Intermediate asymptotics of the capillary-driven thin-film equation

被引：19

作者：

Benzaquen, Michael ^{[1
]}

Salez, Thomas ^{[1
]}

Raphael, Elie ^{[1
]}

机构：

[1] ESPCI, UMR CNRS Gulliver 7083, Lab Physicochim Theor, F-75005 Paris, France

来源：

EUROPEAN PHYSICAL JOURNAL E | 2013年 / 36卷 / 08期

关键词：

SURFACE-DIFFUSION; POLYMER-FILMS; LIQUID-FILMS; GROWTH; DYNAMICS; CURRENTS; MODELS;

D O I：

10.1140/epje/i2013-13082-3

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

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.

引用

页数：7

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