The study of the deformation and flow of fluids and includes the fundamental parameters of elasticity, plasticity, and viscosity. The state of a fluid is characterized by three principal types of behaviour depending on the nature of flow:

1. 1 Time-independent fluids. Examples include Newtonian fluids in which the ratio of shear stress to shear rate is a constant, such as water, oils, and honey; pseudoplastic fluids in which the apparent viscosity decreases with increasing shear rate, such as (p. 329) polymer melts, paper pulp, wallpaper paste, printing inks, tomato purée, mustard, and rubber solutions; and dilatants in which the apparent viscosity increases with increasing shear rate. These are more rare and include titanium dioxide suspensions, cornflour/sugar suspensions, cement aggregates, starch solutions, and certain honeys.

2. 2 Time-dependent fluids. For these fluids, the relation between shear stress and shear rate depends on the time and flow history of the fluid. They are classified as being either thixotropic or antithixotropic (or rheopectic). For thixotropic fluids, the shear stress decreases with time for a given shear stress. This is due to a structural breakdown of the fluid. If a cyclic experiment is carried out, a hysteresis loop is formed. Examples include greases, printing inks, jelly, paints, and drilling muds. In antithixotropic fluids the shear stress increases with time for a given shear stress. Examples include clay suspensions and gypsum suspensions.

3. 3 Viscoelastic fluids. Fluids that possess the properties of both viscosity and elasticity. Unlike purely viscous fluids where the flow is irreversible, viscoelastic fluids recover part of their deformation. The rheological measurement of these fluids is understandably very difficult. Examples include polymeric solutions, partially hydrolyzed polymer melts such as polyacrylamide, thick soups, crème fraîche, ice cream, and some melted products such as cheese.