1. Introduction; 2. Historical notes; 3. Boundary conditions for viscous fluids; 4. Helmholtz decomposition coupling rotational to irrotational flow; 5. Harmonic functions which give rise to vorticity; 6. Radial motions of a spherical gas bubble in a viscous liquid; 7. Rise velocity of a spherical cap bubble; 8. Ellipsoidal model of the rise of a Taylor bubble in a round tube; 9. Rayleigh-Taylor instability of viscous fluids; 10. The force on a cylinder near a wall in viscous potential flows; 11. Kelvin-Helmholtz instability; 12. Irrotational theories of gas-liquid flow: viscous potential flow (VPF), viscous potential flow with pressure correction (VCVPF) and dissipation method (DM); 13. Rising bubbles; 14. Purely irrotational theories of the effect of the viscosity on the decay of waves; 15. Irrotational Faraday waves on a viscous fluid; 16. Stability of a liquid jet into incompressible gases and liquids; 17. Stress induced cavitation; 18. Viscous effects of the irrotational flow outside boundary layers on rigid solids; 19. Irrotational flows which satisfy the compressible Navier-Stokes equations; 20. Irrotational flows of viscoelastic fluids; 21. Purely irrotational theories of stability of viscoelastic fluids; 22. Numerical methods for irrotational flows of viscous fluid; Appendices; References; List of illustrations; List of tables.
Potential Flows of Viscous and Viscoelastic Liquidsby Jing Wang, Toshio Funada, Daniel Joseph
Pub. Date: 12/17/2007
Publisher: Cambridge University Press
The goal of this book is to show how potential flows enter into the general theory of motions of viscous and viscoelastic fluids. Traditionally, the theory of potential flows is thought to apply to idealized fluids without viscosity. Here we show how to apply this theory to real fluids that are viscous. The theory is applied to problems of the motion of bubbles; to
The goal of this book is to show how potential flows enter into the general theory of motions of viscous and viscoelastic fluids. Traditionally, the theory of potential flows is thought to apply to idealized fluids without viscosity. Here we show how to apply this theory to real fluids that are viscous. The theory is applied to problems of the motion of bubbles; to the decay of waves on interfaces between fluids; to capillary, Rayleigh-Taylor, and Kelvin-Hemholtz instabilities; to viscous effects in acoustics; to boundary layers on solids at finite Reynolds numbers; to problems of stress-induced cavitation; and to the creation of microstructures in the flow of viscous and viscoelastic liquids.
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