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Theoretical analysis of dip-coating of uniformly wetting and chemically micropatterned surfaces with an Ellis fluid

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Abstract

Dip-coating of a chemically micropatterned surface is an important technique for selective material deposition in a confined region for various applications. An analysis of the dip-coating of a micropatterned surface with a pure Newtonian liquid was performed by Davis (Phys. Fluids 17, 03852 (2005)). In this study, the analysis of dip-coating of the heterogeneous substrate is extended to the deposition of an Ellis Fluid. Governing equations are derived using lubrication theory to determine the thickness of a liquid film deposited on the O(10 μm) stripe at small capillary number. A uniformly wetting surface is also considered using a consistent treatment of the governing equations for comparison. The effect of the Ellis model parameters on the thickness of the entrained liquid film is found to be much less for the micropatterned surfaces because of the dominant effect of the lateral fluid confinement due to heterogeneous wettability. This confinement imposes a geometric length scale in case of the patterned surface that replaces the dynamic capillary length used for the analysis of the dip-coating of a uniform surface. A composite equation is further developed for the Ellis fluid to include the effect of gravity on the dip-coated film thickness on both types of surfaces. The film thinning due to gravity drainage is found to be negligible for the case of patterned substrate.

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References

  1. A.A. Darhuber, S.M. Troian, J.M. Davis, S.M. Miller, S. Wagner, J. Appl. Phys. 88, 5119 (2000).

    Article  ADS  Google Scholar 

  2. P. Schunk, A. Hurd, C. Brinker, in Liquid Film Coating, edited by S. Kistler, P. Schweizer (Chapman & Hall, London, 1993) chapt. 13.

  3. D. Qin, Y. Xia, B. Xu, H. Yang, C. Zhu, G.M. Whitesides, Adv. Mater. 11, 1433 (1999).

    Article  Google Scholar 

  4. H. Fan, Y. Lu, A. Stump, S. Reed, T. Baer, R. Schunk, V. Perez-Luna, G. Lopez, C. Brinker, Nature 405, 56 (2000).

    Article  ADS  Google Scholar 

  5. H.G. Braun, E. Meyer, Thin Solid Films 345, 222 (1999).

    Article  ADS  Google Scholar 

  6. S.J. Oh, Y. Cheng, J. Zhang, H. Shimoda, O. Zhou, Appl. Phys. Lett. 82, 2521 (2003).

    Article  ADS  Google Scholar 

  7. H. Ko, S. Peleshanko, V. Tsukrut, J. Phys. Chem. B 108, 4385 (2004).

    Article  Google Scholar 

  8. V. Santhanam, R. Andres, J. Am. Chem. Soc. 4, 41 (2004).

    Google Scholar 

  9. Q. Guo, X. Teng, S. Rahman, H. Yang, J. Am. Chem. Soc. 125, 630 (2003).

    Article  Google Scholar 

  10. L.D. Landau, B.V.G. Levich, Acta Physicochim. URSS 17, 42 (1942).

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. J.M. Davis, Phys. Fluids 17, 038101 (2005).

    Article  ADS  Google Scholar 

  14. N. Tiwari, J.M. Davis, Phys. Fluids 18, 022102 (2006).

    Article  ADS  Google Scholar 

  15. S. Siau, A. Vervaet, S. Degrande, E. Schacht, A.V. Calster, Appl. Surf. Sci. 245, 353 (2005).

    Article  ADS  Google Scholar 

  16. C. Gutfinger, J.A. Tallmadge, AIChE J. 11, 403 (1965).

    Article  Google Scholar 

  17. K. Adachi, R.P. Spiers, W.L. Wilikinson, J. Non-Newton. Fluid Mech. 3, 331 (1978).

    Article  MATH  Google Scholar 

  18. A. Dutta, R.A. Mashelkar, Rheol. Acta. 21, 52 (1982).

    Article  Google Scholar 

  19. M.N. Tekic, V.O. Popadic, Chem. Eng. Sci. 38, 285 (1983).

    Article  Google Scholar 

  20. O. Campanella, J. Galazzo, R. Cerro, Chem. Eng. Sci. 41, 2707 (1986).

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. N. Tiwari, J.M. Davis, Phys. Fluids 20, 022102 (2008).

    Article  ADS  Google Scholar 

  23. J.A. Tallmadge, AIChE J. 12, 1011 (1966).

    Article  Google Scholar 

  24. R.E. Hildebrand, J.A. Tallmadge, Canad. J. Chem. Eng. 46, 394 (1968).

    Article  Google Scholar 

  25. K. Afanasiev, A. Munch, B. Wagner, Phys. Rev. E 76, 036307 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  26. F. Kamish, Chem. Eng. Proc. 42, 569 (2003).

    Article  Google Scholar 

  27. R. Bird, R. Armstrong, O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1977).

  28. J.C. Berg, A. Acrivos, Chem. Eng. Commun. 20, 737 (1965).

    Google Scholar 

  29. R.M. Turian, AICHE J. 13, 999 (1967).

    Article  Google Scholar 

  30. R.P. Chhabra, C. Tiu, P.H.T. Uhlherr, Rheol. Acta. 20, 346 (1981).

    Article  Google Scholar 

  31. R.P. Chhabra, I. Machac, P.H.T. Uhlherr, Rheol. Acta. 23, 457 (1984).

    Article  Google Scholar 

  32. S.D.R. Wilson, J. Eng. Math. 16, 209 (1982).

    Article  ADS  MATH  Google Scholar 

  33. P.C. Huzyak, K.W. Koelling, J. Non-Newton. Fluid. Mech. 71, 73 (1997).

    Article  Google Scholar 

  34. L.W. Schwartz, J. Eng. Math. 39, 171 (2001).

    Article  MATH  Google Scholar 

  35. H.S. Kheshgi, S.F. Kistler, L.E. Scriven, Chem. Eng. Sci. 47, 683 (1992).

    Article  Google Scholar 

  36. K. Ruschak, AIChE J. 24, 705 (1978).

    Article  Google Scholar 

  37. S.J. Weinstein, K.J. Ruschak, Annu. Rev. Fluid Mech. 36, 29 (2004).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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  1. Department of Chemical Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, UP, India

    Naveen Tiwari

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Tiwari, N. Theoretical analysis of dip-coating of uniformly wetting and chemically micropatterned surfaces with an Ellis fluid. Eur. Phys. J. E 37, 123 (2014). https://doi.org/10.1140/epje/i2014-14123-1

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