F213 液膜のレイリー・テイラー不安定性の潤滑近似による数値的研究

概要

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A two-dimensional nonlinear evolution equation which describes the three-dimensional spatiotemporal behavior of the air-liequid interface of a thin liquid film lying on the undreside of a horizontal plate, is investigated numerically and analytically. The final patterns observed in the experiments by Fermigier et al. [J. Fluid Mech. (1992) 236,349-383] such as the axial symmetries, the hexagonal ones and so on, are reproduced by numerical simulations. It is shown that quasi-steady axisymmetric peaks are well described by the steady axisymmetric solution : ζ=ζ_1J_0(√<Boγ>)+ζ_0,where J_0 (γ) is the zeroth-order of the Bessel function, ζ_1 and ζ_0 are constants and Bo is the Biot number. The constants are not uniquely determined but depend on initial conditions and time. Time-evolutions of the peaks are divided into two stages : one is that the peak accumulates the liquid with increasing its height ζ_1+ζ_0 and the other is that its height grows gradually keeping the volume of the peak region. It is shown numerically that the steady axisymmetric solution is stable irrespective of the constants ζ_1 and ζ_0.
日本流体力学会の論文
2001-07-31