Study of the dynamics of thin liquid films sheared by gas flows
Résumé
We investigate the long-wave instability of a thin liquid film sheared by a concurrent gas flow. The film flows down an inclined plane and is driven by a constant shear stress and a pressure gradient. The height of the film is small compared to the wavelength, which justifies a long-wave approach. We adopt this procedure to approximate the Saint-Venant (or shallow water) equations. A linear stability analysis is thus developed and the limit between stable and unstable conditions is analyzed in terms of a critical Reynolds number. It comes out that the constant shear stress, applied at the free surface of the film, tends to stabilize the liquid layer to long waves. This is true when the mass flow of the film is kept unaltered. On the other side, the role of the pressure gradient is the same as the longitudinal component of gravity, which is known to be a destabilizing factor for the liquid film.
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