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  Relaxation and intermediate asymptotics of a rectangular trench in a viscous film

Bäumchen, O., Benzaquen, M., Salez, T., McGraw, J. D., Backholm, M., Fowler, P., et al. (2013). Relaxation and intermediate asymptotics of a rectangular trench in a viscous film. Physical Review E, 88(3): 035001. doi:10.1103/PhysRevE.88.035001.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-767D-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-767E-A
Genre: Journal Article

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Bäumchen, Oliver1, Author              
Benzaquen, Michael2, Author
Salez, Thomas2, Author
McGraw, Joshua D.2, Author
Backholm, Matilda2, Author
Fowler, Paul2, Author
Raphaël, Elie2, Author
Dalnoki-Veress, Kari2, Author
Affiliations:
1Group Dynamics of fluid and biological interfaces, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063300              
2External Organizations, ou_persistent22              

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 Abstract: The surface of a thin liquid film with nonconstant curvature flattens as a result of capillary forces. While this leveling is driven by local curvature gradients, the global boundary conditions greatly influence the dynamics. Here, we study the evolution of rectangular trenches in a polystyrene nanofilm. Initially, when the two sides of a trench are well separated, the asymmetric boundary condition given by the step height controls the dynamics. In this case, the evolution results from the leveling of two noninteracting steps. As the steps broaden further and start to interact, the global symmetric boundary condition alters the leveling dynamics. We report on full agreement between theory and experiments for the capillary-driven flow and resulting time dependent height profiles, a crossover in the power-law dependence of the viscous energy dissipation as a function of time as the trench evolution transitions from two noninteracting to interacting steps, and the convergence of the profiles to a universal self-similar attractor that is given by the Green's function of the linear operator describing the dimensionless linearized thin film equation.

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Language(s): eng - English
 Dates: 2013-09-13
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1103/PhysRevE.88.035001
BibTex Citekey: baeumchen-pre-2013
 Degree: -

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Title: Physical Review E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: 5 Volume / Issue: 88 (3) Sequence Number: 035001 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: /journals/resource/954925225012