Nonlinear Stability of the Thin Micropolar Liquid Film Flowing Down on a Vertical Plate

Abstract

A perturbation method is used to investigate analytically the nonlinear stability behavior of a thin micropolar liquid film flowing down a vertical plate. In this analysis, the conservation of mass, momentum, and angular momentum are considered and a corresponding nonlinear generalized kinematic equation for the film thickness is thereby derived. Results show that both the supercritical stability and the subcritical instability can be found in the micropolar film flow system. This analysis shows that the effect of the micropolar parameter R (=κ/μ) is to stabilize the film flow, that is, the stability of the flowing film increases with the increasing magnitude of the micropolar parameter R. Also, the present analysis shows that the micropolar coefficients, Δ (=h02/j) and Λ (=γ/μj), have very little effects on the stability of the micro-polar film.