincent, J.-L. 2008 Mortality rates for patients with acute lung injury/ARDS have decreased over time. Chest 133, 11201127.
50. Zimmer, M. E., Williams, H. A. R. & Gaver, D. P. III 2005 The pulsatile motion of a semi-infinite bubble in a channel: flow fields, and transport of an inactive surface-associated contaminant. J. Fluid Mech. 537, 133.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed