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Intermediate asymptotics of the capillary-driven thin-film equation

The European Physical Journal E volume 36, Article number: 82 (2013) Cite this article

Abstract

We present an analytical and numerical study of the two-dimensional capillary-driven thin-film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green’s function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green’s function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the extension of our results to the nonlinear equation.

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Affiliations

  1. Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France

    Michael Benzaquen, Thomas Salez & Elie Raphaël

Authors
  1. Michael Benzaquen
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  2. Thomas Salez
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  3. Elie Raphaël
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Correspondence to Thomas Salez.

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Benzaquen, M., Salez, T. & Raphaël, E. Intermediate asymptotics of the capillary-driven thin-film equation. Eur. Phys. J. E 36, 82 (2013). https://doi.org/10.1140/epje/i2013-13082-3

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  • DOI: https://doi.org/10.1140/epje/i2013-13082-3

Keywords

  • Flowing Matter: Interfacial phenomena