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Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems

Published online by Cambridge University Press:  26 April 2006

Yuan C. Severtson  and
Cyrus K. Aidun
Yuan C. Severtson
Affiliation:
Institute of Paper Science and Technology and The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street, N.W. Atlanta, GA 30318-5794, USA
Cyrus K. Aidun
Affiliation:
Institute of Paper Science and Technology and The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street, N.W. Atlanta, GA 30318-5794, USA
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Abstract

To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. Only one mode of instability, the interfacial mode, is obtained in the long-wave asymptotic limit. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer Orr-Sommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. Results from the stability analysis of the flow near the contact line where air entrainment occurs are consistent with previous experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 173 - 200
Copyright
© 1996 Cambridge University Press

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References

Aidun, C. K. & Severtson, Y. C. 1996 A new mode in two-layer stratified flow in inclined channels. In preparation.
Aidun, C. K., Veverka, P. J. & Scriven, L. E. 1991 Onset of air entrainment: Mechanism. AIChE Annual Meeting, Paper No.11b.
Aidun, C. K., Veverka, P. J. & Scriven, L. E. 1992 Interfacial instability and excessive air entrainment. AIChE Spring National Meeting, Paper No.49A.
Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554.Google Scholar
Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Nature 282, 489.Google Scholar
Deryagin, B. M. & Levi, S. M. 1959 Film Coating Theory. Focal Press, London.
Doedel, E. & Kerneves, J. P. 1986 Auto: Software for continuation and bifurcation problems in ordinary differential equations.
Gottlieb, D. Orszag, S. A. 1977 Numerical Analysis of Spectral Methods SIAM.
Hooper, A. P. 1989 The stability of two superposed viscous fluids in a channel. Phys. Fluids A 1, 1133.Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507.Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1987 Shear-Flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. 179, 201.Google Scholar
Kistler, S. F. 1984 The fluid mechanics of curtain coating and related viscous free surface flows with contact lines. PhD dissertation, University of Minnesota.
Lezzi, A. M. & Prosperetti, A. 1991 The stability of an air film in a liquid flow. J. Fluid Mech. 226, 319.Google Scholar
Loewenherz, D. S. & Lawrence, C. J. 1989 The effect of viscosity stratification on the stability of a free surface flow at low Reynolds number. Phys. Fluids A 1, 1686.Google Scholar
Miyamoto, K. 1991 On the mechanism of air entrainment. Indust. Coating Res. 1, 71.Google Scholar
Miyamoto, K. & Scriven, L. E. 1982 Breakdown of air film entrained by liquid coated on web. AIChE Annual Meeting, Los Angeles, CA.
Renardy, Y. Y. 1985 Instability at the interface between two shearing fluids in a channel. Phys. Fluids 28, 3341.Google Scholar
Renardy, Y. Y. 1987 The thin-layer effect and interfacial stability in a two-layer Couette flow with similar liquids. Phys. Fluids 30, 1627.Google Scholar
Reynolds, W. C. & Potter, M. C. 1967 Finite-amplitude instability of parallel shear flows. J. Fluid Mech. 27, 465.Google Scholar
Scriven, L. E. 1982 How does air entrain at wetting lines. AIChE Spring National Meeting, Orlando, FL.
Severtson, Y. C. 1996 Stability analysis of thin film coating systems. PhD dissertation, Georgia Institute of Technology.
Smith, M. K. 1990 The mechanism for the long-wave instability in thin liquid films. J. Fluid Mech. 217, 469.Google Scholar
Tilley, B. S., Davis, S. H. & Bankoff, S. G. 1994 Linear stability theory of two-layer fluid flow in an inclined channel. Phys. Fluids 6, 3906.Google Scholar
Veverka, P. J. & Aidun, C. K. 1991 Air entrainment and dynamic contact line instability in low speed roll coating. Tappi J. 74(9), 203.Google Scholar
Yiantsios, S. G. & Higgins, B. G. 1988 Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids 31, 3225.Google Scholar
Yih, C. S. 1963 Stability of liquid flow down an inclined plane. J. Fluid Mech. 6, 321.Google Scholar
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337.Google Scholar