Skip to main content Accessibility help
×
Home

Ribbing Instability Analysis of Forward Roll Coating

  • K. N. Lie (a1), Y. M. Chiu (a2) and J. Y. Jang (a2)

Abstract

The ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.

Copyright

Corresponding author

*Associate Professor
**Graduate student
***Professor

References

Hide All
1.Pearson, J. R. A., “The Instability of Uniform Viscous Flow under Rollers and Spreaders,” J. Fluid Mechanics, 7, pp. 481500 (1959).
2.Yih, C. S., “Instability of a Rotating Liquid Film with a Free Surface,” Proc. Roy. Soc. Section A., 258, pp. 6389 (1960).
3.Pitts, E. and Greiller, J., “The Flow of Thin Liquid Films Between Rollers,” J. Fluid Mechanics, 11, pp. 3350 (1961).
4.Mill, C. C. and South, G. R., “Formation of Ribs on Rotating Rollers,” J. Fluid Mechanics, 28, pp. 523529 (1967).
5.Savage, M. D., “Mathematical Model for the Onset of Ribbing,” AIChE J., 30, pp. 9991002 (1984).
6.Coyle, D. J., “The Fluid Mechanics of Roll Coating: Steady Flows, Stability and Rheology,” Ph.D. Dissertation, University of Minnesota, Minneapolis, MN. (1984).
7.Coyle, D. J., Macosko, C. W. and Scriven, L. E., “Film-Splitting Flows in Forward Roll Coating,” J. Fluid Mechanics, 171, pp. 183207 (1986).
8.Coyle, D. J., Macosko, C. W. and Scriven, L. E., “Film-Splitting Flows of Shear-Thinning Liquids in Forward Roll Coating,” AIChE J., 33, pp. 741746 (1987).
9.Coyle, D. J., Macosko, C. W. and Scriven, L. E., “Stability of Symmetric Film-Splitting between Counter-Rotating Cylinders,” J. Fluid Mechanics, 216, pp. 437458 (1990).
10.Coyle, D. J., “Forward Roll Coating with Deformable Rolls: A Simple One-Dimensional Elastohydrodynamic Model,” Chem. Eng. Sci., 43, pp. 26732684 (1988).
11.Carvalho, M. S. and Scriven, L. E., “Three Dimensional Stability Analysis of Free Surface Flows: Application to Forward Deformable Roll Coating,” Journal of Computational Physics, 151, pp. 534562 (1999).
12.Benkreira, H., Edward, M. F. and Wilkinson, W. L., “Roll Coating of Viscous Liquids,” Chem. Eng. Sci., 36, pp. 429434 (1981).
13.Baumann, T., Sullivan, T. and Middleman, S., “Ribbing Instability in Coating Flows: Effect of Polymer Additives,” Chem. Eng. Commun., 14, pp. 3546 (1982).
14.Pulkrabek, W. W. and Munter, J. D., “Knurl Roll Design for Stable Rotogravure Coating,” Chem. Eng. Sci., 38, pp. 13091314 (1983).
15.Varela Lopez, F., Pauchard, L., Rosen, M. and Rabaud, M., “Non-Newtonian Effects on Ribbing Instability Threshold,” J. Non-Newtonian Fluid Mech., 103, pp. 123139 (2002).
16.Hirt, C. W. and Nichols, B. D., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Computational Physics, 39, pp. 201225 (1981).

Keywords

Ribbing Instability Analysis of Forward Roll Coating

  • K. N. Lie (a1), Y. M. Chiu (a2) and J. Y. Jang (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed