Surfactant-laden film lining an oscillating cap: nonlinear dynamics and monolayer collapse

A spherical cap, lined internally with a surfactant-laden liquid film, is studied numerically as a model of lung alveoli. Large-amplitude oscillations are considered (deep breathing), which may lead to collapse of the surfactant monolayer during compression, with formation of a sub-surface reservoir that replenishes the monolayer during re-expansion. Independent conservation equations are satisfied for the monolayer and the total surface concentration of surfactant and a novel kinetic expression is introduced to model the two-way internal transport with the reservoir. Marangoni stresses, which drive shearing flow, are not significantly hindered by the collapse of the monolayer, unless the latter is singularly stiff. However, volumetric flow rate and wall shear stress exhibit abrupt changes with monolayer collapse, mainly because of the strong modification of capillary stresses. These changes induce complex temporal variability in the epithelial shear, a condition known to stimulate enhanced surfactant secretion. The effect may counterbalance the predicted increase with amplitude in surfactant drift from the alveolar opening, thereby contributing to homeostasis. Nano-particles deposited on the liquid layer are slowly transported by the flow towards the alveolar rim, with exit half-time in order-of-magnitude agreement with in vivo data. Thus, Marangoni stresses are proposed as a key mechanism of alveolar clearance. Both particle displacement speed and surfactant drift from the alveoli are found to vary with solubility, with the former increasing monotonically and the latter exhibiting maximum at intermediate solubilities.