Abstract
Faraday waves are created in experiment by mechanically vibrating a cylindrical container. Frequency scans are performed, and the acceleration threshold above which a surface wave appears is measured using a laser light approach, giving the instability tongue in frequency-acceleration space. The spatial structure of the surface wave, which conforms to the cylindrical container for wavelengths comparable to the container size, is determined using long-exposure-time white light imaging and is defined by the mode number pair . Edge conditions at the container sidewall are controlled to create a (i) pinned or (ii) freely sliding contact-line. The driving frequency with the smallest threshold acceleration is identified as the natural frequency for that particular mode number pair. A theoretical model is developed using a viscous potential approximation to compute the natural oscillations of a viscoelastic material in a cylindrical container with a flat interface for both a pinned and a freely sliding contact-line. A closed-form expression is given for the freely sliding case, and a Rayleigh-Ritz procedure is used for the pinned case. The agreement is good between theoretical predictions and experimental observations for Triton/water mixtures, glycerol/water mixtures, and agarose gels, notwithstanding the large range in parameter space and the very different boundary conditions considered.
- Received 19 May 2021
- Accepted 4 January 2022
DOI:https://doi.org/10.1103/PhysRevFluids.7.014803
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