This talk studies the dynamics of a thin viscous liquid film
coating the inner or outer surface of a sphere in the presence of gravity,
surface tension and Marangoni effects. An asymptotic model describing the
evolution of the film thickness is derived based on the lubrication
approximation. We study the cases when the surface tension gradient is due
to an externally imposed temperature field or the presence of surfactant
molecules. In the former case, we consider two different heating regimes
with axial or radial thermal gradients and discuss the resulting dynamics.
In the latter case, we derive and study a model for the coating flow
inside the alveolar compartment of the lungs, taking into account the
effect of pulmonary surfactant and its production and degradation. We
derive a degenerate system of two coupled parabolic partial differential
equations that describe the time evolution of the thickness of the coating
film together with that of the surfactant concentration at the liquid-air
interface. We present numerical simulations of the dynamics using
parameter values consistent with experimental measurements.