Rate-Type Models

Spatial interaction and memory effects are among the possible features of non-simple materials. As to memory effects in fluids, the inadequacy of the classical Navier-Stokes theory to describe rheological complex fluids, such as geological materials, liquid foams, and polymeric fluids, has led to the development of several theories of non-Newtonian fluids. In this chapter, memory effects are described by rate-type equations: among others, the elastic-plastic and the Kelvin-Voigt solids and the Bingham, the Maxwell-Wiechert, and the Jeffreys fluids are shown to follow from rheological models. Spatial interaction is modelled through materials of higher-order grade as, for example, the Oldroyd-B fluid and the White-Metzner fluid.