Absolute instability in the proximal airways

Camassa et al. ( J. Fluid Mech. 745, 2014, 682–715) demonstrated excellent agreement between the theoretical predictions using the longwave equation and experimental observations for the absolute instability-induced plug formation in the gravity-driven flow of a liquid coating the inner surface of a tube. A similar flow of airway surface liquid (ASL) exists in the proximal airways, driven by the turbulent airflow in addition to gravity. Motivated by the conclusions of previous studies, we probe for the existence of absolute instability in the proximal airways in the present study to determine plug formation and subsequent airway closure by considering ASL elasticity, cylindrical flow geometry and the effect of inhaled air temperature. To accomplish this, we derive a longwave evolution equation, which is then used to obtain the dispersion relation. In contradistinction to the distal airways, the analysis predicts the absence of absolute instability-induced airway closure in the proximal airways for a healthy lung. However, an increased ASL thickness and/or elasticity due to excessive secretion of mucus and mucins in a diseased lung could lead to airway closure due to ASL plugs. Furthermore, inhaling colder air (than body temperature) enhances the absolute instability region, and the opposite is true for inhaling warmer air (than body temperature). For lungs with increased ASL thickness (due to diseases), plug formation is aggravated by colder air inhalation, thus demonstrating that inhaling colder (warmer) air is detrimental (beneficial) for diseased lungs. The predictions of the present analysis are in agreement with clinical observations.