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Reduced-dimension model of liquid plug propagation in tubes

Hideki Fujioka*

David Halpern†

Jason Ryans‡ and Donald P. Gaver, III§

  • Center for Computational Science, Tulane University, New Orleans, Louisiana 70118, USA

  • Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487, USA

  • Department of Biomedical Engineering, Tulane University, New Orleans, Louisiana 70118, USA

  • *fuji@tulane.edu
  • †dhalpern@ua.edu
  • ‡jryans@tulane.edu
  • §dpg@tulane.edu
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Phys. Rev. Fluids 1, 053201 – Published 6 September, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.053201

Abstract

We investigate the flow resistance caused by the propagation of a liquid plug in a liquid-lined tube and propose a simple semiempirical formula for the flow resistance as a function of the plug length, the capillary number, and the precursor film thickness. These formulas are based on computational investigations of three key contributors to the plug resistance: the front meniscus, the plug core, and the rear meniscus. We show that the nondimensional flow resistance in the front meniscus varies as a function of the capillary number and the precursor film thickness. For a fixed capillary number, the flow resistance increases with decreasing precursor film thickness. The flow in the core region is modeled as Poiseuille flow and the flow resistance is a linear function of the plug length. For the rear meniscus, the flow resistance increases monotonically with decreasing capillary number. We investigate the maximum mechanical stress behavior at the wall, such as the wall pressure gradient, the wall shear stress, and the wall shear stress gradient, and propose empirical formulas for the maximum stresses in each region. These wall mechanical stresses vary as a function of the capillary number: For semi-infinite fingers of air propagating through pulmonary airways, the epithelial cell damage correlates with the pressure gradient. However, for shorter plugs the front meniscus may provide substantial mechanical stresses that could modulate this behavior and provide a major cause of cell injury when liquid plugs propagate in pulmonary airways. Finally, we propose that the reduced-dimension models developed herein may be of importance for the creation of large-scale models of interfacial flows in pulmonary networks, where full computational fluid dynamics calculations are untenable.

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Phys. Rev. Fluids 1, 053201– Published 6 September, 2016
  • Received 17 February 2016
Article part of CHORUS

©2016 American Physical Society

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