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

This paper investigates the non-linear long-wave stability of power-law liq uid films flow down an inclined plane. The method of long-wave theory is fi rst used to derive a non-linear evolution equation of film thickness. After linearizing the non-linear evolution equation, the method of normal mode i s applied to study its linear stability. Then the method of perturbation wi th multiple scales is used to solve this non-linear equation. The results r eveal that the system will be more unstable when power-law exponent n decre ases. Near the neutral stable state, the subcritical instability and explos ive solution are possible at small n, and the supercritical and uncondition al stable region exist only when n exceeds a certain value. Also, decreasin g the magnitude of n will increase the dimensional wave speed of the unstab le mode. (C) 2000 Elsevier Science Ltd. All rights reserved.