Abstract
Capillary instability of a two-layer liquid film lining a rigid tube is studied computationally as a model for liquid plug formation and closure of human airways. The two-layer liquid consists of a serous layer, also called the periciliary liquid layer, at the inner side and a mucus layer at the outer side. Together, they form the airway surface liquid lining the airway wall and surrounding an air core. Liquid plug formation occurs due to Plateau–Rayleigh instability when the liquid film thickness exceeds a critical value. Numerical simulations are performed for the entire closure process, including the pre- and post-coalescence phases. The mechanical stresses and their gradients on the airway wall are investigated for physiologically relevant ranges of the mucus-to-serous thickness ratio, the viscosity ratio, and the air–mucus and serous–mucus surface tensions encompassing healthy and pathological conditions of a typical adult human lung. The growth rate of the two-layer model is found to be higher in comparison with a one-layer equivalent configuration. This leads to a much sooner closure in the two-layer model than that in the corresponding one-layer model. Moreover, it is found that the serous layer generally provides an effective protection to the pulmonary epithelium against high shear stress excursions and their gradients. A linear stability analysis is also performed, and the results are found to be in good qualitative agreement with the simulations. Finally, a secondary coalescence that may occur during the post-closure phase is investigated.
Highlights
The pulmonary airways are a branching tubular network internally coated with a bi-layer liquid film
After the closure, |∂zpw|max increases monotonically as the plug grows. It is seen in figure 6 that decreasing the serous layer thickness reduces both the wall pressure and shear stress excursions as well as their gradients, and after = 7, for the thinner serous layer depths, the peak levels of the mechanical stresses essentially remain unchanged. These results suggest that the presence of the serous layer reduces the risk of mechanical-stress-induced epithelial cell damage in the airway epithelium, but the excessive amount of serous might be detrimental as well
Our results indicate that the surface tension at the air–mucus interface plays a critical role on the severity of mechanical stresses, and in surfactant-deficient conditions, these stresses can reach dangerous levels for the airway epithelial cells (Bilek et al 2003)
Summary
The pulmonary airways are a branching tubular network internally coated with a bi-layer liquid film. In their experimental studies, Bilek, Dee & Gaver (2003), Huh et al (2007) and Tavana et al (2011) examined liquid plug propagation and rupture, and subsequent airway reopening, in both the surfactant-laden and clean environments, and quantified the cellular injury They showed that mechanical stresses and their gradients can reach fatal levels for airway epithelial cells during these processes. Romanò et al (2021) modelled the one-layer liquid as an Oldroyd-B fluid and illustrated the effects of the viscoelasticity on airway closure They observed a second peak of the wall shear stresses that can be as high as the first one after the coalescence due to an elasto-inertial instability.
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