Simplified modeling of slide-fed curtain coating flow

Hyun Wook Jung; Joo Sung Lee; Jae Chun Hyun; See Jo Kim; L. E. Scriven

Korea-Australia Rheology Journal, Vol.16, No.4, 227-233, December, 2004

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Simplified modeling of slide-fed curtain coating flow

Hyun Wook Jung^†, Joo Sung Lee, Jae Chun Hyun , See Jo Kim¹, and L. E. Scriven²

Department of Chemical and Biological Engineering, Korea University, Seoul 136-701, Korea
¹Department of Mechanical Engineering, Andong National University, Andong 760-749, Korea
²Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA

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Simplified model of slide-fed curtain coating flow has been developed and tested in this study. It rests on the sheet profile equations for curtain thickness in curtain flow and its trajectory derived by the integral momentum balance approach of Higgins and Scriven (1979) and Kistler (1983). It also draws on the film profile equation of film thickness variation in flow down a slide. The equations have been solved in finite difference approximation by Newton iteration with continuation. The results show that how inertia (Reynolds number), surface tension (capillary number), inclination angle of the slide, and air pressure difference across the curtain affect sheet trajectory and thickness profile. It has been revealed that approximate models can be useful to easily analyze coating flow dynamics without complex computations, giving qualitative agreement with full theory and with experiment.

Keywords:curtain coating;slide flow;curtain flow;sheet profile equation;curtain trajectory;integral momentum balance;simplified modeling

[References]

Brown DR, J. Fluid Mech., 10, 297 (1961)
Clarke NS, J. Fluid Mech., 31, 481 (1968)
Cohen D, Two-Layer Slot Coating: Flow Visualization and Modeling, M.S. Thesis, University of Minnesota. (1993)
Coyle DJ, The Fluid Mechanics of Roll Coating, Ph.D. Thesis, University of Minnesota. (1984)
Finnicum DS, Weinstein SJ, Ruschak KJ, J. Fluid Mech., 255, 647 (1993)
Higgins BG, Scriven LE, Ind. Eng. Chem. Fundam., 18, 208 (1979)
Jung HW, Choi SM, Hyun JC, AIChE J., 45(5), 1157 (1999)
Jung HW, Scriven LE, Stability and frequency response of the simplified curtain flow, In preparation. (2004)
Katagiri Y, Comparative study of unsteady behavior in slide and curtain coating, The AIChE Spring National Meeting. Orlando, FL. (1992)
Kistler SF, The Fluid Mechanics of Curtain Coating and Related Viscous Free Surface Flows with Contact Lines, Ph.D. Thesis, University of Minnesota. (1983)
Lee JS, Jung HW, Hyun JC, Korea-Aust. Rheol. J., 15(2), 91 (2003)
Lin SP, J. Fluid Mech., 104, 111 (1981)
Miyamoto K, Katagiri Y, Ch. 11c. Curtain Coating, Liquid Film Coating, Edited by S.F. Kistler and P.M. Schweizer, Chapman & Hall, Cambridge. (1997)
Nagashima K, Slide Coating Flow: Splice Passage, M.S. Thesis, University of Minnesota. (1993)
Ogawa S, Scriven LE, Analysis of curtain coating flow, The AIChE Spring National Meeting, Orlando, FL. (1990)
Oki K, Scriven LE, Stability of multilayer curtain coating flow, The 11th International Coating Science and Technology Symposium, Minneapolis, MN. (2002)
Weinstein SJ, Clarke A, Simister EA, Phys. Fluids, 9, 3625 (1997)
Yeow YL, J. Fluid Mech., 66, 613 (1974)

[Referenced By]

[Related Articles]

[1] Brown DR, J. Fluid Mech., 10, 297 (1961)

[2] Clarke NS, J. Fluid Mech., 31, 481 (1968)

[3] Cohen D, Two-Layer Slot Coating: Flow Visualization and Modeling, M.S. Thesis, University of Minnesota. (1993)

[4] Coyle DJ, The Fluid Mechanics of Roll Coating, Ph.D. Thesis, University of Minnesota. (1984)

[5] Finnicum DS, Weinstein SJ, Ruschak KJ, J. Fluid Mech., 255, 647 (1993)

[6] Higgins BG, Scriven LE, Ind. Eng. Chem. Fundam., 18, 208 (1979)

[7] Jung HW, Choi SM, Hyun JC, AIChE J., 45(5), 1157 (1999)

[8] Jung HW, Scriven LE, Stability and frequency response of the simplified curtain flow, In preparation. (2004)

[9] Katagiri Y, Comparative study of unsteady behavior in slide and curtain coating, The AIChE Spring National Meeting. Orlando, FL. (1992)

[10] Kistler SF, The Fluid Mechanics of Curtain Coating and Related Viscous Free Surface Flows with Contact Lines, Ph.D. Thesis, University of Minnesota. (1983)

[11] Lee JS, Jung HW, Hyun JC, Korea-Aust. Rheol. J., 15(2), 91 (2003)

[12] Lin SP, J. Fluid Mech., 104, 111 (1981)

[13] Miyamoto K, Katagiri Y, Ch. 11c. Curtain Coating, Liquid Film Coating, Edited by S.F. Kistler and P.M. Schweizer, Chapman & Hall, Cambridge. (1997)

[14] Nagashima K, Slide Coating Flow: Splice Passage, M.S. Thesis, University of Minnesota. (1993)

[15] Ogawa S, Scriven LE, Analysis of curtain coating flow, The AIChE Spring National Meeting, Orlando, FL. (1990)

[16] Oki K, Scriven LE, Stability of multilayer curtain coating flow, The 11th International Coating Science and Technology Symposium, Minneapolis, MN. (2002)

[17] Weinstein SJ, Clarke A, Simister EA, Phys. Fluids, 9, 3625 (1997)

[18] Yeow YL, J. Fluid Mech., 66, 613 (1974)