Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-19T21:57:19.534Z Has data issue: false hasContentIssue false

The flow and stability of thin liquid films on a rotating disk

Published online by Cambridge University Press:  29 March 2006

A. F. Charwat
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles
R. E. Kelly
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles
C. Gazley
Affiliation:
The RAND Corporation, Santa Monica, California

Abstract

Measurements of the thickness and the stability of thin films of liquid (1–150 μmthick) formed on a rotating horizontal disk are presented and correlated in terms of an asymptotic-expansion solution of the thin-film equations. Water, various alcohols and water with wetting activities were used to cover a range of viscosity (1-2.5cP) and surface tension (20-72 dynes/cm). Smooth flow was found to occur in a region defined by the flow rate, rotational speed and physical properties of the liquid. Outside this region various wave patterns were observed (concentric, spiral and irregular waves). A linear theory of the stability of the film based on an extension of classical stability theories for plane films on inclined planes is given and contrasted with the experimental results. Surface phenomena associated with the use of wetting agents were found to have a strong effect on the stability of the film.

Type
Research Article
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aroesty, J., Gross, J. F., Illickal, M. M. & Maloney, J. V. 1967 Blood oxygenation: a study in bioengineering Mass transfer. Digest Seventh Int. Conf. on Medical and Biological Engineering, Stockholm, p. 527. (See also, 1967 Rand Corporation, Rep.P-8732.)Google Scholar
Benjamin, T. B. 1957 Wave formation in lamina flow down an inclined plane. J. Fluid Mech. 2, 554574.Google Scholar
Benjamin, T. B. 1964 Effects of surface contamination on wave formation in falling liquid films. Arch. Mech. Stos., 16, 615626.Google Scholar
Binnie, A. M. 1957 Experiments on the onset of wave formation on a film of water flowing down an inclined plane. J. Fluid Mech., 2, 551553.Google Scholar
Bromley, L. A. 1965 Saline water conservation research. Water Resources Center, University of Calqornia, San Diego Contribution, no. 100, 2430.
Cearwat, A. F., Kelly, R. E., Gazley, C. & Campfield, L. A. 1970 The development and the stability of thin liquid films on a rotating disk. U.C.L.A. Tech. Rep. ENG-7047.Google Scholar
Cralk, A. D. D. 1966 Wind-generated waves in thin liquid films. J. Fluid Mech., 26, 369392Google Scholar
Dorfman, L. A. 1967 Heat transfer and viscous liquid flow on a rotating disk. J. Engng. Phys. 12, 309316Google Scholar
Esplg, H. & Hoyle, R. 1965 Waves in a thin liquid layer on a rotating disk. J. Fluid Mech 22, 671677Google Scholar
Fulford, G. D. 1964 The flow of liquids in thin flims. Advances in Chem. Eng. 5, 151263.Google Scholar
Gazley, C. & Charwat, A. F. 1968 The characteristics of thin liquid 61ms on a spinning disk. Proc. Third All-Union Conference on Heat and Mass Transfer, Minsk. (See also, 1968 Rand Corporation. Rep. P-3851.)Google Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. Roy. Soc. A 248, 155199.Google Scholar
Lilly, D. K. 1966 On the instability of Ekman boundary flow. J. Atmos. Sci. 23, 481494.Google Scholar
Rauscher, J. W. 1969 Stability of a liquid film on a spinning disk. U.G.L.A. School of Engineering and Applied Science Rep. no. 69–44. (See also 1969 M.S. thesis, U.C.L.A.)Google Scholar
Rauscher, J. W., Kelly, R. E. & Cole, J. D. 1972 An a aymptotic solution for laminar flow of a thin film on rotating disk. J. Appl. Mech. (to be published).Google Scholar
Scelichting, H. 1960 Boundary Layer Theory, 4th edn. MoGraw-Hill.
Tailby, S. R. & Portalski, S. 1962 The determination of the wavelength on a vertioal film of liquid flowing down a hydrodynamically smooth plate. Trans. Inst. Chem. Eng., 40, 114121.Google Scholar
Weitaker, S. 1964 Effect of surface active agents on the stability of falling liquid films. Indust. & Engng. Chem. Fund., 3, 132142.Google Scholar
Yih, C.-S. 1960 Instability of a rotating fdm with a free surface. Proc. Roy. SOC. A 258, 6381Google Scholar
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids, 6, 321334.Google Scholar
Yih, C.-S. 1966 Dynamics of Nonhomogeneous Fluids. Macmillan.