Potential Flows of Viscous and Viscoelastic Liquids (Cambridge Aerospace Series, Series Number 21)

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. "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 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 and in all university courses on fluid mechanics, but it is deeply 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."--Jacket 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.