The study carried out with respect to the different types of viscosity of liquids is based on studying the different speed profiles that are generated under certain types of conditions, always first considering the Newtonian idea, in which viscosity is a constant that will depend mainly on temperature and to a lesser extent will depend on pressure. Fluids in which the shear stress is directly proportional to the deformation rate are called Newtonian fluids. Newtonian fluids can be classified depending on the relationship between the shear stress applied to the flow and the speed of deformation resulting from this stress. They comply with Newton’s law of viscosity. ![]() The Newtonian fluid was named by Isaac Newton, who described it as a viscous flow.The viscosity of the liquid is inversely proportional to the increase in its temperature.As the temperature increases in a fluid, its viscosity decreases.It is said that these fluids have a normal behavior, in which there is very little viscosity, and this does not vary with forces that are applied on it.When they are at a fixed temperature, their viscosity does not change and remains constant.Viscosity also depends on the different pressures at which it is found.The mid-plane viscosities of the corresponding numerical simulations are plotted in the rightmost column for comparison and closely. From: Biomaterials, Artificial Organs and Tissue Engineering, 2005. ( c) Newtonian fluid (water) at a high flow for comparison. They are incomprehensible, isotropic and unreal. A Newtonian fluid is defined as one with constant viscosity, with zero shear rate at zero shear stress, that is, the shear rate is directly proportional to the shear stress.Newtonian fluids have no elastic properties.Unlike the flow of Newtonian fluids through the annuli, the friction geometry parameter and thus the friction factor is highly influenced by the rheological parameters of the fluid, the fluid flowrate, inner pipe rotary speed and eccentricity. In general, for shear thinning non-Newtonian fluids, pipe rotation can improve the fluid flow in the region of lower flow in the eccentric annuli. For annuli flows of non-Newtonian fluids, the effect of inner pipe rotation on the axial pressure gradient is dependent on the fluid flowrate and at high fluid flowrates, the influence of the inner pipe rotation on the fluid hydraulics decreases. Results showed that for a fully developed flow of non-Newtonian shear thinning fluids, if the fluid flowrate is kept constant, an increase in inner pipe rotation leads to a decrease in the axial frictional pressure gradient when the pipe is rotating on its axis. Stereoscopic Particle Image Velocimetry and Line Integral Convolution Methods: Application to a Sphere Sedimenting Near a Wall in a Non-Newtonian Fluid. New analytical and numerical models were developed to obtain the fluid velocity and viscosity field distribution and determine the frictional pressure gradient for laminar and turbulent flows in the concentric and eccentric annuli with and without inner pipe rotation and were compared and validated favourably with models previously presented in literature. Techniques of computational fluid dynamics for fully developed steady-state fluid flow were applied to obtain detailed information of the flow field in the annuli. In this study, an analytical and numerical approach were carried out to investigate and evaluate the hydrodynamic behaviour of the axial and helical isothermal flow of Newtonian and non-Newtonian fluids through the annuli. ![]() Furthermore, there have been inconsistencies in the description of the effect of inner pipe rotation on the pressure losses experienced for both Newtonian and non-Newtonian flows in concentric and eccentric annuli. However, many studies in literature have developed or applied theoretical models that were either only valid for Newtonian annuli flows or have not considered the combined effect of the fluid rheological parameters with the inner pipe rotary speed and eccentricity when calculating the frictional annuli pressure losses for non-Newtonian shear thinning fluids. ![]() Previous studies have shown that the pressure losses and fluid velocity distributions in the annuli are highly influenced by the rheological properties of the fluid, inner pipe rotary speed and eccentricity. The accurate prediction of the fluid dynamics and hydraulics of the axial or helical flow of non-Newtonian drilling fluids in the annuli is essential for the determination and effective management of wellbore pressure during drilling operations.
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