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

Abstract: We computationally investigate the effects of elastoviscoplasticity on liquid plug propagation and rupture in an airway model using the Oldroyd-B and Saramito-Herschel-Bulkley constitutive laws. Physiologically relevant parameters are chosen to represent the eight- to twelveth-generation branches of a typical adult lung, where the airway diameter is millimetric and gravitational effects are negligible. The applied pressure difference, driven by respiration, pushes forward a previously formed liquid plug, which deposits a trailing film thicker than the leading film. This asymmetry leads to plug drainage and eventual rupture.

To model airway reopening, we consider a rigid, axisymmetric tube internally coated with a thin non-Newtonian liquid film. We explore the influence of key parameters, including the Laplace number, Weissenberg number, Bingham number, power-law index, and the solvent-to-total dynamic viscosity ratio. A critical transition in elastic behavior is identified: at low Weissenberg numbers (subcritical), viscoelastic stress is primarily released within the liquid plug, whereas at high Weissenberg numbers (supercritical), stretched polymeric chains transfer stress into the trailing film. This results in (i) hoop stress, which increases film thickness, and (ii) axial stress, which accelerates the plug.

Under supercritical conditions, a resonance phenomenon can emerge, amplifying stresses within the system. We propose a mechanical analogy to explain this resonance, characterized by the square root of the Weissenberg-to-Laplace ratio, akin to the relationship between natural and forcing frequencies. Resonance robustly occurs when this ratio is approximately 1, persisting across variations in Weissenberg number, Laplace number, solvent-to-total viscosity ratio, and even in the presence of elastoviscoplasticity. This novel elasto-capillary mechanism increases the risk of epithelial cell damage, independent of plug rupture. The robustness of these findings is confirmed through extensive parametric numerical investigations.

Bio: Francesco Romanò is an Associate Professor at the Department of Fluid Mechanics and Energetics, Arts et Métiers, Lille (France), since 2019. He holds Bachelor’s and Master’s degrees in Aerospace Engineering from the University of Pisa (Italy) and a PhD in Mechanical Engineering from TU Wien (Austria) under the supervision of Prof. Hendrik C. Kuhlmann. He completed a 1.5-year PostDoc at TU Wien, focusing on hydrodynamic instabilities and Lagrangian topology, and another 1.5-year PostDoc at the University of Michigan (US) with James B. Grotberg, studying pulmonary flows. He has authored over 50 journal papers, one book chapter, and over 15 conference papers, and has given more than 30 invited talks. He serves as Review Editor for Frontiers in Space Technologies and Microgravity, on the section editor of Bioflows for Discover Fluid Mechanics (Springer). He is also the organizer of the LMFL Fluid Mechanics Webinar, that hosts about 40 seminars a year. His research interests include cavity mixing, chaos theory, microfluidic multiphase flows, biological and non-Newtonian flows, thermo- and soluto-capillary effects, stability analysis, and more recently, flow control and turbomachinery.