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 10 th 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 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.