Introduction to Rheology

In order to obtain velocity profiles, flow rates, and pressures in any fluid flow situation of interest, as might occur in practical food or polymer processing, one has to solve the momentum balance or the Cauchy equation of motion simultaneously with the mass balance or the continuity equation. The equation of motion contains stress components that, in general, depend on the imposed deformation and deformation rate. For low molecular weight, i.e., Newtonian liquids, the stress versus deformation rate relationship involves only a single material constant, the viscosity. For non-Newtonian fluids, the relationships are much more complex, and there is no single accepted equation relating the three-dimensional stress to the three-dimensional strain or rate of strain. In view of this, one relates a single component of the stress tensor to a single component of the rate-of-strain tensor in a well-defined flow field. This is known as a material function. Here, we define the different material functions that are commonly measured using standard instruments. Results obtained depend on temperature and also on material composition and reveal the constitutive nature of the material. They are obviously useful for characterization and quality control purposes but also for allowing one to propose and validate constitutive equations.