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.

1.
Ahmadi
G.
,
1976
, “
Stability of a Micropolar Fluid Layer Heated from Below
,”
International Journal of Engineering Science
, Vol.
14
, pp.
81
89
.
2.
Benney
D. J.
,
1966
, “
Long Waves on Liquid Films
,”
Journal of Mathematics and Physics
, Vol.
45
, pp.
150
155
.
3.
Chang
H. C.
,
1994
, “
Wave Evolution on a Falling Film
,”
Annual Review of Fluid Mechanics
, Vol.
26
, pp.
103
136
.
4.
Datta
A. B.
, and
Sastry
V. U. K.
,
1976
, “
Thermal Instability of a Horizontal Layer of Micropolar Fluid Heated from Below
,”
International Journal of Engineering Science
, Vol.
14
, pp.
631
637
.
5.
Eringen
A. C.
,
1964
, “
Simple Microfluids
,”
International Journal of Engineering Science
, Vol.
2
, pp.
205
217
.
6.
Eringen
A. C.
,
1967
, “
Theory of Micropolar Fluids
,”
Journal of Mathematics & Mechanics
, Vol.
16
, pp.
1
18
.
7.
Eringen
A. C.
,
1980
, “
Theory of Anisotropic Micropolar Fluids
,”
International Journal of Engineering Science
, Vol.
18
, pp.
5
17
.
8.
Franchi
F.
, and
Straughan
B.
,
1992
, “
Nonlinear Stability for Thermal Convection in a Micropolar Fluid with Temperature Dependent Viscosity
,”
International Journal of Engineering Science
, Vol.
30
, pp.
1349
1360
.
9.
Hwang
C. C.
, and
Weng
C. L.
,
1987
, “
Finite-Amplitude Stability Analysis of Liquid Films Down a Vertical Wall with and without Interfacial Phase Change
,”
International Journal of Multiphase Flow
, Vol.
13
, pp.
803
814
.
10.
Kolpashchikov
V. L.
,
Migun
N. P.
, and
Prokhorenko
P. P.
,
1983
, “
Experimental Determination of Material Micropolar Fluid Constants
,”
International Journal of Engineering Science
, Vol.
21
, pp.
405
411
.
11.
Krishna
M. V. G.
, and
Lin
S. P.
,
1977
, “
Nonlinear Stability of a Viscous Film with Respect to Three-Dimensional Side-Band Disturbances
,”
The Physics of Fluids
, Vol.
20
, pp.
1039
1044
.
12.
Lin
S. P.
,
1974
, “
Finite Amplitude Side-Band Stability of a Viscous Film
,”
Journal of Fluid Mechanics
, Vol.
63
, pp.
417
429
.
13.
Liu
C. Y.
,
1970
, “
On Turbulent Flow of Micropolar Fluids
,”
International Journal of Engineering Science
, Vol.
8
, pp.
457
466
.
14.
Liu
C. Y.
,
1971
, “
Initiation of Instability in Micropolar Fluids
,”
The Physics of Fluids
, Vol.
14
, pp.
1808
1809
.
15.
Payne
L. E.
, and
Straughan
B.
,
1989
, “
Critical Rayleigh Numbers for Oscillatory and Nonlinear Convection in an Isotropic Thermomicropolar Fluid
,”
International Journal of Engineering Science
, Vol.
27
, pp.
827
836
.
16.
Stokes, V. K., 1984, Theories of Fluids with Microstructures—An Introduction, Chapter 6, Springer-Verlag, Berlin.
17.
Tsai, J. S., Hung, C. I., and Chen, C. K., 1996, “Nonlinear Hydromagnetic Stability Analysis of Condensation Film Flow Down a Vertical Plate,” Acta Mechanica, to appear.
18.
Yih, C. S., 1954, “Stability of Parallel Laminar Flow with a Free Surface,” Proceedings of the 2nd U.S. National Congress of Applied Mechanics, pp. 623–628.
This content is only available via PDF.
You do not currently have access to this content.