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

Abstract

We computationally investigate the unsteady pulsatile propagation of a finger of air through a liquid-filled cylindrical rigid tube using a combined boundary element method and lubrication theory approach. The flow-field is governed by the dimensionless parameters Ca(Q)(t) = Ca(M) + Ca(Omega) sin(Omegat) = muQ*(t*)/piR(2)gamma, Omega = muomegaR/gamma and A = 2Ca(Omega)/Omega. Here, Ca(Q)(t) consists of both mean (Ca(M)) and oscillatory (Ca(Omega)) components. It is shown that the behavior of this system is appropriately described by steady-state responses until the onset of reverse flow, wherein the system operates in the unsteady regime (Ca(Omega) > Ca(M)). When flows in this regime are considered, converging and diverging stagnation points move dynamically throughout the cycle and may temporarily separate from the interface at high Omega. We have also found that for Ca(Omega) < 10Ca(M) the bubble tip pressure drop DeltaP(tip) may be estimated accurately from the pressure measured downstream of the bubble tip when corrections for the pressure drop due to Poiseuille flow are applied. The normal stress gradient at the tube wall ( partial differentialtau(n)/ partial differentialz) is discussed in detail, as this is believed to be the primary factor in airway epithelial cell damage (Bilek et al 2003). In the unsteady regime we find that local film-thinning produces high partial differentialtau(n)/ partial differentialz at low Ca(Omega). Film thickening at moderate Ca(Omega) in the unsteady regime protects the tube wall from the large gradients near the bubble tip, therefore reducing partial differentialtau(n)/ partial differentialz. We find that the stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be of interest to our field of study, pulmonary airway reopening.