Group 1

Faraday Waves and Nonlinear Patterns

Background

Eponymously discovered by Faraday[1], Faraday Waves are standing waves on a fluid caused by vertical oscillatory motion. At given frequencies, these standing waves give surface paterns of n dimensional rotational symmetry; mainly square, hexagonal, and 8-fold quasi-static paterns. This experiment is designed to reproduce the results of quantifying the observance of these waves by Binks and W. van de Water [3]. The expected results should also agree with Zhang and Vinals' [2] prediction of the amplitudes of the standing waves. The experiment will go a step further and not only test the theory out for different fluids (including a non-newtonian fluid), but for different oscillatory patterns.

Experiment

1. Reproduce the experiments of Binks and Van de Water
   1. Fill a 440 mm diameter circular container with 20 mm height of experimental fluid
   2. Attach a 2 cm thick plate on the bottom of the container and a hollow conical structure attached to an electromagnetic exciter below that.
   3. Place piezo-electric accelerometers on the cone (one on bottom, two on top) to measure the acceleration cone. This allows control of the oscillation frequency.
   4. A high speed CCD camera is placed above the container to take snapshots of the standing waves. It is required that the frames per second of the snapshots are greater than the oscillation period of the standing waves.
   5. The amplitude of the oscillations are controlled by the electromagnetic exciter and increased in small steps (about 1%) where each wave is held for 2000 seconds first before taking 1000 s of images of the waves.

Videos of Faraday Waves

Faraday Waves on Cornflour
Faraday Waves set to music

Group Members

• Juan Orphee
• Paul Cardenas-Lizana
• Michael Lane
• Elan Grossman

Sources

[1] M. Faraday, Philos. Trans. R. Soc. London 121, 319 (1831)

[2] W. Zhang and J. Viñals, Phys. Rev. E 53, R4286 (1996)

[3] D. Binks and W. van de Water, Phy. Rev. Lett. 78, 4043 (1997)

[4] Peilong Chen and J. Vinals, Phys. Rev. Lett, 79, 2670 (1997)