We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from periodic and localized initial conditions as separate cases. The particular (similarity) solutions in each of these two cases exhibit the generic property that the profiles are weakly singular (that is, higher-order derivatives do not exist) at points where the pressure gradient vanishes. Numerical simulations of the thin film equation, with either periodic or localized initial condition, are shown to approach the appropriate particular solution.

Blood flow rheology is a very complex phenomenon. Hemodynamics owns Newtonian or non-Newtonian characteristic is still debatable. Recently, studies related to blood tend to classify blood as non-Newtonian fluid. In this research, power law, Casson and Carreau which are being the most popular non-Newtonian models are applied to investigate the hemodynamics variables that influence formation of thrombosis and predict damageability to blood cell. The branched arterial system is simplified as T-junction geometry and the computational fluid dynamics software Fluent 6.2 with finite volume method is utilized to analyze the blood flow rheology in cases of continuous and pulsatile flow. The analysis results are compared with that of Newtonian model and give out very interesting hemodynamics predictions for each model. The size of recirculation zone is different from each model that is observed significantly. The wall shear stress of Carreau model gets the highest value, 14% in case of continuous flow and around 17% in pulsatile case bigger than that of Newtonian model. The results of pulsatile flow show that the Newtonian model is closed to power law model while the Casson model is similar to the Carreau model.

The crude oil is a non-Newtonian fluid exhibiting, during its flow, phenomena which cannot be described with the traditional models which consider the fluid as homogeneous. Thus, it is necessary to use or develop a more realistic approach which can take into account the microstructure characteristics of crude oils in the law of behaviour. The application of a non-linear differential model in the case of crude oil flow can not be used. This paper deals with the modelling approach resulting from rheology of the polymer solutions. The Modified Phan-Thien and Tanner model (MPTT) is considered in this paper for an axisymmetric flow in a pipe. The shear stresses calculation with this model is an important step as it allows to study subsequently some important phenomena as the corrosion or the pressure drop which is controlled by the friction factor under turbulent flow conditions. The calculations were about different crude oils and the obtained results are compared to experiments. Some discussions are given.