Adaptive Lagrangian–Eulerian computation of propagation and rupture of a liquid plug in a tube

Abstract

SUMMARYLiquid plug propagation and rupture occurring in lung airways can have a detrimental effect on epithelial cells. In this study, a numerical simulation of a liquid plug in an infinite tube is conducted using an Eulerian-Lagrangian approach and the continuous interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information about the interface mesh. Results prior to the rupture are in reasonable agreement with the study of Fujioka et al. in which a Lagrangian method is used. For unity non-dimensional pressure drop and a Laplace number of 1000, rupture time is shown to be delayed as the initial precursor film thickness increases and rupture is not expected for thicknesses larger than 0.10 of tube radius. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage. The peak values of those stresses increase as the initial precursor film thickness is reduced. After rupture, the peaks in mechanical stresses decrease in magnitude as the plug vanishes and the flow approaches a fully developed behavior. Increasing initial pressure drop is shown to linearly increase maximum variations in wall pressure and shear stress. Decreasing the pressure drop and increasing the Laplace number appear to delay rupture because it takes longer for a fluid with large inertial forces to respond to the small pressure drop.

Dynamics of liquid plugs in prewetted capillary tubes: from acceleration and rupture to deceleration and airway obstruction

“…The sources of experimental uncertainties are (i) the response time of the MFCS controller (about 100 ms ), (ii) the uncertainty of 7.5 µbar on the pressure imposed by the MFCS controller and (iii) the variations of the initial plug length l (about 5%). The present theory is also in qualitative agreement with the numerical simulations of Hassan et al 42 , who found a transition between acceleration and deceleration dynamics for h p = 0.09 − 0.10 andl = 1 at ∆P c = 0.5, and forh p = 0.05, 6 Phase diagram of the dynamics of a 3 µL (length l =3.80 mm) liquid plug pushed at different pressure head ∆P inside tubes covered with prewetting films of different thicknessesh p . Blue empty points correspond to the acceleration regime and green filled points to the deceleration regime.…”

Three-dimensional model of surfactant replacement therapy

“…The fluid viscosity, μ, and surface tension, σ, combine with U p and a to create the trailing film of thickness h. This deposited film reduces the plug volume, so less is delivered distally. If the remaining local plug volume in any airway is fully deposited into the trailing film, the plug ruptures, reinstating continuous gas flow, but halting further delivery downstream from that point (30)(31)(32). That reduces overall efficiency as well as homogeneity.…”

A microfluidic model to study fluid dynamics of mucus plug rupture in small lung airways

“…5(a)) means the film would be long at high yield stress, small pressure drop, and long initial plug. The reason is that each of the three conditions results in slow plug motion, and the film is thin and therefore long as the plug moves slowly (Fujioka and Grotberg, 2004;Fujioka et al, 2008;and Hassan et al, 2011). For the plug studied here with initial length no shorter than 0.59a, the film is generally longer than 2a (the channel width).…”

“…Shear stress and pressure at walls are maximal at the front meniscus of the plug (Fujioka and Grotberg, 2004). Stresses reach their peaks shortly after the rear meniscus catches up with the front meniscus and rupture happens (Hassan et al, 2011). The high shear stress and pressure may cause lethal damage to underlying epithelial cells, especially at the rupture location (Huh et al, 2007).…”

“…As the trailing film is thicker than the precursor film, the plug deposits more into the film than it picks up. This decreases its volume and may eventually lead to rupture (Fujioka et al, 2008;Hassan et al, 2011). Studies on a single Newtonian liquid plug using a rigid airway model show that higher pressure drop along the plug results in faster plug propagation, thicker trailing film, and faster rupture if rupture happens (Fujioka and Grotberg, 2004;Fujioka et al, 2008;and Hassan et al, 2011).…”