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Thin viscoelastic dewetting films of Jeffreys type subjected to gravity and substrate interactions

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Abstract.

This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is derived as a long-wave approximation of the Navier-Stokes equations for incompressible viscoelastic liquids under the effect of gravity, with the Jeffreys model for viscoelastic stresses. For the particular cases of horizontal or inverted planes, the linear stability analysis is performed to investigate the influence of the physical parameters involved on the growth rate and length scales of instabilities. Numerical simulations of the nonlinear regime of the dewetting process are presented for the particular case of an inverted plane. Both gravity and the disjoining pressure are found to affect not only the length scale of instabilities, but also the final configuration of dewetting, by favoring the formation of satellite droplets, that are suppressed by the slippage with the solid substrate.

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References

  1. P.-G. de Gennes, Rev. Mod. Phys. 57, 827 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  2. R. Scardovelli, S. Zaleski, Annu. Rev. Fluid Mech. 31, 567 (1999)

    Article  ADS  Google Scholar 

  3. G. Tryggvason, R. Scardovelli, S. Zaleski, Direct Numerical Simulations of Gas-Liquid Multiphase Flows (Cambridge University Press, Cambridge, 2011)

  4. H. Jeffreys, The Earth: Its Origin, History, and Physical Constitution (Cambridge University Press, Cambridge, 1952)

  5. J. Israelachvili, Intermolecular & Surface Forces (Academic Press, London, 1985)

  6. R.A. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Vol. 1: Fluid mechanics (Wiley-Interscience, Toronto, 1987)

  7. O. Reynolds, Philos. Trans. R. Soc. London 177, 157 (1886)

    Article  ADS  Google Scholar 

  8. A. Oron, S. Davis, G. Bankoff, Rev. Mod. Phys. 69, 931 (1997)

    Article  ADS  Google Scholar 

  9. F. Brochard-Wyart, G. Debregeas, R. Fondecave, P. Martin, Macromolecules 30, 1211 (1997)

    Article  ADS  Google Scholar 

  10. G. Reiter, Phys. Rev. Lett. 68, 75 (1992)

    Article  ADS  Google Scholar 

  11. S.A. Safran, J. Klein, J. Phys. II 3, 749 (1993)

    Google Scholar 

  12. S. Gabriele, S. Sclavons, G. Reiter, P. Damman, Phys. Rev. Lett. 96, 156105 (2006)

    Article  ADS  Google Scholar 

  13. M. Rauscher, A. Münch, B. Wagner, R. Blossey, Eur. Phys. J. E 17, 373 (2005)

    Article  Google Scholar 

  14. R. Blossey, A. Münch, M. Rauscher, B. Wagner, Eur. Phys. J. E 20, 267 (2006)

    Article  Google Scholar 

  15. R. Blossey, Thin Liquid Films, Dewetting and Polymer Flow (Springer, New York, 2012)

  16. V. Barra, S. Afkhami, L. Kondic, J. Non-Newton. Fluid Mech. 237, 26 (2016)

    Article  MathSciNet  Google Scholar 

  17. G. Tomar, V. Shankar, S.K. Shukla, A. Sharma, G. Biswas, Eur. Phys. J. E 20, 185 (2006)

    Article  Google Scholar 

  18. M. Benzaquen, T. Salez, E. Raphaël, EPL 106, 36003 (2014)

    Article  ADS  Google Scholar 

  19. J.C. Maxwell, Philos. Trans. R. Soc. Lond. 157, 49 (1867)

    Article  ADS  Google Scholar 

  20. H.E. Huppert, Nature 300, 427 (1982)

    Article  ADS  Google Scholar 

  21. D.-Y. Hsieh, Phys. Fluids 8, 1785 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  22. L.W. Schwartz, Phys. Fluids A: Fluid 1, 443 (1989)

    Article  ADS  Google Scholar 

  23. R.E. Kelly, D.A. Goussis, S.P. Lin, F.K. Hsu, Phys. Fluids A: Fluid 1, 819 (1989)

    Article  ADS  Google Scholar 

  24. D.-Y. Hsieh, Phys. Fluids A: Fluid 2, 1145 (1990)

    Article  ADS  Google Scholar 

  25. L. Kondic, SIAM Rev. 45, 95 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  26. J.M. Gomba, J. Diez, R. Gratton, A.G. Gonzlez, L. Kondic, Phys. Rev. E 76, 046308 (2007)

    Article  ADS  Google Scholar 

  27. H.J. Kull, Phys. Rep. 206, 197 (1991)

    Article  ADS  Google Scholar 

  28. S.P. Kapitza, Zh. Eksp. Teor. Fiz. 18, 3 (1948)

    ADS  Google Scholar 

  29. N. Kofman, W. Rohlfs, F. Gallaire, B. Scheid, C. Ruyer-Quil, Int. J. Multiphase Flow 104, 286 (2018)

    Article  MathSciNet  Google Scholar 

  30. M.A. Lam, L.J. Cummings, T.-S. Lin, L. Kondic, J. Eng. Math. 94, 97 (2015)

    Article  Google Scholar 

  31. M.S. Tshehla, Math. Probl. Eng. 2013, 754782 (2013)

    Article  MathSciNet  Google Scholar 

  32. D. Picchi, P. Poesio, A. Ullmann, N. Brauner, Int. J. Multiphase Flow 97, 109 (2017)

    Article  MathSciNet  Google Scholar 

  33. B.J. Kaus, Becker T.W., Geophys. J. Int. 168, 843 (2006)

    Article  ADS  Google Scholar 

  34. V. Barra, S.A. Chester, S. Afkhami, Comput. Fluids 175, 36 (2018)

    Article  MathSciNet  Google Scholar 

  35. A. Münch, B. Wagner, M. Rauscher, R. Blossey, Eur. Phys. J. E 20, 365 (2006)

    Article  Google Scholar 

  36. R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, Oxford, 1999)

  37. D.A. Siginer, Stability of Non-Linear Constitutive Formulations for Viscoelastic Fluids (Springer, New York, 2014)

  38. F. Mainardi, G. Spada, Eur. Phys. J. ST 193, 133 (2011)

    Article  Google Scholar 

  39. D. Gutierrez-Lemini, Engineering Viscoelasticity (Springer, New York, 2014)

  40. R. Fetzer, K. Jacobs, A. Münch, B. Wagner, T.P. Witelski, Phys. Rev. Lett. 95, 127801 (2005)

    Article  ADS  Google Scholar 

  41. A. Münch, B. Wagner, T.P. Witelski, J. Eng. Math. 53, 359 (2005)

    Article  Google Scholar 

  42. J.A. Diez, L. Kondic, Phys. Fluids 19, 072107 (2007)

    Article  ADS  Google Scholar 

  43. G. Teletzke, H.T. Davis, L.E. Scriven, Chem. Eng. Commun. 55, 41 (1987)

    Article  Google Scholar 

  44. I. Seric, S. Afkhami, L. Kondic, J. Fluid Mech. 755, R1 (2014)

    Article  ADS  Google Scholar 

  45. K. Mahady, S. Afkhami, L. Kondic, J. Comput. Phys. 294, 243 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  46. T.-S. Lin, L. Kondic, Phys. Fluids 22, 052105 (2010)

    Article  ADS  Google Scholar 

  47. J.A. Diez, L. Kondic, J. Comput. Phys. 183, 274 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  48. A.L. Bertozzi, Not. Am. Math. Soc. 45, 689 (1998)

    Google Scholar 

  49. M.A. Lam, L.J. Cummings, T.-S. Lin, L. Kondic, J. Fluid Mech. 841, 925 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  50. K.B. Glasner, T.P. Witelski, Phys. Rev. E 67, 016302 (2003)

    Article  ADS  Google Scholar 

  51. J.R. De Bruyn, Phys. Rev. A 46, R4500 (1992)

    Article  ADS  Google Scholar 

  52. T. Qian, X.P. Wang, P. Sheng, Commun. Math. Sci. 1, 333 (2003)

    Article  MathSciNet  Google Scholar 

  53. T.G. Myers, SIAM Rev. 3, 441 (1998)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA

    Valeria Barra, Shahriar Afkhami & Lou Kondic

Authors
  1. Valeria Barra
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  2. Shahriar Afkhami
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  3. Lou Kondic
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Correspondence to Shahriar Afkhami.

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Barra, V., Afkhami, S. & Kondic, L. Thin viscoelastic dewetting films of Jeffreys type subjected to gravity and substrate interactions. Eur. Phys. J. E 42, 12 (2019). https://doi.org/10.1140/epje/i2019-11774-2

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  • DOI: https://doi.org/10.1140/epje/i2019-11774-2

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