Non-Newtonian and surfactant effects on the liquid plug rupture in an airway reopening model

Abstract

Elastoviscoplastic effects on liquid plug propagation and rupture occurring in airways are studied computationally using the Oldroyd-B and Saramito-Herschel-Bulkley models. The relevant parameters are selected from physiological values representative of the eighth-to-tenth generation branches of a typical adult lung. The respiration pushes the liquid plug, depositing a trailing film thicker than the leading film. As a result, the liquid plug gets drained and eventually ruptures. We model airway reopening considering a rigid axisymmetric tube whose inner surface is coated by a thin non-Newtonian liquid film. A critical elastic behaviour is revealed: for low Weissenberg number (subcritical), the viscoelastic stress is released in the liquid plug, while for high Weissenberg number (supercritical), the stretched polymeric chains release their stresses in the trailing film, giving rise to (i) hoop stress that increases the film thickness and (ii) axial stress that leads to a speed-up of the liquid plug. Under supercritical conditions, we also identify a resonance that amplifies the elastic stresses. A mechanical analogy is proposed to elucidate the resonance phenomenon. The occurrence of the resonance is robust upon a variation of Weissenberg number, Laplace number, reference solvent-to-total dynamic viscosity ratio, the surfactant elastoviscoplastic mucus. Our simulations confirm that a presence of surfactants do not significantly affect the results, except for the expected delay of airway reopening due to air-mucus surface contamination. Such a novel elastocapillary mechanism increases the risk of epithelial cell damage regardless of the occurrence of plug rupture.