## ABSTRACT

Rheology is a subject which addresses the deformation of fluids. By this it is meant that whenever surface forces, called stresses, are applied to a body of fluid, that body deforms or flows. We can describe this behavior mathematically by means of a set of constitutive equations. A constitutive equation defines the cause and effect relationships in terms of the properties or characteristics of the fluid material. To develop such relationships balance equations must be derived. A balance equation is merely a mathematical statement of the universal laws of conservation of mass, energy, and momentum that are specific to the system of interest. By way of a simple example found in many fluid dynamic textbooks (Cheremisinoff, 1982; Azbel and Cheremisinoff, 1983), consider a shearing force applied to a rectangular body of incompressible fluid as illustrated in Figure 1. For steady-state, isothermal flow conditions we may write the following mass balance (continuity equation) and momentum balance (equation of motion): Mass balance: () d d x ρ V x = 0 = ρ d V x d x https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203742853/0cc42c74-5683-414c-aca6-2272749eedf3/content/eq1.tif"/> Fluid body subjected to constant force. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203742853/0cc42c74-5683-414c-aca6-2272749eedf3/content/fig1_1_OB.tif"/>