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

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 Ca-Q(t)=mu Q*(t*)/pi R(2)y, where R is the tube radius, Q* is the dimensional flow rate, t* is the dimensional time, mu is the viscosity, and gamma is the surface tension. Pulsatility is imposed by CaQ(t) consisting of both mean (Ca-M) and oscillatory (Ca-Omega components such that Ca-Q(t) = Cam + Ca-Omega sin(Omega t). Dimensionless frequency and amplitude parameters are defined, respectively, as Omega = mu omega R/gamma and A = 2Ca(Omega)/Omega, with omega epresenting the frequency of oscillation. The system is accurately described by steady-state behaviour if Ca-Omega < Ca-M; however, when Ca-Omega > 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 Omega. For Ca-Omega < 10Ca(M), the bubble tip pressure drop Delta P-tip 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 partial derivative tau(n)/partial derivative 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 partial derivative tau(n)/partial derivative z at low Ca-Omega; however, film thickening at moderate Ca protects the tube wall from large partial derivative tau(n)/partial derivative(z). This stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be used to reduce ventilator-induced lung injury.