Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7174468 | International Journal of Non-Linear Mechanics | 2018 | 10 Pages |
Abstract
We investigated interfacial instability of a thin liquid film flowing down an inclined plane, considering the linear variation of fluid properties such as density, dynamical viscosity, surface tension and thermal diffusivity, for the small variation of temperature. Using long wave expansion method and considering order analysis specially for very small Biot number (Bi) we obtained a single surface equation in terms of the free surface h(x,t). Considering sinusoidal perturbation method we carried out linear stability analysis and obtained the critical Reynolds number (Rec) and linear phase speed (cr), both of which depend on Kμ,KÏ but independent of KÏ,Kκ. Using the method of multiple scales, weakly nonlinear stability analysis is carried out. We demarcated subcritical, supercritical, unconditional and explosive zones and their variations for the variation of Kμ,KÏ and KÏ. Also we discussed the variations of threshold amplitude in the subcritical as well as in the supercritical zones for the variation of Kμ,KÏ and KÏ. Finally we discussed the variation of nonlinear wave speed Ncr for the variation of Kμ,KÏ and KÏ.
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Authors
Anandamoy Mukhopadhyay, Souradip Chattopadhyay,