Many common fluids, including air, water, honey, and liquid metals, are accurately represented by the Newtonian constitutive equation. However, there are also many materials whose behavior is distinctly non-Newtonian: molten polymers, molten glass, semisolid metals, grease, many types of paint, and foods such as mayonnaise, peanut butter, and melted cheese. Non-Newtonian fluids obey the same mass and momentum balance equations as Newtonian fluids, but they have different constitutive equations for stress. In this chapter we show how to develop constitutive equations for non-Newtonian fluids, and we demonstrate their use in the solving of flow problems. We also develop a simplified set of governing equations for viscous flow in narrow gaps, the generalized Hele–Shaw approximation.

The study of the deformation and flow of materials, particularly of non-Newtonian fluids, is the subject called rheology. Rheologists create experimental techniques to measure viscosity and other flow properties, they develop constitutive equations that describe non-Newtonian material behavior, and they relate that material behavior to microscopic structure. A full treatment of rheology is beyond the scope of this book, and readers may wish to consult some of the excellent texts on the subject (Tanner, 1985; Bird et al., 1987; Barnes et al., 1989; Dealy and Wissbrun, 1990; Macosko, 1994).

NON-NEWTONIAN BEHAVIOR

PURELY VISCOUS FLUIDS

There is only one type of Newtonian fluid behavior, and one Newtonian fluid differs from another only by its value of viscosity.