Finite amplitude long-wave instability of power-law liquid films

This paper investigates the non-linear long-wave stability of power-law liquid films flow down an inclined plane. The method of long-wave theory is first used to derive a non-linear evolution equation of film thickness. After linearizing the non-linear evolution equation, the method of normal mode is applied to study its linear stability. Then the method of perturbation with multiple scales is used to solve this non-linear equation. The results reveal that the system will be more unstable when power-law exponent n decreases. Near the neutral stable state, the subcritical instability and explosive solution are possible at small n, and the supercritical and unconditional stable region exist only when n exceeds a certain value. Also, decreasing the magnitude of n will increase the dimensional wave speed of the unstable mode. (C) 2000 Elsevier Science Ltd. All rights reserved.