Modeling coating flow and surfactant dynamics inside the alveolar compartment

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. With Marangoni effects being significant, it is found that any initial non-uniformity in surfactant concentration leads to a very fast redistribution of surfactant and accompanying change in film thickness, followed by a much slower relaxation of the film thickness to equilibrium during which surfactant concentration remains relatively uniform.