Abstract.
We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.
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References
R. Seemann, S. Herminghaus, K. Jacobs, J. Phys. Condens. Matter 13, 4925 (2001).
P. Müller-Buschbaum, J. Phys. Condens. Matter 15, R1549 (2003).
J. Becker, G. Grün, R. Seemann, H. Mantz, K. Jacobs, K.R. Mecke, R. Blossey, Nature Mater. 2, 59 (2003).
G. Reiter, Phys. Rev. Lett. 87, 186101 (2001).
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Butterworth-Heinemann, Oxford, 1987).
S.A. Safran, J. Klein, J. Phys. II 3, 749 (1993).
S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002).
S. Herminghaus, K. Jacobs, R. Seemann, Eur. Phys. J. E 12, 101 (2003).
T. Vilmin, E. Raphaël, cond-mat/0502228 (2005).
J. Jäckle, J. Phys. Condens. Matter 10, 7121 (1998).
M.A. Spaid, G.M. Homsy, Phys. Fluids 8, 460 (1996).
D.E. Weidner, L.W. Schwartz, Phys. Fluids 6, 3535 (1994).
A. Carré, F. Eustache, C. R. Acad. Sci. Paris, Ser. II b 325, 709 (1997).
A. de Ryck, D. Quéré, Langmuir 14, 1911 (1998).
F. Saulnier, E. Raphaël, P.G. de Gennes, Phys. Rev. Lett. 88, 196101 (2002).
V. Shenoy, A. Sharma, Phys. Rev. Lett. 88, 236101 (2002).
R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Fluids, Vol. 1 (Wiley & Sons, New York, 1977).
G. Böhme, Strömungsmechanik nichtnewtonscher Fluide (Teubner, Stuttgart, 2000).
We note that there are different sign conventions on $\Stress$ in the literature
M.A. Spaid, G.M. Homsy, J. Non-Newtonian Fluid Mech. 55, 259 (1994).
R. Khayat, J. Non-Newtonian Fluid Mech. 95, 199 (2000).
Y.L. Zhang, O.K. Matar, R.V. Craster, J. Non-Newtonian Fluid Mech. 105, 53 (2002).
R. Konrad, K. Jacobs, A. Münch, B. Wagner, T.P. Witelski, submitted to Phys. Rev. Lett. (2004).
A. Münch, B. Wagner, T.P. Witelski, submitted to J. Eng. Math.
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Rauscher, M., Münch, A., Wagner, B. et al. A thin-film equation for viscoelastic liquids of Jeffreys type. Eur. Phys. J. E 17, 373–379 (2005). https://doi.org/10.1140/epje/i2005-10016-8
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DOI: https://doi.org/10.1140/epje/i2005-10016-8