Effect of including a gas layer on the gel formation process during the drying of a polymer solution

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Abstract.

In this paper, we study the influence of the upper gas layer on the drying and gelation of a polymer solution. The gel is formed due to the evaporation of the binary solution into (inert) air. A one-dimensional model is proposed, where the evaporation flux is more realistically described than in previous studies. The approach is based on general thermodynamic principles. A composition-dependent diffusion coefficient is used in the liquid phase and the local equilibrium hypothesis is introduced at the interface to describe the evaporation process. The results show that the high thickness of the gas layer reduces evaporation, thus leading to longer drying times. Our model is also compared with more phenomenological descriptions of evaporation, for which the mass flux through the interface is described by the introduction of a Peclet number. A global agreement is found for appropriate values of the Peclet numbers and our model can thus be considered as a tool allowing to link the value of the empirical Peclet number to the physics of the gas phase. Finally, in contrast with other models, our approach emphasizes the possibility of very fast gelation at the interface, which could prevent all Marangoni convection during the drying process.

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Keywords

Flowing Matter: Liquids and Complex Fluids 

References

  1. 1.
    P.L. Evans, L.W. Schwartz, R.V. Roy, J. Colloid Interface Sci. 227, 191 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    S.D. Howison, J.A. Moriarty, J.R. Ockendon, E.L. Terrill, S.K. Wilson, J. Eng. Math. 32, 377 (1997)CrossRefGoogle Scholar
  3. 3.
    P. Mokarian-Tabari, M. Geoghegan, J.R. Howse, S.Y. Heriot, R.L. Thompson, R.A.L. Jones, Eur. Phys. J. E 33, 283 (2010)CrossRefGoogle Scholar
  4. 4.
    S. Walheim, E. Schäffer, J. Mlynek, U. Steiner, Science 283, 520 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    A. Munch, C.P. Please, B. Wagner, Phys. Fluids 23, 102101 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    B. Guerrier, C. Bouchard, C. Allah, C. Benard, AIChE J. 44, 791 (1998)CrossRefGoogle Scholar
  7. 7.
    B.J. de Gans, U.S. Schubert, Langmuir 20, 7789 (2004)CrossRefGoogle Scholar
  8. 8.
    T. Kawase, T. Shimoda, C. Newsome, H. Sirringhaus, R.H. Friend, Thin Solid Films 438-439, 279 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    B.J. de Gans, P.C. Duineveld, U.S. Schubert, Adv. Mater. 16, 203 (2004)CrossRefGoogle Scholar
  10. 10.
    B. Li, Y.P. Cao, X.Q. Feng, H. Gao, Soft Matter 8, 5728 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    A.F. Routh, Rep. Prog. Phys. 76, 046603 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    D.E. Bornside, C.W. Macosko, L.E. Scriven, J. Appl. Phys. 66, 5185 (1989)ADSCrossRefGoogle Scholar
  13. 13.
    P.G. de Gennes, Eur. Phys. J. E 7, 31 (2002)CrossRefGoogle Scholar
  14. 14.
    M. Tsige, G.S. Grest, Macromolecules 37, 4333 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    Y. Reyes, Y. Duda, Langmuir 21, 7057 (2005)CrossRefGoogle Scholar
  16. 16.
    A.F. Routh, W.B. Zimmerman, Chem. Eng. Sci. 59, 2961 (2004)CrossRefGoogle Scholar
  17. 17.
    A.M. Konig, T.G. Weerakkody, J.L. Keddie, D. Johannsmann, Langmuir 24, 7580 (2008)CrossRefGoogle Scholar
  18. 18.
    A. Sarkar, M.S. Tirumkudulu, Langmuir 25, 4945 (2009)CrossRefGoogle Scholar
  19. 19.
    F. Buss, C.C. Roberts, K.S. Crawford, K. Peters, L.F. Francis, J. Colloid Interface Sci. 359, 112 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    K.Y. Ozawa, T. Okuzono, M. Doi, Jpn. J. Appl. Phys. 45, 8817 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    M.G. Hennessy, C.J.W. Breward, C.P. Please, SIAM J. Appl. Math. 76, 1711 (2016)MathSciNetCrossRefGoogle Scholar
  22. 22.
    M.G. Hennessy, G.L. Ferretti, J.T. Cabral, O.K. Matar, J. Colloid Interface Sci. 488, 61 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    H. Machrafi, A. Rednikov, P. Colinet, P.C. Dauby, Eur. Phys. J. ST 192, 71 (2011)CrossRefGoogle Scholar
  24. 24.
    T. Okuzono, M. Doi, Phys. Rev. E 77, 1 (2008)CrossRefGoogle Scholar
  25. 25.
    H. Machrafi, A. Rednikov, P. Colinet, P.C. Dauby, Phys. Rev. E 91, 053018 (2015)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1999)Google Scholar
  27. 27.
    A.E. Nesterov, Y.S. Lipatov, Thermodynamics of Polymer Blends (CRC Press, 1998)Google Scholar
  28. 28.
    P. Atkins, Physical Chemistry (Oxford University Press, Oxford, 2001) Chapt. “Simple Mixtures”Google Scholar
  29. 29.
    H. Machrafi, A. Rednikov, P. Colinet, P.C. Dauby, Phys. Fluids 25, 084106 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.University of Liège, Thermodynamics of Irreversible PhenomenaLiègeBelgium

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