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.

Nonlinear Stability Analysis of Thin Viscoelastic Film Flowing Down on the Inner Surface of a Rotating Vertical Cylinder

“…The flow conditions of the thin film can be obtained by inserting above expressions into Equations (21)- (25) and then solving systematically the resulting equations. In practice, the nondimensional surface tension S is a large value; the term α 2 S can be treated as a quantity of zeroth order [18,26].…”

“…where h * 0 is the constant film thickness of local base flow and u * 0 the reference velocity which can be expressed as [25] …”

Nonlinear stability analysis of thin condensate falling film inside a rotating vertical cylinder

“…(14)- (20) and then solving systematically the resulting equations. In practical application, the non-dimensional surface tension S is a large value and the term a 2 S is taken to be of order one [9,10,14,15]. Further, in the analysis, Re ' O(1) and…”

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

“…These properties are of primary importance for the design of process devices, and it is therefore desirable to have a better understanding of these mechanisms that occur under various conditions and to develop a theoretical behavior that allows nonlinear effects. Apart from a detailed analysis by Chang [22], Chang et al [23], and Cheng and Chang [24] on the nonlinear stability of falling films, there have been many investigations on the weakly nonlinear stability analysis of the falling film flow system (down an inclined/vertical wall or on the surface of the cylinder) which include the investigations by Usha and Uma [25], Uma and Usha [26], Chen et al [27], Lai et al [28], Ünsal and Thomas [29] and Hung et al [30]. These investigations have examined the growth of an initially unstable periodic surface perturbation and its nonlinear interaction with the higher harmonics.…”

“…Using perturbation methods, Ünsal and Thomas [29] have investigated the nonlinear stability of vertical condensate film flow. Hung et al [30] have investigated analytically the nonlinear stability of thin micropolar liquid film flowing down a vertical plane. The weakly nonlinear stability analysis of the generalised kinematic equation for the film thickness shows that both the supercritical stability and the subcritical instability exist in the micropolar film flow system.…”