Effects of Surface Tension and Yield Stress on Mucus Plug Rupture: A Numerical Study

Abstract

We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimensional simplified configuration is employed to simulate mucus plug rupture in a collapsed lung airway of the tenth generation. The Herschel–Bulkley model is used to take into account the non-Newtonian viscoplastic fluid properties of mucus. Results show that the maximum wall shear stress greatly changes right prior to the rupture of the mucus plug. The surface tension influences mainly the late stage of the rupture process when the plug deforms greatly and the curvature of the mucus–air interface becomes significant. High surface tension increases the wall shear stress and the time needed to rupture since it produces a resistance to the rupture, as well as strong stress and velocity gradients across the mucus–air interface. The yield stress effects are pronounced mainly at the beginning. High yield stress makes the plug take a long time to yield and slows down the whole rupture process. When the effects induced by the surface tension and yield forces are comparable, dynamical quantities strongly depend on the ratio of the two forces. The pressure difference (the only driving in the study) contributes to wall shear stress much more than yield stress and surface tension per unit length. Wall shear stress is less sensitive to the variation in yield stress than that in surface tension. In general, wall shear stress can be effectively reduced by the smaller pressure difference and surface tension.

Surface-tension-driven evolution of a viscoplastic liquid coating the interior of a cylindrical tube

“…Experiments and numerical modelling of plug rupture (Hu et al. 2015, 2020) suggest that, once an airway does close, increased yield stress makes airway reopening more difficult, which would contribute to the increased prevalence of plugged airways in CF. Our results also suggest that airway closure could be triggered if is suddenly decreased, which could be caused by applying certain therapies which are commonly used in CF, such as mucolytics which decrease the mucus yield stress (Patarin et al.…”

“…Rupture of viscoplastic liquid plugs has also been modelled both experimentally (Hu et al. 2015) and numerically (Hu, Romanò & Grotberg 2020), showing that increased yield stress can inhibit plug rupture because a larger pressure drop is required across the plug to make it yield. Recently, Bahrani et al.…”

Capillary instability of a two-layer annular film: an airway closure model

“…(2019) studied the whole plug propagation and rupture phases computationally for both the clean and contaminated cases, and confirmed the protective effects of surfactant for epithelial cells. Non-Newtonian viscoplastic features of pulmonary mucus are taken into account by Hu, Romanò & Grotberg (2020) in a three-dimensional simplified configuration incorporating the Herschel–Bulkley model. They deduced that the yield stress decelerates the rupture process, but its variation has a little effect on the wall shear stresses.…”

The effect of viscoelasticity in an airway closure model

“…Additional considerations are reserved to the effect of non-uniform surface tension and yield stress on plug rupture (Ghadiali & Gaver 2008; Muradoglu et al. 2019; Hu, Romanò & Grotberg 2020), and compliance of airway walls, which enhance the level of stress on the epithelial cells (Zheng et al. 2009).…”