A theoretical analysis for the instability of a fluid film around a cylinder in an immiscible fluid is presented. A general dispersion equation, relating wave number to growth rate, is derived with consideration of the effects of the cylindrical interface and a finite film thickness. Application of the dispersion equation to the breakup of a liquid film around a cylindrical body in still air leads to a prediction of the dominant wavelength by λ=2π2/(1/R2+ρ1g/q)⁠, where R is the radius of the cylinder, ρ1 is the density of the liquid, g is the acceleration due to gravity, σ is the surface tension. Experiments showed good agreement with the present analysis. The dominant wavelength decreases with a decrease in the radius of the cylindrical body. A previous report on the breakup of a liquid film around a horizontal cylindrical body is shown to be in error.

Issue Section:
Technical Papers
Topics:
Fluids, Rayleigh-Taylor instability, Cylinders, Liquid films, Wavelength, Density, Errors, Film thickness, Fluid films, Gravitational acceleration, Surface tension, Theoretical analysis, Waves
1.
Bellman
R.
, and
Pennington
R. H.
,
1954
, “
Effects of Surface Tension and Viscosity on Taylor Instability
,”
Quart. Appl. Math.
, Vol.
12
, pp.
151
–
162
.
2.
Bland, D. R. 1965, Solutions of Laplace’s Equation, Routledge and Kegan Paul, London.
3.
Dhir
V. K.
, and
Lienhard
J. H.
,
1973
, “
Taylor Stability of Viscous Fluids with Application to Film Boiling
,”
Int. J. Heat Mass Transfer
, Vol.
16
, pp.
2097
–
2109
.
4.
Harrison
W. J.
,
1908
, “
The Influence of Viscosity on the Oscillations of Superposed Fluids
,”
Proc. London Math. Soc.
, Vol.
6
, pp.
396
–
405
.
5.
Lamb, H., 1932, Hydrodynamics, Cambridge, U.K., pp. 370–372.
6.
Lee
S. L.
,
1963
, “
Taylor Instability of a Liquid Film Around a Long, Horizontal, Circular Cylindrical Body in Still Air
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
30
, Vol. 85, pp.
443
–
447
.
7.
Lewis
D. J.
,
1951
, “
The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. II
,”
Proc. Roy. Soc., London
, Vol.
A202
, pp.
81
–
96
.
8.
Li
R.
, and
Harris
R.
,
1993
, “
On the Dominant Unstable Wavelength During Film Boiling on a Horizontal Cylinder
,”
ASME J. Heat Transfer
, Vol.
115
, No.
2
, pp.
498
–
501
.
9.
Lienhard
J. H.
, and
Wong
P. T. Y.
,
1964
, “
The Dominant Unstable Wavelength and Minimum Heat Flux During Film Boiling on a Horizontal Cylinder
,”
ASME J. Heat Transfer
, Vol.
88
, pp.
220
–
226
.
10.
Rayleigh, L., 1990, “Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density,” Scientific Papers, Vol. II, Cambridge University Press, Cambridge, U.K., pp. 200–207.
11.
Taylor
G.
,
1950
, “
The Stability of Fluid Surfaces when Accelerated in a Direction Perpendicular to their Planes. I
,”
Proc. Roy. Soc., London
, Vol.
A201
, pp.
192
–
196
.
12.
Tk-Solver, 1989, Universal Technical Systems, Rockford, IL.
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