On evolution equations for thin films flowing down solid surfaces

Journal Article · Fri Oct 01 04:00:00 EDT 1993 · Physics of Fluids A; (United States)

DOI:https://doi.org/10.1063/1.858895· OSTI ID:6217664

Frenkel, A L ^[1]

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1. Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350 (United States)

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.

• DOE Contract Number: FG05-90ER14100
• OSTI ID: 6217664
• Journal Information: Physics of Fluids A; (United States), Journal Name: Physics of Fluids A; (United States) Vol. 5:10; ISSN PFADEB; ISSN 0899-8213
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNULAR SPACE
CONFIGURATION
CYLINDERS
DIMENSIONS
FILM FLOW
FILMS
FLUID FLOW
PERTURBATION THEORY
SPACE
SURFACE PROPERTIES
SURFACE TENSION
THICKNESS
THIN FILMS
VISCOUS FLOW