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The linear stability problem of a n-layered liquid film with a solidified liquid-air interface is reviewed. The general formulation is applied to the special case of a two-layered film flow down an inclined plane. A stability condition is given explicitly in terms of the density, viscosity and thickness ratios. Based on this condition it is found that solidification of the free surface may have the effects of stabilizing the interfacial shear waves and destabilizing the gravity-capillary waves associated with top-heavy density stratification.
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S. P. Lin (1983) studied this question.
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