Nonlinear dynamics of long-wave Marangoni convection in a binary mixture with the Soret effect

2013 ◽  
Vol 25 (5) ◽  
pp. 052107 ◽  
Author(s):  
M. Morozov ◽  
A. Oron ◽  
A. A. Nepomnyashchy
Keyword(s):  
Nonlinear Dynamics ◽  
Binary Mixture ◽  
Marangoni Convection ◽  
Soret Effect ◽  
Long Wave

Influence of low-frequency vibration on thermocapillary instability in a binary mixture with the Soret effect: long-wave versus short-wave perturbations

2013 ◽  
Vol 714 ◽  
pp. 190-212 ◽  
Author(s):  
Irina S. Fayzrakhmanova ◽  
Sergey Shklyaev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Binary Mixture ◽  
Soret Effect ◽  
Low Frequency ◽  
Short Wave ◽  
Pure Liquid ◽  
Long Wave ◽  
Empirical Criterion ◽  
Low Frequency Vibration ◽  
Thermocapillary Instability ◽  
Limiting Case

AbstractWe study the influence of low-frequency vibration on Marangoni instability in a layer of a binary mixture with the Soret effect. A linear stability analysis is performed numerically for perturbations of a finite wavelength (short-wave perturbations). Competition between long-wave and short-wave modes is found: the former ones are critical at smaller absolute values of the Soret number $\chi $, whereas the latter ones lead to instability at higher $\vert \chi \vert $. In both cases the vibration destabilizes the layer. Two variants of calculations are performed: via Floquet theory (linear asymptotic stability) and taking noise into consideration (empirical criterion). It is found that fluctuations substantially reduce the domains of stability. Further, while studying a limiting case within the empirical criterion, we have found a short-wave instability mode overlooked in former investigations of coupled Rayleigh–Marangoni convection in a layer of pure liquid.

On the vibrational convective instability of a horizontal, binary-mixture layer with Soret effect

1997 ◽  
Vol 330 ◽  
pp. 251-269 ◽  
Author(s):  
G. Z. GERSHUNI ◽  
A. K. KOLESNIKOV ◽  
J.-C. LEGROS ◽  
B. I. MYZNIKOVA
Keyword(s):  
Binary Mixture ◽  
High Frequency ◽  
Soret Effect ◽  
Normal Modes ◽  
Quasi Equilibrium ◽  
Regular Perturbation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Mean Fields ◽  
Parameter Values

A theoretical examination is made of the mechanical quasi-equilibrium stability of a horizontal, binary-mixture layer with Soret effect in the presence of a high-frequency vibrational field. The boundaries of the layer are assumed to be rigid, isothermal and impermeable. The axis of vibration is longitudinal. The study is based on the system of equations describing the behaviour of mean fields. The conditions of quasi-equilibrium are formulated. A linear stability analysis for normal modes is carried out. In the limit of long-wave disturbances the regular perturbation method is used with the wavenumber as a small parameter. For the case of an arbitrary wavenumber, the calculations are made using straight forward numerical integration. The boundaries of stability and the critical disturbance characteristics are determined for representative parameter values. Different instability mechanism and forms are discussed.

Numerical Analysis of Ludwig-Soret Effect of One Binary Mixture and Two Ternary Mixtures in an Al2O3 Porous Cavity

2006 ◽  
Author(s):  
T. J. Jaber ◽  
M. Z. Saghir
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Numerical Analysis ◽  
Binary Mixture ◽  
Ternary Mixture ◽  
Soret Effect ◽  
Ternary Mixtures ◽  
Thermosolutal Convection ◽  
Left Wall ◽  
Porous Cavity

A cavity of 10 mm in width, 10 mm in height, and 32.1 mm in horizontal length filled with Al2O3 porous medium designed in Pau project to investigate thermal diffusion phenomena, or Ludwig-Soret effect. A lateral heating condition was applied with 10 °C at the left wall and 50 °C at the right wall. The thermosolutal convection of a binary mixture of water-ethanol at 75.0 MPa pressure, a ternary mixture with methane, n-butane, and n-dodecan at 35.0 MPa pressure, and a ternary mixture of n-dodecane, isobutylbenzene, and tetrahydonaphthalene at atmosphere pressure inside the Al2O3 porous medium cavity were numerically investigated. The thermal conductivity and the permeability of Al2O3 porous medium on the Ludwig-Soret effect were analyzed, the former had little influence, but the later had strong impact on the compositional separation at the steady state of thermosolutal convection, which were analyzed globally with separation ratio. The distributions of component mole fraction(s) on the horizontal and vertical lines in the center of the porous cavity were also shown to study the details of the compositional separation at the steady state of thermosolutal convection. Recommendations are made for the experimental design based on the results of numerical analysis

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