Constitutive Equation: General Principles

Abstract

In isothermal flow where the conservation of energy is not relevant, there are four balance equations (one conservation of mass and three conservation of linear momentum), and there are 10 scalar variables (3 velocity, one pressure, and 6 independent stress components — thanks to the conservation of angular momentum). Clearly we do not have a mathematically well-posed problem until 6 extra equations are found. The constitutive equation, or the rheological equation of state, provides the linkage between the stresses and the kinematics and provides the missing information. Modelling a complex fluid, or finding a relevant constitutive equation for the fluid, is the central concern in rheology. In this chapter, we review some of the well-known classical models, and the general principles underlying constitutive modelling.