The Asymptotic Solution of a Class of Third-Order Boundary Value Problems Arising in the Theory of Thin Film Flows

This paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third-order boundary value problems which govern the motion of thin liquid films subject to viscous, capillary and gravitational forces. Precise conditions specifying where and when the th...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 43; no. 5; pp. 993 - 1004
Main Author Howes, F. A.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.10.1983
Subjects
Applied mathematics
Approximation
Boundary conditions
Boundary layers
Boundary value problems
Differential equations
Exact sciences and technology
Flow velocity
Fluid dynamics
fluid mechanics
Fundamental areas of phenomenology (including applications)
Liquids
Mathematical constants
numerical analysis
Other topics in fluid dynamics
perturbation
Physics
Reynolds number
Thin films
Velocity
viscous flow
Theoretical study
Boundary value problem
Asymptotic approximation
Liquid layer
Thin film
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Summary:This paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third-order boundary value problems which govern the motion of thin liquid films subject to viscous, capillary and gravitational forces. Precise conditions specifying where and when the third-order derivative terms in the differential equations can be neglected are derived, and improved estimates for the actual solutions in terms of solutions of the lower-order models are constructed. The paper also contains a technique for replacing a third-order problem with an asymptotically equivalent second-order one that may have wider applicability.
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ISSN:0036-1399
1095-712X
DOI:10.1137/0143065