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Lagrangian transport properties of pulmonary interfacial flows

Published online by Cambridge University Press:  09 November 2011

Bradford J. Smith ,
Sarah Lukens ,
Eiichiro Yamaguchi  and
Donald P. Gaver III
Bradford J. Smith
Affiliation:
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, USA
Sarah Lukens
Affiliation:
Mathematics Department, Tulane University, New Orleans, LA 70118, USA Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Eiichiro Yamaguchi
Affiliation:
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, USA
Donald P. Gaver III*
Affiliation:
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Biological Fluid Dynamics: Pulmonary fluid mechanics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 705: Special issue dedicated to Professor T. J. Pedley on his 70th birthday , 25 August 2012 , pp. 234 - 257
Copyright
Copyright © Cambridge University Press 2011

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