The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

被引：24

作者：

Barenblatt, GI

Beretta, E

Bertsch, M

机构：

[1] UNIV CALIF BERKELEY,LAWRENCE BERKELEY LAB,BERKELEY,CA 94720

[2] CNR,IST ANAL GLOBALE & APPLICAZ,I-50139 FLORENCE,ITALY

[3] UNIV ROMA TOR VERGATA,DIPARTIMENTO MATEMAT,I-00163 ROME,ITALY

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 1997年 / 94卷 / 19期

关键词：

D O I：

10.1073/pnas.94.19.10024

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin, In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness, A class of self-similar solutions to this free boundary problem is considered.

引用

页码：10024 / 10030

页数：7