ArticleThe European physical journal. E, Soft matter2013
Intermediate asymptotics of the capillary-driven thin-film equation.
Article in The European physical journal. E, Soft matter, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Advancements in Novel Mechano-Rheological Probes for Studying Glassy Dynamics in Nanoconfined Thin Polymer Films.ACS polymers Au · 2024Review
- Monitoring Photochemical Reactions Using Marangoni Flows.Langmuir : the ACS journal of surfaces and colloids · 2017Article
- Experimental evidence of ultrathin polymer film stratification by AFM force spectroscopy.The European physical journal. E, Soft matter · 2015Article
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3 authors.
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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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