Air-liquid interfacial movement in models simulating airway reopening

In this model study, we simulated the initial airway reopening event in a rigid tube model. The air-liquid interface during airway reopening was assumed to be a simple axisymmetric meniscus similar to that of a two-phase flow in a rigid tube (radius R), where the applied pressures and the meniscus velocities were measured experimentally for fluids of different viscosities and surface tensions (gamma). Bulk flow contribution was deducted from the applied pressure to obtain the pressure accounting for interfacial movement (P*(int)). A semi-empirical formula for the interface was generated by dimensional analysis. The dimensionless interfacial pressure (P(int) = P*(int),R/gamma) was found to approach 2 for sufficiently small velocities, consistent with Bretherton's theoretical prediction. This formula also resembles that previously obtained in collapsible tubes simulating airways. The result suggests that the critical pressures required to reopen a collapsible airway and a non-collapsible one with the same radius are similar in magnitude (approximately 2 - 3gamma/R). However, in a collapsible airway, no significant bulk flow of lining fluids would develop while the interface proceeds, leading to a much smaller overall pressure for further reopening. Airway wall collapsibility thus could play a crucial role in maintaining proper ventilation through rapid reopening of the airway.