Phase dependence of effective surface diffusivity in surfactant monolayers dilatated far from equilibrium

Modeling the flow of insoluble surfactant monolayers undergoing rapid expansion and compression remains a long-standing challenge in hydrodynamics. In a recent letter, compressible flow of a DPPC monolayer in the coexisting liquid-expanded/liquid-condensed phase was accurately described with Newtonian and Fickian modeling by using large effective surface diffusivity, many orders of magnitude larger than the monolayer's equilibrium diffusivity, along with finite surface dilatational viscosity. The large effective diffusivity was attributed to monolayer phase coexistence. Here, the applicability of large effective diffusivity is investigated through flow measurements of DPPC and vitamin K1 monolayers over a wide range of concentrations, from gas phase to collapse. Effective surface diffusivity and surface viscosity were determined by fitting numerical simulations, via Navier-Stokes bulk flow coupled to a Boussinesq-Scriven interface with monolayer advection-diffusion, to spatio-temporal surface velocity measurements. Results reveal that large effective surface diffusivity is not limited to coexisting phases, producing good fits for all monolayers outside gaseous phases. The failure of this theoretical framework when applied to gaseous monolayers is likely due to their extreme compressibility. The extreme diffusivity in non-gaseous phases motivates future exploration of non-Newtonian and non-Fickian interfacial models.