Role of edge effects and fluid depth in azimuthal Faraday waves

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 (n, l). 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.

Automated summary

This study investigates Faraday waves generated by mechanically vibrating a cylindrical container. Frequency scans are used to measure the acceleration threshold for the appearance of surface waves, and the spatial structure of the waves is determined using imaging techniques. Theoretical models are developed to calculate the natural oscillations of different materials in the cylindrical container under varying boundary conditions, with good agreement between theoretical predictions and experimental observations.