Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate - Archive ouverte HAL Access content directly
Journal Articles Journal of Fluid Mechanics Year : 2008

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

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, 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.
Fichier principal
Vignette du fichier
JFMHu2008.pdf (285.21 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-00439755 , version 1 (09-12-2009)

Identifiers

Cite

Jun Hu, Hamda Ben Hadid, Daniel Henry, Abdelkader Mojtabi. Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate. Journal of Fluid Mechanics, 2008, 599, pp.269-298. ⟨10.1017/S0022112007000110⟩. ⟨hal-00439755⟩
153 View
211 Download

Altmetric

Share

Gmail Facebook X LinkedIn More