  Materials adsorbed to the surface of a fluid -- for instance, crude oil,
biogenic slicks, or industrial/medical surfactants -- will move in response to
surface waves. Due 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 traveling 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 moir\'e-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 traveling 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, suggesting the presence of longitudinal
waves.
