Spatiotemporal measurement of surfactant distribution on gravity–capillary waves

Abstract

Materials adsorbed onto the surface of a fluid – for instance, crude oil, biogenic slicks or industrial/medical surfactants – will move in response to surface waves. Owing to the difficulty of non-invasive measurement of the spatial distribution of a molecular monolayer, little is known about the dynamics that couple the surface waves and the evolving density field. Here, we report measurements of the spatiotemporal dynamics of the density field of an insoluble surfactant driven by gravity–capillary waves in a shallow cylindrical container. Standing Faraday waves and travelling waves generated by the meniscus are superimposed to create a non-trivial surfactant density field. We measure both the height field of the surface using moiré imaging, and the density field of the surfactant via the fluorescence of NBD-tagged phosphatidylcholine, a lipid. Through phase averaging stroboscopically acquired images of the density field, we determine that the surfactant accumulates on the leading edge of the travelling meniscus waves and in the troughs of the standing Faraday waves. We fit the spatiotemporal variations in the two fields using an ansatz consisting of a superposition of Bessel functions, and report measurements of the wavenumbers and energy damping factors associated with the meniscus and Faraday waves, as well as the spatial and temporal phase shifts between them. While these measurements are largely consistent for both types of waves and both fields, it is notable that the damping factors for height and surfactant in the meniscus waves do not agree. This raises the possibility that there is a contribution from longitudinal waves in addition to the gravity–capillary waves.