LINEAR-STABILITY OF POWER-LAW LIQUID-FILM FLOWS DOWN AN INCLINED PLANE

The linear stability of power law liquid film flows down an inclined plane is investigated. The integral method is used to derive nonlinear evolution equations for film thickness and local flow rate. After linearizing the nonlinear evolution equations, the method of normal mode is applied to study its linear stability. The results reveal that, in the case of fixing the value of power law exponent n, the stability characteristics in terms of generalized Reynolds number Re-n and generalized Weber number We(n) are the same as those of Newtonian liquids, i.e. to increase the Reynolds number, or to decrease the Weber number will destabilize the film flow system. Furthermore, decreasing only the magnitude of n will cause more unstable film flow, and make the dimensional wave speed faster.