Potential flows of viscous and viscoelastic fluids / Daniel Joseph, Toshio Funada, Jing Wang.

This book illustrates how potential flows enter into the general theory of motions of viscous and viscoelastic fluids. Traditionally, the theory of potential flow is presented as a subject called 'potential flow of an inviscid fluid'; when the fluid is incompressible these fluids are, curiously, said to be 'perfect' or 'ideal'. This type of presentation is widespread; it can be found in every book on fluid mechanics, but it is flawed. It is never necessary and typically not useful to put the viscosity of fluids in potential (irrotational) flow to zero. The dimensionless description of potential flows of fluids with a nonzero viscosity depends on the Reynolds number, and the theory of potential flow of an inviscid fluid can be said to rise as the Reynolds number tends to infinity. The theory given here can be described as the theory of potential flows at finite and even small Reynolds numbers.

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.

Includes bibliographical references (p. 473-486) and index.