In the course of miniaturization of electronic and microfluidic devices, reliable predictions of the stability of ultrathin films have a strategic role for design purposes. Consequently, efficient computational techniques that allow for a direct comparison with experiment become increasingly important. Here we demonstrate, for the first time, that the full complex spatial and temporal evolution of the rupture of ultrathin films can be modelled in quantitative agreement with experiment. We accomplish this by combining highly controlled experiments on different film-rupture patterns with computer simulations using novel numerical schemes for thin-film equations. For the quantitative comparison of the pattern evolution in both experiment and simulation we introduce a novel pattern analysis method based on Minkowski measures. Our results are fundamental for the development of efficient tools capable of describing essential aspects of thin-film flow in technical systems.
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Kagan, C.R., Mitzi, D.B. & Dimitrakopoulos, C.D. Organic-inorganic hybrid materials as semi-conducting channels in thin-film field-effect transistors. Science 286, 945–947 (1999).
Seemann, R., Herminghaus, S. & Jacobs, K. Dewetting patterns and molecular forces: a reconcialiation. Phys. Rev. Lett. 86, 5534–5537 (2001).
Acheson, D.J. Elementary Fluid Dynamics (Oxford Univ. Press, Oxford, 1990).
Oron, A., Davis, S. & Bankoff, S.G. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980 (1997).
Dussan V, E.B. & Davis, S. On the motion of a fluid-fluid interface along a solid surface. J. Fluid. Mech. 65, 71–95 (1974).
Bernis, F. & Friedman, A. Higher order nonlinear degenerate parabolic equations. J. Differ. Equations 83, 179–206 (1990).
Dal Passo, R., Garcke, H. & Grün, G. On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behavior of solutions. SIAM J. Math. Anal. 29, 321–342 (1998).
Bertozzi, A.L. & Pugh, M. The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions. Comm. Pure Appl. Math. 49, 85–123 (1996).
Grün, G. & Rumpf, M. Nonnegativity preserving convergent schemes for the thin film equation. Num. Math. 87, 113–152 (2000).
Grün, G. On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions. Math. Comp. (in the press).
Seemann, R., Herminghaus, S. & Jacobs, K. Gaining control of pattern formation of dewetting liquid films. J. Phys. Condens. Mat. 13, 4925–4938 (2001).
Herminghaus, S., Seemann, R. & Jacobs, K. The glass transition of thin polymer films: some questions and a possible answer. Eur. Phys. J. E 5, 531–538 (2001).
Vrij, A. Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33 (1966).
Ruckenstein E. & Jain, R.K. Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. II 132–147 (1974).
Brochard, F. & Daillant, J. Drying of solids wetted by thin liquid films. Can. J. Phys. 68, 1084–1088 (1990).
Reiter, G. Dewetting of thin polymer films. Phys. Rev. Lett. 68, 751–754 (1992).
Bischof, J., Scherer, D., Herminghaus, S. & Leiderer, P. Dewetting modes of thin metallic films: nucleation of holes and spinodal dewetting. Phys. Rev. Lett. 77, 1536–1539 (1996).
Jacobs, K., Mecke, K.R. & Herminghaus, S. Thin liquid polymer films rupture via defects. Langmuir 14, 965–969 (1998).
Herminghaus, S. et al., Spinodal dewetting in liquid crystal and liquid metal films. Science 82, 916–919 (1998).
Sharma, A. & Khanna, R. Pattern formation in unstable liquid films. Phys. Rev. Lett. 81, 3463–3466 (1998).
Ghatak, A., Khanna, R. & Sharma, A. Dynamics and morphology of holes in dewetting of thin films. J. Colloid Interface Sci. 212, 483–494 (1999).
Kargupta, K. & Sharma, A. Creation of ordered patterns by dewetting of thin films on homogeneous and heterogeneous substrates. J. Colloid Interface Sci. 245, 99–115 (2002).
Blossey, R. Nucleation at first-order wetting transitions. Int. J. Mod. Phys. B 9, 3489–3525 (1995).
Seemann, R., Herminghaus, S. & Jacobs, K. Shape of a liquid front upon dewetting. Phys. Rev. Lett. 81, 1251–1254 (2001).
Mecke, K.R. Integral geometry and statistical physics. Int. J. Mod. Phys. B 12, 861–899 (1998).
Mecke, K.R. & Stoyan, D. (eds.) Statistical Physics and Spatial Statistics - The Art of Analysing and Modelling Spatial Structures and Pattern Formation Lecture Notes in Physics, Vol. 554, (Springer, Berlin, 2000).
Mecke, K.R. Morphological characterization of patterns in reaction-diffusion systems. Phys. Rev. E 53, 4794–4800 (1996).
Gau, H., Herminghaus, S., Lenz, P. & Lipowsky, R. Liquid morphologies on structured surfaces. Science 283, 46–49 (1999)
Herminghaus, S., Seemann, R. & Jacobs, K. Generic morphologies of viscoelastic dewetting fronts. Phys. Rev. Lett. 89, 056101 (2002).
Barrett, J.W., Blowey, J.F. & Garcke, H. Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Num. Math. 80, 525–556 (1998).
Zhornitskaja, L. & Bertozzi, A.L. Positivity preserving numerical schemes for lubrication-type equations. SIAM J. Num. Anal. 37, 523–555 (2000).
Grün, G. & Rumpf, M. Simulation of singularities and instabilities in thin film flow. Europ. J. Appl. Math. 12, 293–320 (2001).
Oron, A. Three-dimensional nonlinear dynamics of thin liquid films. Phys. Rev. Lett. 85, 2108–2111 (2000).
We thank Stephan Herminghaus for many stimulating discussions and Renate Konrad for help in calculating the Minkowski measures. This work was supported by the Priority Program Wetting and Structure Formation at Interfaces of the German Science Foundation through individual research grants to the participating groups. This program provided an ideal forum for the interaction of mathematicians, theoretical and experimental physicists which lead to this interdisciplinary work.
The authors declare no competing financial interests.
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Becker, J., Grün, G., Seemann, R. et al. Complex dewetting scenarios captured by thin-film models. Nature Mater 2, 59–63 (2003). https://doi.org/10.1038/nmat788
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