Linear-stability analysis of thermocapillary-buoyancy convection in annular two-layer system with a radial temperature gradient

2015 ◽  
Vol 66 ◽  
pp. 58-62 ◽  
Author(s):  
Xi-Wu Gong ◽  
Dong-Ming Mo ◽  
Chun-Mei Wu ◽  
You-Rong Li
Keyword(s):  
Stability Analysis ◽  
Temperature Gradient ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Radial Temperature Gradient ◽  
Layer System ◽  
Radial Temperature ◽  
Buoyancy Convection

Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities

1998 ◽  
Vol 359 ◽  
pp. 143-164 ◽  
Author(s):  
R. J. RILEY ◽  
G. P. NEITZEL
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Thin Layers ◽  
Hydrothermal Wave ◽  
Oscillatory State ◽  
Buoyancy Convection ◽  
Wave Instabilities ◽  
Oscillatory Instabilities

Combined thermocapillary–buoyancy convection in a thin rectangular geometry is investigated experimentally, with an emphasis on the generation of hydrothermal-wave instabilities. For sufficiently thin layers, pure hydrothermal waves are observed, and are found to be oblique as predicted by a previous linear-stability analysis (Smith & Davis 1983). For thicker layers, both a steady multicell state and an oscillatory state are found to exist, but the latter is not in the form of a pure hydrothermal wave.

Faraday instability of a liquid layer on a lubrication film

2019 ◽  
Vol 879 ◽  
pp. 422-447 ◽  
Author(s):  
Sicheng Zhao ◽  
Mathias Dietzel ◽  
Steffen Hardt
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Single Layer ◽  
Bottom Layer ◽  
Slip Boundary Condition ◽  
Immiscible Liquid ◽  
Layer System ◽  
Faraday Instability ◽  
Lubrication Effect

The Faraday instability in a system of two conjugated immiscible liquid layers with disparate thicknesses is investigated. The top layer is relatively thick and undergoes short-wavelength instabilities, while the bottom layer is thin and undergoes long-wavelength instabilities. The two layers are coupled by the kinematic and dynamic relations at the interface. Through linear stability analysis, a lubrication effect, which significantly reduces the destabilization threshold, is identified. Especially when the vibration frequency is low, the lubrication effect is seen to influence the transition between the harmonic and subharmonic instability modes. It is studied how far the system with two layers can be approximated by a single-layer system with a Navier-slip boundary condition at the bottom. In corresponding experiments it is found that the time-periodic excitation of the system creates a steady-state deformation of the bottom layer. This indicates nonlinear dynamics of the system and the violation of reversibility. The excellent agreement between experimental and theoretical results for the onset of the instability underpins the validity of the linear stability analysis.

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