NONLINEAR STABILITY OF THE THIN MICROPOLAR LIQUID-FILM FLOWING DOWN ON A VERTICAL PLATE

A perturbation method is used to investigate analytically the nonlinea r stability behavior of a thin micropolar liquid film flowing down a v ertical plate. In this analysis, the conservation of mass, momentum, a nd angular momentum are considered and a corresponding nonlinear gener alized kinematic equation for the film thickness is thereby derived. R esults show that both the supercritical stability and the subcritical instability can be found in the micropolar film flow system. This anal ysis shows that the effect of the micropolar parameter R (=kappa/mu) i s to stabilize the film flow, that is, the stability of the flowing fi lm increases with the increasing magnitude of the micropolar parameter R. Also, the present analysis shows that the micropolar coefficients, Delta (=h(0)(2)/j) and Lambda (=gamma/mu j), have very little effects on the stability of the micropolar film.