Curvature-driven transport of thin Bingham fluid layers in airway bifurcations

The mucus on the bronchial wall forms a thin layer of non-Newtonian fluid. One of the roles of mucus is to protect the lungs by capturing inhaled pollutants. It is transported by mucocilliary clearance toward the tracheo-pharyngeal bifurcation, where it is eliminated. Due to the corrugation of its interface with air, the mucus layer is subject to surface tension forces that interact with its rheology. It is still not clear whether these forces can affect mucus displacement and, if they can, under what conditions and how this displacement can occur. In this work, we model the mucus as a thin Bingham fluid layer located on the wall of idealized, multi-scaled airway bifurcations. We analyze the resulting physical system using lubrication theory and 3D simulations. The theoretical analysis allows us to characterize the nonlinear behavior of the system and determine the geometric conditions under which the Bingham fluid can be moved by surface tension. 3D simulations are then used to quantify the effects in idealized airway bifurcations on a range of scales corresponding to those of bronchial bifurcations. Our results suggest that surface tension effects can displace overly thick mucus layers in airway bifurcations, a typical situation in obstructive lung pathologies (asthma, BPCO, cystic fobrosis, etc.). Moreover, our results indicate that this movement can disrupt mucociliary clearance and the homogeneity of the layer thickness, thus increasing the risk of lung infection.