Skip to main content
SpringerLink
Log in

On slip effect in free coating of non-Newtonian fluids

  • Original Contributions
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

The failure of the current theories to predict the coating thickness of non-Newtonian fluids in free coating operations is shown to be a result of the effective slip at the moving rigid surface being coated. This slip phenomenon is a consequence of stress induced diffusion occurring in flow of structured liquids in non-homogeneous flow fields. Literature data have been analysed to substantiate the slip hypothesis proposed in this work. The experimentally observed coating thickness is shown to lie between an upper bound, which is estimated by a no-slip condition for homogeneous solution and a lower bound, which is estimated by using solvent properties. Some design considerations have been provided, which will serve as useful guidelines for estimating coating thickness in industrial practice.

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

Similar content being viewed by others

Abbreviations

fa :

exponent in eq. (15)

b :

n/(4 −n)(n + 1)

Ca :

Capillary number

D :

diffusivity

De :

Deborah number

g :

acceleration due to gravity

G :

Goucher number

h :

thickness profile

h 0 :

final coating thickness

K :

consistency index

L :

length available for diffusion

L t :

tube length

n :

power-law index

ΔP :

pressure drop

Q :

flow rate

R :

cylinder radius

R t :

tube radius

t :

time available for diffusion

T 0 :

dimensionless thickness without slip

T s :

dimensionless thickness with slip

U c :

theoretically calculated withdrawal velocity to match the film thickness

u s :

slip velocity

U :

withdrawal velocity

U w :

theoretically calculated withdrawal velocity based on solvent properties

U * :

effective withdrawal velocity

x :

distance in the direction of flow

y :

distance transverse to the flow direction

α :

curvature coefficient

β :

slip coefficient

δ :

curvature coefficient

Δ :

rate of deformation tensor

θ :

u s /U

λ :

relaxation time

ρ :

density

σ :

surface tension

σ′ :

shear stress in tube flow

σ w :

wall shear stress in tube flow

τ :

stress tensor

τ w :

wall shear stress

φ :

T s /T 0

References

  1. Landau, L., B. V. Levich, Acta Physchim. URSS17, 41 (1942).

    Google Scholar 

  2. White, D. A., J. A. Tallmadge, Chem. Eng. Sci.20, 33 (1965).

    Google Scholar 

  3. Spiers, R. P., C. V. Subbaraman, W. L. Wilkinson, Chem. Eng. Sci.29, 389 (1974).

    Google Scholar 

  4. Soroka, A. J., J. A. Tallmadge, Amer. Inst. Chem. Eng. J.17, 505 (1971).

    Google Scholar 

  5. Esmail, M. N., R. L. Hummel, Amer. Inst. Chem. Eng. J.21, 958 (1975).

    Google Scholar 

  6. Gutfinger, C., J. A. Tallmadge, Amer. Inst. Chem. Eng. J.11, 403 (1965).

    Google Scholar 

  7. Tallmadge, J. A., Chem. Eng. Sci.24, 471 (1969).

    Google Scholar 

  8. Tallmadge, J. A., Amer. Inst. Chem. Eng. J.16, 925 (1970).

    Google Scholar 

  9. Tallmadge, J. A., Amer. Inst. Chem. Eng. J.12, 1011 (1966).

    Google Scholar 

  10. Spiers, R. P., C. V. Subbaraman, W. L. Wilkinson, Chem. Eng. Sci.30, 379 (1975).

    Google Scholar 

  11. Hildebrand, R. E., J. A. Tallmadge, Can. J. Chem. Eng.46, 394 (1968).

    Google Scholar 

  12. Groenveld, P., Chem. Eng. Sci.25, 1579 (1970).

    Google Scholar 

  13. Gutfinger, C., Ph. D. Thesis, Yale University, 1965.

  14. Roy, S. C., Can. J. Chem. Eng.49, 583 (1971).

    Google Scholar 

  15. Tallmadge, J. A., Amer. Inst. Chem. Eng. J.14, 837 (1968).

    Google Scholar 

  16. Middleman, S., Polym. Eng. Sci.18, 355 (1978).

    Google Scholar 

  17. Middleman, S., Fundamentals of Polymer Processing, p. 223, McGraw-Hill (New York 1977).

    Google Scholar 

  18. Astarita, G., G. Marrucci, G. Palumbo, Ind. Eng. Chem. Fund.3, 333 (1964).

    Google Scholar 

  19. Carreau, P. J., Q. H. Bui, P. Leroux, Rheol. Acta18, 600 (1979).

    Google Scholar 

  20. Jastrzebski, Z. D., Ind. Eng. Chem. Fund.6, 445 (1967).

    Google Scholar 

  21. Kozicki, W., S. N. Pasari, A. R. K. Rao, C. Tui, Chem. Eng. Sci.25, 41 (1970).

    Google Scholar 

  22. Metzner, A. B., Y. Cohen, C. Rangel-Nafaile, J. Non-Newtonian Fluid Mech.5, 449 (1979).

    Google Scholar 

  23. Tirrell, M., M. F. Malone, J. Polym. Sci.15, 1569 (1977).

    Google Scholar 

  24. Janssen, L. P. B. M., Rheol. Acta19, 32 (1980).

    Google Scholar 

  25. Fessler, J. H., A. G. Ogston, Trans. Far. Soc.47, 667 (1951).

    Google Scholar 

  26. Couper, A., R. F. T. Stepto, Trans. Far. Soc.65, 2486 (1969).

    Google Scholar 

  27. Kedem, O., A. Katchalsky, J. Polym. Sci.15, 321 (1955).

    Google Scholar 

  28. Mashelkar, R. A., A. Dutta, Chem. Eng. Sci., in press (1982).

  29. Astarita, G., G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, p. 57, McGraw-Hill, (London, 1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chemical Engineering Division, National Chemical Laboratory, 411008, Pune, India

    A. Dutta & R. A. Mashelkar

Authors
  1. A. Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Mashelkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

NCL-Communication No. 2818

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dutta, A., Mashelkar, R.A. On slip effect in free coating of non-Newtonian fluids. Rheol Acta 21, 52–61 (1982). https://doi.org/10.1007/BF01520705

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01520705

Key words

Search

Navigation