Impact of the Equation of State in Models for Surfactant Spreading Experiments

Pulmonary surfactant spreading models often rely on an equation of state relating surfactant concentration to surface tension.~ Mathematically, these models have been analyzed with simple functional relationships.~ However, to model an experiment with a given fluid and surfactant, a physically meaningful equation of state can be derived from experimentally obtained isotherms.~ We discuss the comparison between model and experiment for NBD-PC lipid (surfactant) spreading on glycerol for an empirically-determined equation of state, and compare those results to simulations with traditionally employed functional forms.~ In particular we compare the timescales by tracking the leading edge of surfactant, the central fluid height and dynamics of the Marangoni ridge.~ We consider both outward spreading of a disk-shaped region of surfactant and the hole-closure problem in which a disk-shaped surfactant-free region self-heals.