CEF model in the industrial application of non-Newtonian fluids

Among the constitutive equations developed from the continuum mechanics viewpoint, the second-order Rivlin-Ericksen model is generally preferred because it describes the real behaviour of the fluids with sufficient accuracy, and also because its application is not very cumbersome. On the other hand, the material coefficients used being constant, it is not in good agreement with experimental results in case the shear strain-rate is not very small. The (CEF) Criminale-Ericksen-Filbey constitutive equation removes this draw-back by taking these coefficients variable and dependent of the shear strain-rate. As an example, we can consider the settling of small particles in a non-Newtonian fluid medium. The knowledge of the rate of settling of particles in practice is particularly significant in determining the shelflife of materials such as foodstuffs, cleaning materials and many others. Thus, this problem has great importance in many natural and physical processes and in a large number of industrial applications such as chemical genetic and biomedical engineering operations.