In this study, the settling of small particles in a non-Newtonian fluid medium is considered. The simulation of this problem according to the fluid mechanics principles may be realized by the flow of a non-Newtonian fluid around a sphere falling along the centerline of a cylindrical tube. The knowledge of the rate of settling of particles in practice is particularly significant in determining the shelf life 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. The majority of the theoretical, experimental and numerical studies available in the literature deal with Newtonian fluids. Conversely, for non-Newtonian fluids the problem is considerably more complex. It is well-recognized that extensional behaviour in non-Newtonian fluids plays a major role in complex flows. Most non-Newtonian fluids such as polymeric solutions and melts exhibit shear-thinning behaviour. In this study it is aimed to determine the equations governing this process and some important conclusions about the properties of polymeric liquids related to their viscoelastic constitution are drawn. Effectively, it is found that for polymeric liquids, the elastic behaviour characterized by the normal stress coefficients, implies relatively increased normal stresses with respect to the generalized Newtonian fluids, whereas the shear stresses tend to decrease, thus changing somewhat the category of the flow from shear-flow into extensional flow in a small rate. Hence, the viscoelastic property of the polymeric liquids must be stressed by their constitutive equation choice, which led us to the CEF model.
Part of the book: Polymer Rheology