Flows of Non-Newtonian Fluids

The present paper summarizes various problems on non-Newtonian fluid mechanics. Due to complex rheological behaviors of non-Newtonian fluids, constitutive equations have highly nonlinear character. As two approaches to obtain constitutive equations, continuum mechanics and molecular theory are described, and then a number of models are presented. Various flow problems are discussed. With regard to measuring methods, the hole pressure error and the first normal stress difference of dilute polymer solutions are stated. Moreover, steady flow in straight pipes, entrance flow through abrupt contractions, flow instabilities, Toms effect, and numerical method are briefly described.