ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Fingering instabilities involving fluids confined between two plates sometimes give rise to a typical wavelength λ proportional to the gap h. This unexplained behavior is investigated for the case of the Rayleigh–Taylor instability between two liquids of the same viscosity. Using qualitative scaling arguments and linear stability analysis for a simplified model of hydrodynamics, we show that, in the miscible case, h becomes a natural cut-off when diffusion is negligible, i.e., when the Péclet number Pe=h3Δρg/(ηD) is large (η viscosity, g gravitational acceleration, D diffusivity, Δρ density difference). The same result holds in the immiscible case for large capillary number Ca=h2Δρg/(12γ) (γ surface tension). In this saturation regime, the dominant wavelength is given by λ(approximate)2.3h, while in the opposite limit (low Pe or low Ca) λ scales, respectively, as h/Pe or h/Ca1/2. These results are in agreement with a recent experimental study. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1410120
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