Surfactant spreading on liquid films in the Stokes regime

Characterizing the spreading of surfactants on the surface of a liquid film is central to our understanding of natural and technological processes ranging from cell propulsion and drug delivery in pulmonary airways to cleaning food processing surfaces. In this work, we analyze the spreading dynamics of a drop of insoluble surfactants in a perfectly viscous (i.e., Stokes) regime. Using simple scaling arguments, we estimate that the size of a small surfactant drop grows as a power-law with time with an exponent of [Formula: see text]. The estimated scaling is then corroborated and better characterized using direct numerical simulations. Furthermore, the simulation results help establish the transition from the initial [Formula: see text] scaling with time to the later [Formula: see text] scaling that is expected when the spreading drop grows larger than the film thickness.