The role of higher-order viscous and interfacial effects on the onset of surfactant-covered faraday waves.

This article focuses on deriving an analytic expression for the onset acceleration (\(a_c\)) of sub-harmonic Faraday waves—gravity-capillary waves that form on a vertically vibrated fluid surface—specifically in a finite-depth, infinite-breadth Newtonian fluid covered by an insoluble surfactant. The study incorporates surface tension, Marangoni (surface tension gradient) effects, and Boussinesq (surface viscosity) effects, introducing modified dimensionless numbers to balance surfactant and inertial contributions. The analytic solution, valid up to second order in a low-viscosity expansion parameter, recovers known surfactant-free results and quantitatively agrees with previous numerical studies across a wide range of parameters. Notably, the analysis reveals that in sufficiently shallow fluid layers, adding surfactant can reduce the onset acceleration—contrary to the expectation that surfactants increase viscous dissipation—suggesting potential applications in low-cost surface viscometry and enhanced mixing in thin films.