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Rivulet Instability with Effect of Coriolis Force

Published online by Cambridge University Press:  05 May 2011

H.-C. Cho*
Affiliation:
Department of Mechanical Engineering, National Central University, Jhong-li, Taiwan 32001, R.O.C.
F.-C. Chou*
Affiliation:
Department of Mechanical Engineering, National Central University, Jhong-li, Taiwan 32001, R.O.C.
*
*Graduate student
**Professor
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Abstract

The effect of Coriolis force on the rivulet (fingering) instability, the onset of rivulet phenomena during spin coating, is investigated by flow visualization experiments incorporating with dimensional analysis. This study demonstrates that the Coriolis force will affect significantly the critical radius of rivulet instability and the deflection angle of instability rivulet. For the cases of low Bond number, the effect of Coriolis force is a stabilizing factor, and the dimensionless critical radius increases slightly with increasing rotational Reynolds number Reω. In the case of high Bond number, the effect of Coriolis force becomes a destabilizing factor while Reω < 1, and a characteristic length is found by balancing the viscous force with the surface tension. For Reω > 1, the radial Corilois force, which is always pointing inward, plays a stabilizing role with magnitude Reω2.

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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References

1.Emslie, A. G., Bonner, F. T. and Peck, L. G., “Flow of a Viscous Liquid on a Rotating Disk,” J. Appl. Phys., 29, pp. 858862 (1958).CrossRefGoogle Scholar
2.Acrivos, A., Shan, M. and Petersen, E. E., “On the Flow of a Non-Newtonian Liquid on a Rotating Disk,” J. Appl. Phys., 31, pp. 963968 (1960).CrossRefGoogle Scholar
3.Jenekhe, S. A. and Schuldt, S. B., “Coating Flow of Non-Newtonian Fluids on a Flat Rotating Disk,” Ind. Eng. Chem. Fundam., 23, pp. 432436 (1984).CrossRefGoogle Scholar
4.Middleman, S., “The Effect of Induced Air-Flow on the Spin Coating of Viscous Liquids,” J. Appl. Phys., 62, pp. 25302532 (1987).CrossRefGoogle Scholar
5.Ma, F. and Hwang, J. H., “The Effect of Air Shear on the Flow of a Thin Liquid Film Over a Rough Rotating Disk,” J. Appl. Phys., 68, pp. 1261271 (1990).CrossRefGoogle Scholar
6.Jenekhe, S. A., “Effects of Solvent Mass Transfer on Flow of Polymer Solutions on a Flat Rotating Disk,” Ind. Eng. Chem. Fundam., 23, pp. 425432 (1984).CrossRefGoogle Scholar
7.Faller, A. J., “An Experimental Study of the Instability of the Laminar Ekman Boundary Layer,” J. FluidMech., 15, pp. 560576 (1963).CrossRefGoogle Scholar
8.Caldwell, D. R. and Van Atta, C. W., “Characteristics of Ekman Boundary Layer Instabilities,” J. Fluid Mech., 44, pp. 7995 (1970).CrossRefGoogle Scholar
9.Caldwell, D. R., Van Atta, C. W. and Helland, K. N., “A Laboratory Study of the Turbulent Ekman Layer,” Geophys. Fluid Dynamics., 3, pp. 125160 (1972).CrossRefGoogle Scholar
10.Momoniat, E. and Mason, D. P., “Investigation of the Effect of the Coriolis Force on a Thin Fluid Film on a Rotating Disk,” Int. J. Non-Linear Mechanics, 33, pp. 10691088 (1998).CrossRefGoogle Scholar
11.Myers, T. G. and Charpin, J. P. F., “The Effect of the Coriolis Force on a Axisymmetric Rotating Thin Film Flows,” Int. J. Non-Linear Mechanics, 36, pp. 629635 (2001).CrossRefGoogle Scholar
12.Melo, F., Joanny, J. F. and Fauve, S., “Fingering Instability of Spinning Drops,” Phys. Rev. Lett., 63, pp. 19581961 (1989)CrossRefGoogle Scholar
13.Fraysse, N. and Homsy, G. M., “An Experimental Study of Rivulet Instabilities in Centrifugal Spin Coating of Viscous Newtonian and Non-Newtonian Fluids,” Phys. Fluids, 6, pp. 14911504 (1994).CrossRefGoogle Scholar
14.Spaid, M. A. and Homsy, G. M., “Stability of Viscoelastic Dynamic Contact Lines: An Experimental Study,” Phys. Fluids, 9, pp. 823832 (1997).CrossRefGoogle Scholar
15.Wang, M. W. and Chou, F. C., “Fingering Instability and Maximum Radius at High Rotational Bond Number,” J. Electrochem. Soc., 148, G283–G290 (2001).CrossRefGoogle Scholar
16.Cho, H. C., Chou, F. C., Wang, M. W. and Tsai, C. S., “Rivulet Instability with Effect of Coriolis Force,” Jpn. J. Appl. Phys., 44, L606–L609 (2005).CrossRefGoogle Scholar
17.Wilson, S. K., Hunt, R. and Duffy, B. R., “The Rate of Spreading in Spin Coating,” J. Fluid Mech., 413, pp. 6588 (2000).CrossRefGoogle Scholar
18.Schwartz, L. W. and Roy, R. V., “Theoretical and Numerical Results for Spin Coating of Viscous Liquids,” Phys. Fluids, 16, pp. 569584 (2004).CrossRefGoogle Scholar
19.Brun, K. and Kurz, R., “Analysis of Secondary Flows in Centrifugal Impellers,” Int. J. Rotating Machinery, 1, pp. 4552 (2005).CrossRefGoogle Scholar
20.Naletova, V. A., Kim, L. G. and Turkov, V. A., “Hydrodynamics of a Horizontally Rotating Thin Magnetizable Liquid Film,” J. Magnetism & Magnetic Materials, 149, pp. 162164 (1995).CrossRefGoogle Scholar
21.Troian, S. M., Herbolzheimer, E., Safran, S. A. and Joanny, J. F., “Fingering Instabilities of Driven Spreading Films,” Europhys. Lett., 10, pp. 2530 (1989).CrossRefGoogle Scholar