Oscillatory Instabilities of two-layer Rayleigh-Marangoni-Bénard Convection

Paper number

IAC-05-A2.4.03

Author

Dr. Qiu-Sheng Liu, Chinese Academy of Sciences, China

Year

2005

Abstract

Both surface or/and interfacial tension gradients and buoyancy may drive convective motion in aliquid layer with a free surface/interface when heated from below. In two or more superposed layers of liquid-liquid systems, the convective instabilities and its mechanisms become more complex than the single layer systems, due to the competition between instabilities in the separate layers and the various interfacial surface tension driven modes. The two-layer Rayleigh-Marangoni-Bénard(R-M-B) convection instability is a typical physical model of such phenomenon that has been
investigated for a long time. For simplification, most previous works were performed mainly on the instability behaviors induced by buoyancy force, especially on the oscillatory behavior at onset of
the whole system. But, the oscillatory instability (Rayleigh-Bénard instability), which neglects interfacial deformations and Marangoni effect, exists in a very narrow region[1-3]. In the gravity
reduced field or thin liquid layer, the domination of thermocapillary effect must be considered. In the present paper, the linear and nonlinear oscillatory instabilities of the R-M-B convection in two-layer fluid system have been investigated theoretically and numerically. Its more attention
focus on the oscillatory instability induced by the real interaction between Rayleigh-Bénard instability and Marangoni instability in two-layer systems, such as the Silicon oil(10cSt)-Fluorinert (FC70) and the Silicon oil (2cSt)-water. Our both linear instability analysis and 2D numerical simulation results show that the onset oscillatory instability region is enlarged through the coupling of Rayleigh instability and Marangoni effect for different depth ratios of
two-layer liquids (with reducing the Ra/Ma values). The results are different from the previous study on the Rayleig-Bénard instability and show the strong effects of  the interfacial thermocapillary force on the time-dependent oscillations arising at or after the onset of instability convection. For the nonlinear instability of R-M-B convection in two-layer system, a Hopf bifurcation on the secondary convective instability has been found in the real two-layer system of silicon oil over water. This secondary instability phenomenon could explain the existent difference of the previous theoretical predictions in the comparison of Degen's experimental
observation performed in 1998[4]. Both standing wave and traveling wave are also predicted numerically in the regime of the oscillatory instability near the onset of R-M-B convection.

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