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The pulsatile propagation of a finger of air within a fluid-occluded cylindrical tube

Published online by Cambridge University Press:  25 April 2008

BRADFORD J. SMITH  and
DONALD P. GAVER III
BRADFORD J. SMITH
Affiliation:
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, [email protected]
DONALD P. GAVER III
Affiliation:
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, [email protected]
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Abstract

We computationally investigate the unsteady pulsatile propagation of a finger of air through a liquid-filled cylindrical rigid tube. The flow field is governed by the unsteady capillary number CaQ(t)=μQ*(t*)/πR2γ, where R is the tube radius, Q* is the dimensional flow rate, t* is the dimensional time, μ is the viscosity, and γ is the surface tension. Pulsatility is imposed by CaQ(t) consisting of both mean (CaM) and oscillatory (CaΩ components such that CaQ(t)=CaM+CaΩ sin(Ωt). Dimensionless frequency and amplitude parameters are defined, respectively, as Ω=μωR/γ and A=2CaΩ/Ω, with Ω epresenting the frequency of oscillation. The system is accurately described by steady-state behaviour if CaΩ<CaM; however, when CaΩ>CaM, reverse flow exists during a portion of the cycle, leading to an unsteady regime. In this unsteady regime, converging and diverging surface stagnation points translate dynamically along the interface throughout the cycle and may temporarily separate to create internal stagnation points at high Ω. For CaΩ<10CaM, the bubble tip pressure drop ΔPtip may be estimated accurately from the pressure measured downstream of the bubble tip when corrections for the downstream viscous component of the pressure drop are applied. The normal stress gradient at the tube wall ∂τn/∂z is examined in detail, because this has been shown to be the primary factor responsible for mechanical damage to epithelial cells during pulmonary airway reopening (Bilek, Dee & Gaver III 2003; Kay et al. 2004). In the unsteady regime, local film-thinning produces high ∂τn/∂z at low CaΩ; however, film thickening at moderate Ca protects the tube wall from large ∂τn/∂z. This stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be used to reduce ventilator-induced lung injury.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 601 , 25 April 2008 , pp. 1 - 23
Copyright
Copyright © Cambridge University Press 2008

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