2023/08/02 by Stephen L. Strickland, Karen E. Daniels, Strickland, Stephen L. +3
Computer Science · Earth and Planetary Sciences · Engineering · #Characterization and Applications of Magnetic Nanoparticles #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Dynamics and Pattern Formation #Ocean Waves and Remote Sensing
paper · pdf · doi:10.48550/arxiv.2308.01426
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Faraday waves are gravity-capillary waves that emerge on the surface of a vertically vibrated fluid when the energy injected via vibration exceeds the energy lost due to viscous dissipation. Because this dissipation primarily occurs in the free surface boundary layer, their emergence is particularly sensitive to free surface properties including the surface tension, elasticity, and viscosity of surfactants present at the free surface. We study this sensitivity by considering a Newtonian fluid bath covered by an insoluble surfactant subject to vertical vibrations which produce sub-harmonic Faraday waves. By assuming a finite-depth, infinite-breadth, low-viscosity bulk fluid and accounting for surface tension, Marangoni, and Boussinesq effects, we derive an expression for the onset acceleration up to second order in the expansion parameter Υ= √\tfrac1Re. We recover the results of previous numerical investigations, but only by modifying the Marangoni and Boussinesq numbers to account for the low-viscosity limit. The analytic expression allows us to consider a range of parameters not previously studied, including a wide variety of fluid depths and driving frequencies. In addition, we uncover regions of parameter space for which our model predicts that the addition of surfactant would lower, rather than elevate, the onset acceleration. We discuss the possible use of this model in developing a surface viscometer for surfactant monolayers.