The Faraday threshold in small cylinders and the sidewall non-ideality

Abstract

In this work we investigate, by way of experiments and theory, the Faraday instability threshold in cylinders at low frequencies. This implies large wavelengths where effects from mode discretization cannot be ignored. Careful selection of the working fluids has resulted in an immiscible interface whose apparent contact line with the sidewall can glide over a tiny film of the more wetting fluid, without detachment of its actual contact line. This unique behaviour has allowed for a system whose primary dissipation is defined by the bulk viscous effects, and in doing so, for the first time, close connection is seen with the viscous linear stability theory for which a stress-free condition is assumed at the sidewalls. As predicted, mode selection and co-dimension 2 points are observed in the experiment for a frequency range including subharmonic, harmonic, and superharmonic modes. While agreement with the predictions are generally excellent, there are deviations from the theory for certain modes and these are explained in the context of harmonic meniscus waves. A review of previous work on single-mode excitation in cylinders is given, along with comparison to the viscous model and analysis based upon the conclusions of the current experiments.

Quantumlike statistics of deterministic wave-particle interactions in a circular cavity

“…Uncertainty in the boundary conditions further complicates mode identification. Ideal Dirichlet boundary conditions (zero velocity where the liquid-air interface meets the solid walls) could have been expected if the contact line was pinned [34]. But in experiments contact lines are avoided on purpose because the vibration of the associated meniscus would be a source of parasitic capillary waves.…”

Faraday forcing of high-temperature levitated liquid metal drops for the measurement of surface tension

“…Drop levitation significantly reduces gravitational effects and allows for containerless experimentation, eliminating sidewall effects that have been shown to be detrimental to the agreement between Faraday instability theory and experiments. 2 Though Faraday forcing has never been used to measure surface tension in levitated samples, similar resonant forcing techniques have been employed in constrained geometries for this measurement. For example, Chung et al 3 correlated the measurement of interfacial tension to the behavior of capillary wave resonance modes utilizing quasi-elastic laser scattering to measure the resonance.…”

Footprint geometry and sessile drop resonance

“…For both, typical observables are mode shapes [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], resonance frequencies [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and the evolution of surface waves with forcing amplitude [18,23,[29][30][31][33][34][35]. The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low.…”

“…The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low. However, an elevated acceleration triggers modes which oscillate at half the forcing frequency [15,18,19,21,[30][31][32], called half-frequency subharmonic modes.…”

“…This has been identified as a parametric response, often modeled by the Mathieu-Hill equation [15,18,19,25,31,32,36,37]. These common features apparently imply that resonance of drops and Faraday waves are closely related, although they have been separate studies in the literature mostly.…”