Long-wave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect: Linear theory

2005 ◽  
Vol 17 (10) ◽  
pp. 104104 ◽  
Author(s):  
A. Podolny ◽  
A. Oron ◽  
A. A. Nepomnyashchy
Keyword(s):  
Linear Theory ◽  
Liquid Layer ◽  
Soret Effect ◽  
Marangoni Instability ◽  
Binary Liquid ◽  
Long Wave ◽  
Deformable Interface

scholarly journals Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

2008 ◽  
Vol 599 ◽  
pp. 269-298 ◽  
Author(s):  
JUN HU ◽  
HAMDA BEN HADID ◽  
DANIEL HENRY ◽  
ABDELKADER MOJTABI
Keyword(s):  
Soret Effect ◽  
Short Wave ◽  
Heated Plate ◽  
Surface Mode ◽  
Wave Instability ◽  
Binary Liquid ◽  
Long Wave ◽  
Neutral Curves ◽  
Spatio Temporal ◽  
Boundary Curves

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka,G,Pr,L, χ,M,B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ≥0), and oscillatory for χ<0. Moreover, the P-mode which is short-wave unstable for χ=0 remains so for χ<0, but becomes long-wave unstable for χ>0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

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