Fluid Mechanics for Chemical Engineering

Chapter 7

Notions of Rheometry

This chapter is not dedicated to rheology as a discipline. We will not present, therefore, the classical rheological models, which describe the mechanical behavior of many materials.

We shall deal here with rheometry, which concerns the techniques for characterizing the rheological properties of materials. The physical principles underlying the design of rheometers are presented. Stating them here is justified for several reasons:

– It is important to be aware, within a fluid mechanics course, that not all fluids are Newtonian.

– The use of a rheometer should be familiar to an engineer, even one who does not specialize in rheology.

– The operating principle of rheometers is independent from the rheological models whose construction they make possible.

7.1. Rheology

Let us return to the local form, in a Cartesian coordinate system, of the fundamental law of mechanics for a continuum, already seen in Chapter 1 (Table 1.1). The equations are reproduced below, omitting body forces:

[7.1]

They bring in the stress tensor [Σ], which is a symmetrical 3 × 3 matrix. The mechanical behavior of a material is determined by the mathematical expression of the six terms in the stress tensor. The purpose of rheology is to establish these relations (called constitutive ...