  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.
