Next: Introduction: Film flows and evolution equations
[Published in "Mathematical Modeling and Simulation in Hydrodynamic Stability", (ed. D. N. Riahi), World Scientific, Singapore, 1996. pp. 35-81]
DERIVATIONS AND SIMULATIONS OF EVOLUTION EQUATIONS
OF WAVY FILM FLOWS
ALEXANDER L. FRENKEL AND K. INDIRESHKUMAR
Department of Mathematics, University of Alabama
Tuscaloosa, Alabama 35487
Abstract:
Wavy flows of viscous films on solid surfaces are considered. The focus is on approximate decriptions which are hinged on a single evolution equation. Perturbative approaches to constructing such theories are discussed. For several film flows, evolution equations obtained--along with the validity conditions of those theories--with the multiparametric perturbation approach are reviewed. The results of their three-dimensional numerical simulations on extended spatial intervals are discussed. Some unresolved fundamental questions concerning such film-flow studies are posed and discussed.
- Introduction: Film flows and evolution equations
- Perturbation approaches
- Some results
- Three-dimensional inclined-film flow
- General evolution equation; impossibility of a single-equation description of large-amplitude regimes for large times
- Evolution equation for small-amplitude regimes
- Numerical studies of evolution equation
- Unusual patterns on strange attractors for strongly dispersive falling films
- Transient patterns: Qualitative agreement of simulations with experiments
- Flow down a vertical fiber
- Small-amplitude waves in core-annular flows
- Vertical and horizontal core-annular flows with large-amplitude waves
- Three-dimensional inclined-film flow
- Some unresolved questions concerning
foundations of the film flow research - Summary
- Acknowledgments
- References
- About this document ...
Alex Frenkel
Fri Nov 8 23:40:39 CST 1996