Faculdade de Ciências da Universidade do Porto, Portugal
Faraday waves are due to the restoring forces of gravity and surface tension, but they become entirely surface tension driven for small wavelength. In zero gravity, you will just have surface tension for all wavelengths, but the size of a feasible experiment will be small anyhow, so that also the wavelengths will be small and you will be trivially in the surface tension regime." in Willem van de Water.
Parametrically forced surface waves (1) also known as faraday waves are an interesting phenomenon in fluid dynamics. The harmonic oscillation of a liquid at a single frequency origins waves in the liquids free surface with a frequency similar to half the driving frequency.
The first report on this subject was done by Michael Faraday in 1831. In these studies there are two factors to have in consideration, the gravity acceleration and the fluid capillarity. This two factors result in two work modes. Early experiments and studies were dominantly concerned with gravity modes.
However the capillarity modes have been recently studied and knew phenomena were revealed, this experiments, revealed knew regimes and knew dispersion relations (11), droplet ejections (12), stable patterns formation (13), crystalline pattern formation (14-16) quasi crystalline patterns (17) and rotating spiral (18).
In this regime the only stable capillarity ripples appear to be standing waves and there superposition (the phase is the equal to the phase of the pumping field).
Some students from San Diego’s university conducted a zero gravity experiment in which they tried to simulate faraday waves in pure capillarity regime the results of these experiments are revealed in . In these experiments the studies were concentrated in the fluid mixing studied and the faraday interface between them. This work failed in some aspects but generally it confirmed the pure capillarity regime. In this experiment it was confirmed that the pumping oscillation amplitude necessary too ensure the waves is very small. And so we do not need direct contact with the liquids but the pumping can be made by sound speakers. Notice that when you shake a bottle of Italian salad dressing, you generally shake the bottle much harder than the minimum necessary to mix the oil and vinegar. In space, every action has a reaction that is not damped by gravity. When you shake the salad dressing on Earth, the earth shakes in response to your movement.
The schlierem interferometer (20) guarantees the image process resolution that is necessary to study these phenomena. If this is not so we can endure a two dimensional image phase recovery method (21).
In this experiment we expect to encounter dispersion relations, power spectrum distribution, the traditional one half relations between the pumping field and the originated waves. We will probably meet knew regimes.
In the first experiment we expect to study the faraday waves in two non-mixable fluid interface, this study is a knew phenomena and aglow some early work has been done the results were ambiguous. We remember that in zero gravity the fluid mixing depends not on there density but on the intermolecular forces of the same species molecules and the forces between molecules of different species.
- M. Faraday, Philos. Trans. R. Soc. London 121, 319 (1831)
- Rayleigh, Lord. 1883, On maintained vibrations. Phylos. Mag. 15:229-35.
- Benjamin, and Ursell, F. 1954. The stability of plane free surface of a liquid in vertical periodical motion, Proc. R. Soc. London Ser. A 225:505-15.
- Dodge, F.T., Kana, D.D., Abramson, H.N., 1965.Liquid Surface oscillations in longitudinally exited rigid cylindrical containers. AIAA J.3:685-95.
- Ockendon, J.R., Ockendon H. 1973, Resonant suface waves. J. fluid Mech 59 : 397-413.
- Hensttocke W., Sani, R. L., 1974 On stability of the free surface of a cilindical wave of fluid in vertical periodical motion, Lett. Heat Mass Transfer 1:95-102.
- Milles, J. W. 1984 Nonlinear Faraday ressonace. J. Fluid Mech. 146 :285-302
- Meron, E., Procaccia, I., 1986 Low dimetional caus in surface waves,:teorectical analyses of an experiment, Phys. Rev. A 34:3221-37.
- Gu. X. M., Sethna, P. R., Narain, A. 1988, On three dimentional non linear sub atomic ressonant surface waves in a fluid: Part I- theory J. Appl. Mech. 55:213-19
- Milles J., Henderson D., 1990, Parametrically forced surface waves, Annu. Rev. Fluid Mech. 1990. 22:143-65.
- Goodridge, C.L., Hentschel, H.G.E., 1999, Breaking Faraday Wave: Critical Slowing of Droplet Ejection Rates, Phys. Rev. Letters, 1990. 82 (15): 3062(4)
- Holt, R. G., Trinh, E.H., 1996, Faraday Waves Turbulence on a Spherical Liquid Shell, Phys. Rev. Letters, 1996. 77(7): 1274(4)
- Merket, F.S. et al. 2004, Persistent holes in fluid, Phys. Rev. Letters, 2004, 92(18): 184501(4)
- A.B. Ezersky, M.I. Rabinovich, V.P. Reutov, and I.M. Starobi-nets,Zh. Eksp. Teor. Fiz. 91, 2070 ~1986[Sov. Phys. JETP64, 1228 (1986)]
- W.S. Edwards and S. Fauve, J. Fluid Mech. 278, 123 
- K. Kumar and K.M.S. Bajaj, Phys. Rev. E 52, R4606 
- B. Christiansen, P. Alstrom, and M.T. Levinsen, Phys. Rev.Lett. 68, 2157 
- Kiyashko, S.V et al. 1996, Rotating spirals in a Faraday experiment,1996, Physical Review E 54(5): 5037(4)
- Zero Gravity Homepage at the University of San Diego: http://www.sandiego.edu/zerogravity/
- Goldstein, R.J., Kuehn, T.H.,1996, Optical Systems for Flow Interferometric Techniques, ed. Taylor and Francis, Washington DC, 1996.
- Sienup, J.R.1982, Phase Retrieval Algorithms: a comparison.1982, Appl Optics, vol 21 nº15, 2758-2769