ON EVOLUTION-EQUATIONS FOR THIN-FILMS FLOWING DOWN SOLID-SURFACES

被引:21
作者
FRENKEL, AL
机构
[1] Department of Mathematics, University of Alabama, Tuscaloosa
来源
PHYSICS OF FLUIDS A-FLUID DYNAMICS | 1993年 / 5卷 / 10期
关键词
D O I
10.1063/1.858895
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A wavy free-surface flow of a viscous film down a cylinder is considered. It is shown that if the cylinder radius is large, as compared to the film thickness, the long-wave perturbation approach yields a rather simple evolution equation. This nonlinear equation is similar to the well-known Benney equation of planar films, and becomes exactly the latter in the limit of infinite radius. Thus it is the annular-case analog-which was missing in the literature-of the Benney equation. It is argued that under conditions implicitly implied in their derivation, the Benney-type equations are not uniformly valid for large times, However, both the new and Benney equations are important heuristically-as sources of other, simpler, equations which, in certain domains of system parameters, are valid for all time. Also, the new equation of annular films is important as a qualitative model incorporating all significant physical factors.
引用
收藏
页码:2342 / 2347
页数:6
相关论文
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