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- W1871717963 abstract "AbstractIn this paper, I consider a thin suspended liquid film, surrounded bya different fluid. Examples of such a system are soap films and liquidcrystal films, surrounded by air. They are considered good models fortwo dimensional fluid dynamics, although air drag is known to introducestrong deviations. I exactly solve the hydrodynamic equations of the sys-tem composed by the liquid layer and the surrounding fluid in order toevaluate the correlation function of the thermally excited velocity fluctu-ations. Both the temporal and the spatial statistical properties are theones of a two dimensional, hypotetical fluid, only for temporal and spa-tial frequencies higher than critical values; at lower frequencies they showsignificative deviations due to the interactions of the liquid layer with thesurrounding fluid. 1 Introduction A thin, freely suspended liquid layer is generally considered a system that fol-lows two dimensional hydrodynamics, on length scales longer than the layerthickness. Many experiments have been performed on soap films, that consistof two monolayers of amphiphilic molecules around a layer of water. The layerthickness ranges from the 4nm of the Newton black film to many micrometers;features down to a fraction of a millimeter should be considered two dimensional[6].Also smectic A liquid crystals can form films, by a different effect. It spon-taneously form a layered structure, with the elongated molecules alligned tothe surface normal. When a film is drawn from this kind of liquid crystal, itis formed by a set of monolayers, ranging from two to many hundreds [1]; thethickness can be selected with extreme accuracy. Because of the absence oftranslational order in the monolayers, the film behaves as a two dimensionalsystem.Many papers [6, 7, 10, 4, 5] describe experiments in which turbulent flowshave been detected, and discuss the agreemen with two dimensional hydrody-namics. One result is that the role of the air surrounding the film cannot be1" @default.
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- W1871717963 date "2011-03-24" @default.
- W1871717963 modified "2023-09-27" @default.
- W1871717963 title "Correlation function of the velocity field of a thin suspended liquid film" @default.
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