No CrossRef data available.
Article contents
Ribbing Instability Analysis of Forward Roll Coating
Published online by Cambridge University Press: 05 May 2011
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.
- Type
- Articles
- Information
- Copyright
- Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009
References
1.Pearson, J. R. A., “The Instability of Uniform Viscous Flow under Rollers and Spreaders,” J. Fluid Mechanics, 7, pp. 481–500 (1959).CrossRefGoogle Scholar
2.Yih, C. S., “Instability of a Rotating Liquid Film with a Free Surface,” Proc. Roy. Soc. Section A., 258, pp. 63–89 (1960).Google Scholar
3.Pitts, E. and Greiller, J., “The Flow of Thin Liquid Films Between Rollers,” J. Fluid Mechanics, 11, pp. 33–50 (1961).Google Scholar
4.Mill, C. C. and South, G. R., “Formation of Ribs on Rotating Rollers,” J. Fluid Mechanics, 28, pp. 523–529 (1967).Google Scholar
5.Savage, M. D., “Mathematical Model for the Onset of Ribbing,” AIChE J., 30, pp. 999–1002 (1984).CrossRefGoogle Scholar
6.Coyle, D. J., “The Fluid Mechanics of Roll Coating: Steady Flows, Stability and Rheology,” Ph.D. Dissertation, University of Minnesota, Minneapolis, MN. (1984).Google Scholar
7.Coyle, D. J., Macosko, C. W. and Scriven, L. E., “Film-Splitting Flows in Forward Roll Coating,” J. Fluid Mechanics, 171, pp. 183–207 (1986).CrossRefGoogle Scholar
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. 741–746 (1987).CrossRefGoogle Scholar
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. 437–458 (1990).CrossRefGoogle Scholar
10.Coyle, D. J., “Forward Roll Coating with Deformable Rolls: A Simple One-Dimensional Elastohydrodynamic Model,” Chem. Eng. Sci., 43, pp. 2673–2684 (1988).Google Scholar
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. 534–562 (1999).CrossRefGoogle Scholar
12.Benkreira, H., Edward, M. F. and Wilkinson, W. L., “Roll Coating of Viscous Liquids,” Chem. Eng. Sci., 36, pp. 429–434 (1981).Google Scholar
13.Baumann, T., Sullivan, T. and Middleman, S., “Ribbing Instability in Coating Flows: Effect of Polymer Additives,” Chem. Eng. Commun., 14, pp. 35–46 (1982).CrossRefGoogle Scholar
14.Pulkrabek, W. W. and Munter, J. D., “Knurl Roll Design for Stable Rotogravure Coating,” Chem. Eng. Sci., 38, pp. 1309–1314 (1983).CrossRefGoogle Scholar
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. 123–139 (2002).CrossRefGoogle Scholar
16.Hirt, C. W. and Nichols, B. D., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Computational Physics, 39, pp. 201–225 (1981).CrossRefGoogle Scholar