Abstract
We have conducted experiments of the Faraday instability in a network of square cells filled with water for driving frequencies and amplitudes in the intervals 10≤F≤22 Hz and 0.1≤A≤3 mm, respectively. The experiments were aimed at studying the effects of varying the size of the cells on the surface wave patterns. Images of the surface wave patterns were recorded with a high-speed camera. The time series of photographs composing each video was Fourier analyzed, and information about the waveforms was obtained by using a Pearson correlation analysis. For small square cells of side length l=2.5 cm, adjacent cells collaborate synchronously to form regular patterns of liquid bumps over the entire grid, while ordered matrices of oscillons are formed at higher frequencies. As the size of the cells is increased to l=5 cm, collective cell behaviour at lower frequencies is no longer observed. As the frequency is increased, a transition from three triangularly arranged oscillons within each cell to three, or even four, irregularly arranged oscillons is observed. The wave patterns, the waveforms and the energy content necessary to excite Faraday waves are seen to depend on the cell size.
Highlights
When a container that is partially filled with a liquid is subjected to vertical vibrations, a pattern of standing waves is generally observed on the surface of the liquid
In a network of interconnected cells of small size, the relative effect of the numerous capillary menisci at the cell walls is an important factor. This variation of the meniscus height leads to the generation of capillary waves, which dissipate by viscous shear and interact with the Faraday waves, which are excited sub-harmonically
We have reported the observations from a sequence of experiments of Faraday waves in a network of square cells filled with water for forcing frequencies and amplitudes in the intervals
Summary
When a container that is partially filled with a liquid is subjected to vertical vibrations, a pattern of standing waves is generally observed on the surface of the liquid. In 1831, Faraday [1] reported for the first time that the frequency of the vibrations on the liquid surface are sub-harmonic because they oscillate at half of the harmonic excitation frequency This idea was later challenged by Mathiessen [2,3], who found experimentally that the vibrations were synchronous. This disagreement, between Faraday and Matthiessen, led Lord Rayleigh to conduct his own experiments [4], finding in two different ways that their results agreed with Faraday’s statement. It wasn’t until 1954 that Benjamin and Ursell [6] using linear theory confirmed the sub-harmonic nature of the instability
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