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

Hu, Jun and Ben Hadid, Hamda and Henry, Daniel and Mojtabi, Abdelkader Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate. (2008) Journal of Fluid Mechanics, vol. 599. pp. 269-298. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/s0022112007000110

Abstract

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, X, M, B), as well as the inclination angle (beta) 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 (chi >= 0), and oscillatory for chi < 0. Moreover, the P-mode which is short-wave unstable for chi = 0 remains so for chi < 0, but becomes long-wave unstable for chi > 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.

Item Type:Article
Additional Information:Thanks to Cambridge University Press editor. The definitive version is available athttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1804848
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Chinese Academy of Sciences (CHINA)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Other partners > Institut National des Sciences Appliquées de Lyon - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Ecole Centrale de Lyon (FRANCE)
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Deposited By: abdelkader mojtabi
Deposited On:03 Apr 2014 13:14

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