  We derive a new model for the coating flow inside the alveolar compartment,
taking into account pulmonary surfactant production and recycling by Type 2
cells as well as its degradation. As the thickness of alveolar coating is much
smaller than the average radius of the alveoli, we employ the classical
lubrication approximation to describe the thin liquid film dynamics in the
presence of pulmonary surfactant, which is a surface tension reducing agent and
thus prevents the lungs from collapse. In the lubrication limit, we derive a
degenerate system of two coupled parabolic partial differential equations that
describe the time evolution of the thickness of the coating film inside the
alveoli together with that of the surfactant concentration at the interface. We
present numerical simulations using parameter values consistent with
experimental measurements.
