Skip to main content
SpringerLink
Log in

Analysis of influencing parameters in deformable roll coating of counter-rotating rolls

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

Abstract

Roll coating is a comparatively simple and common technology for coating of continuous substrates like paper, coils, or foils, where the fluid is metered through the gap between two rolls. Rolls wrapped with a deformable rubber layer enable a precise metering for low fluid amounts and lead additionally to higher process stability. Many efforts have been made to investigate the influencing factors of deformable roll coating by experimental and numerical methods. Beside configurations with positive gaps, which are comparable to rigid roll setups, negative gaps, where only the elasticity of the rubber layer prevents overlapping of the rolls, are of interest as such configurations enable thin liquid layers. The main influencing factors on the volume flow rate through the gap are viscosity, average velocity, effective radius, Young’s modulus, load or pre-set gap height, and partly rubber thickness, when an influence of the layer height is assumed. The dependency is often given in empirically or numerically based power law relationships. In contrast to this, in the present study, an analytically based solution is used to investigate the influencing factors in deformable roll coating with negative gaps. This continues the authors' previous work, in which the analytical solution was derived. As a result, a general agreement with numerical and experimental results from literature is found. Additionally, the analytical approach allows for the first time the ability to quantify further trends. The proposed power law exponent for the dimensionless load and elasticity numbers from literature cannot be considered as constant in the whole common application range of roll coating but remarkable trends appear. Additionally, a new criterion for the critical rubber cover thickness is developed analytically which describes the limit value of the negligible influence of the rubber cover thickness on the volume flow rate. The present investigation enables the explanation of different literature results and offers a more general view in the understanding of roll coating processes.

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

Access this article

Log in via an institution

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
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. 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. Process. Technol., 209 3187–3197 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. 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 

  4. 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 

  5. Varnam, CJ, Hooke, CJ, “Non-Hertzian Elastohydrodynamic Contacts: An Experimental Investigation.” J. Mech. Eng. Sci., 19 189–192 (1977)

    Article  Google Scholar 

  6. Jaffar, MJ, “Estimation of Minimum Thickness for Line Contacts in the Transition Region Between the Isoviscous, Elastic and the Piezoviscous-Elastic Lubrication Regimes.” Proc. Inst. Mech. Eng. C, 203 379–386 (1989)

    Article  Google Scholar 

  7. Johnson, KL, “Regimes of Elastohydrodynamic Lubrication.” J. Mech. Eng. Sci., 12 (1) 9–16 (1970)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Ascanio, G, Carreau, PJ, Tanguy, PA, “High-Speed Roll Coating with Complex Rheology Fluids.” Exp. Fluids., 40 1–14 (2006)

    Article  Google Scholar 

  10. Gasni, D, Ultrasonic Reflection for Measurement of Oil Film Thickness and Contact between Dissimilar Materials. PhD Thesis, University of Sheffield, 2012

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

    Article  Google Scholar 

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

    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. 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 

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

    Google Scholar 

  16. 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.” Comp. Chem. Eng., 33 1427–1437 (2009)

    Article  Google Scholar 

  17. 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 

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

    Article  Google Scholar 

  19. Abbott, SJ, Kapur, N, Sleigh, PA, Summers, JL, Thompson, HM, “A Review of Deformable Roll Coating Systems.” Convertech & e-Print, 1 (3) 89–93 (2011)

    Google Scholar 

  20. Carvalho, MS, “Effect of Thickness and Viscoelastic Properties of Roll Cover on Deformable Roll Coating Flows.” Chem. Eng. Sci., 58 4323–4433 (2003)

    Article  Google Scholar 

  21. Coyle, DJ, “Nonlinear Theory of Squeeze-Roll Coating.” AIChE Spring National Meeting, Florida, USA, 1990

  22. Hooke, CJ, O’Donoghue, JP, “Elastohydrodynamic Lubrication of Soft, Highly Deformed Contacts.” J. Mech. Eng. Sci., 14 34–48 (1972)

    Article  Google Scholar 

  23. Johnson, MA, Viscoelastic Roll Coating Flows. PhD thesis, University of Maine, 2003

  24. Kistler, SF, Schweizer, PM, Liquid Film Coating—Scientific Principles and Their Technological Implications. Chapman & Hall, London, 1997

    Google Scholar 

  25. Herrebrugh, K, “Solving the Incompressible and Isothermal Problem in Elastohydrodynamic Lubrication Through an Integral Equation.” J. Lubric. Technol., 90 262–270 (1968)

    Article  Google Scholar 

  26. Roberts, AF, Swales, PD, “The Elastohydrodynamic Lubrication of a Highly Elastic Cylindrical Surface.” Br. J. Appl. Phys., 2 1317–1327 (1969)

    Google Scholar 

  27. Willinger, B, Delgado, A, “Analytical Prediction of Roll Coating with Counter-Rotating Deformable Rolls.” J. Coat. Technol. Res., 11 31–37 (2014)

    Article  Google Scholar 

  28. Willinger, B, Epple, P, Delgado, A, “Analytical Model for Deformable Roll Coating with Nip Feed.” Proc. Appl. Math. Mech., 12 599–600 (2012)

    Article  Google Scholar 

  29. Durst, F, Grundlagen der Strömungsmechanik - Eine Einführung in die Theorie der Strömungen von Fluiden. Springer, Berlin, 2006

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  34. Thomas, HR, Hoersch, VA, “Stresses Due to the Pressure of One Elastic Solid Upon Another.” University of Illinois, Engineering Experimental Station Bulletin, 21 66–99 (1930)

    Google Scholar 

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

    Article  Google Scholar 

  36. Cohen, ED, Gutloff, EB, Modern Coating and Drying Technology. Wiley-VCH, New York, 1992

    Google Scholar 

  37. 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 

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

    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 Grashof & Antonio Delgado

Authors
  1. Bettina Grashof
    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 Grashof.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grashof, B., Delgado, A. Analysis of influencing parameters in deformable roll coating of counter-rotating rolls. J Coat Technol Res 12, 63–73 (2015). https://doi.org/10.1007/s11998-014-9629-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11998-014-9629-0

Keywords

Search

Navigation