Skip to main content
SpringerLink
Log in

Analytical prediction of roll coating with counter-rotating deformable rolls

  • Published:
Journal of Coatings Technology and Research Aims and scope Submit manuscript

Abstract

Roll coating is a common technique for applying thin coating films on continuous substrates, e.g., papers and foils. Key advantages are the comparatively simple technology and the possibility of coating thin films using highly viscous fluids. Since roll coating is a self-metered process, the prediction of film thicknesses is of fundamental interest for industrial process control. In the present work, a new analytical approach for the prediction of the film thickness in roll coating with deformable rolls and negative gaps is developed. This method is based on the fluid dynamic theory of lubrication approximation. The film thickness is calculated depending on the geometry of the rolls (including the elasticity of the rubber), the fluid properties of the applied film and the roll velocities. This is gained by using boundary conditions for pressure and—in contrast to former literature—for force. The quality of the predicted results is validated with experimental data from literature. The comparison shows good agreement and thus the derived analytical model offers new possibilities for predicting film thickness and understanding of the associated influence parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Greener, J, Middleman, S, “Theoretical and Experimental Studies of the Fluid Dynamics of a Two-Roll Coater.” Ind. Eng. Chem. Fundam., 18 35–41 (1979)

    Article  Google Scholar 

  2. Savage, MD, “Mathematical Models for Coating Processes.” J. Fluid Mech., 117 443–455 (1982)

    Article  Google Scholar 

  3. Benkreira, H, Edwards, MF, Wilkinson, WL, “A Semi-empirical Model of the Forward Roll Coating Flow of Newtonian Fluids.” Chem. Eng. Sci., 36 423–427 (1981)

    Article  Google Scholar 

  4. Benkreira, H, Edwards, MF, Wilkinson, WL, “Roll Coating of Purely Viscous Liquids.” Chem. Eng. Sci., 36 429–434 (1981)

    Article  Google Scholar 

  5. Mmbaga, JP, Hayes, RE, Bertrand, FH, Tanguy, PA, “Flow Simulation in the Nip of a Rigid Forward Roll Coater.” Int. J. Numer. Meth. Fluids, 48 1041–1066 (2005)

    Article  Google Scholar 

  6. Han, SK, Shin, DM, Park, HY, Jung, HW, Hyun, JC, “Effect of Viscoelasticity on Dynamics and Stability in Roll Coatings.” Eur. Phys. J. Special Top., 166 107–110 (2009)

    Article  Google Scholar 

  7. Szczurek, E, Dubar, M, Deltombe, R, Dubois, A, Dubar, L, “New Approach to the Evaluation of the Free Surface Position in Roll Coating.” J. Mater. Proc. Technol., 209 3187–3197 (2009)

    Article  Google Scholar 

  8. Carvalho, MS, Scriven, LE, “Three-Dimensional Stability Analysis of Free Surface Flows: Application to Forward Deformable Roll Coating.” J. Comput. Phys., 151 534–562 (1999)

    Article  Google Scholar 

  9. Coyle, DJ, “Forward Roll Coating with Deformable Rolls: A Simple One-Dimensional Elastohydrodynamic Model.” Chem. Eng. Sci., 43 2673–2684 (1988)

    Article  Google Scholar 

  10. Carvalho, MS, Scriven, LE, “Effect of Deformable Roll Cover on Roll Coating.” Tappi J., 77 201–208 (1994)

    Google Scholar 

  11. Carvalho, MS, Scriven, LE, “Flows in Forward Deformable Roll Coating Gasp: Comparison between Spring and Plane-Strain Models of Roll Cover.” J. Comput. Phys., 138 449–479 (1997)

    Article  Google Scholar 

  12. Carvalho, MS, “Effect of Thickness and Viscoelastic Properties of Roll Cover on Deformable Roll Coating Flows.” Chem. Eng. Sci., 58 4323–4333 (2003)

    Article  Google Scholar 

  13. Gostling, MJ, Savage, MD, Young, AE, Gaskell, PH, “A Model for Deformable Roll Coating with Negative Gaps and Incompressible Compliant Layers.” J. Fluid. Mech., 489 155–184 (2003)

    Article  Google Scholar 

  14. Cohu, O, Magnin, A, “Forward Roll Coating of Newtonian Fluids with Deformable Rolls: An Experimental Investigation.” Chem. Eng. Sci., 52 1339–1347 (1997)

    Article  Google Scholar 

  15. Devisetti, SK, Bousfield, DW, “Fluid Absorption During Forward Roll Coating of Porous Webs.” Chem. Eng. Sci., 65 3528–3537 (2010)

    Article  Google Scholar 

  16. Bohan, MFJ, Fox, IJ, Claypole, TC, Gethin, DT, “Numerical Modelling of Elastohydrodynamic Lubrication in Soft Contacts Using Non-Newtonian Fluids.” Int. J. Numer. Methods Heat Fluid Flow, 12 494–511 (2002)

    Article  Google Scholar 

  17. Lécuyer, HA, Mmbaga, JP, Hayes, RE, Bertrand, FH, Tanguy, PS, “Modelling of Forward Roll Coating Flows with a Deformable Roll: Application to Non-Newtonian Industrial Formulations.” Comput. Chem. Eng., 33 1427–1437 (2009)

    Article  Google Scholar 

  18. Kang, Y-T, Lee, K-Y, Liu, T-J, “The Effect of Polymer Additives on the Performance of a Two-Roll Coater.” J. Appl. Polym. Sci., 43 1187–1195 (1991)

    Article  Google Scholar 

  19. Lee, JH, Han, SK, Jung, HW, Hyun, JC, “Ribbing Instability in Rigid and Deformable Forward Roll Coating Flows, Ribbing Instability in Rigid and Deformable Forward Roll Coating Flows.” Korea-Aust. Rheol. J., 22 75–80 (2010)

    Google Scholar 

  20. Ascanio, G, Carreau, PJ, Brito-de la Fuente, E, Tamguy, PA, “Forward Deformable Roll Coating at High Speed with Newtonian fluids.” Trans. IChemE, Part A Chem. Eng. Res. Des., 82 390–397 (2004)

    Article  Google Scholar 

  21. Durst, F, Grundlagen der Strömungsmechanik—Eine Einführung in die Theorie der Strömungen von Fluiden. Springer, Berlin (2006)

    Google Scholar 

  22. Hertz, H, “Über die Berührung fester elastischer Körper.” J. Reine Angew. Math., 92 156–171 (1881)

    Google Scholar 

  23. Parish, GJ, “Measurements of Pressure Distribution Between Metal and Rubber Covered Rollers.” Br. J. Appl. Phys., 9 158–161 (1958)

    Article  Google Scholar 

  24. Parish, GJ, “Apparent Slip Between Metal and Rubber-Covered Pressure Rollers.” Br. J. Appl. Phys., 9 428–433 (1958)

    Article  Google Scholar 

  25. Thomas, HR, Hoersch, VA, “Stresses Due to the Pressure of One Elastic Solid Upon Another, One Elastic Solid Upon Another.” University of Illinois, Engineering Experimental Station, Bulletin no. 212, pp. 66-99 (1930)

  26. Hannah, M, “Contact Stress and Deformation in a Thin Elastic Layer.” Q. J. Mech. Appl. Math., 3 94–105 (1950)

    Google Scholar 

  27. Parish, GJ, “Calculation of the Behaviour of Rubber-Covered Pressure Rollers.” Br. J. Appl. Phys., 12 333–336 (1961)

    Article  Google Scholar 

  28. Coyle, DJ, Macosko, CW, Scriven, LE, “Film-Splitting Flows in Forward Roll Coating.” J. Fluid Mech., 171 183–207 (1986)

    Article  Google Scholar 

  29. Decré, M, Gailly, E, Buchlin, JM, “Meniscus Shape Experiments in Forward Roll Coating.” Phys. Fluids, 7 458–467 (1995)

    Article  Google Scholar 

  30. Becerra, MZ, Oldrich, JR, Azevedo, LFA, Carvalho, MS, “Measuring the Velocity Field in Film-Splitting Flows of Newtonian Liquids.” AIChE J., 53 281–289 (2007)

    Article  Google Scholar 

  31. Ascanio, G, Ruiz, G, “Measurement of Pressure Distribution in a Deformable Nip of Counter-Rotating Rolls.” Mess. Sci. Technol., 17 2430–2436 (2006)

    Article  Google Scholar 

  32. Hooke, CJ, “The Elastohydrodynamic Lubrication of a Cylinder on an Elastomeric Layer.” Wear, 111 83–99 (1986)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Fluid Mechanics, Friedrich Alexander University Erlangen-Nuremberg, Cauerstr. 4, 91058, Erlangen, Germany

    Bettina Willinger & Antonio Delgado

Authors
  1. Bettina Willinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bettina Willinger.

Additional information

This paper was presented at the 16th International Science and Technology Symposium, September 9–12, 2012, in Atlanta, GA (USA).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Willinger, B., Delgado, A. Analytical prediction of roll coating with counter-rotating deformable rolls. J Coat Technol Res 11, 31–37 (2014). https://doi.org/10.1007/s11998-013-9506-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11998-013-9506-2

Keywords

Search

Navigation