Carreau model of blood rheology in various geometries domain: A review of theory and applications

In this review article, the author provides an extensive, structured review of around 180 studies on the fluid dynamics of Carreau fluids. The studies are categorised by shape, approach, and dimensionality: 2D and 3D. Through this work, the author aims to capture the pivotal issues that have prevented the advancement of Carreau fluid studies, particularly in biomedical engineering, industrial processing, and the intricate dynamics of fluids. The studies analysed included a diverse array of shapes, ranging from flat plates and channels to porous media, cylindrical vessels, and intricate vascular forms. The author also outlined the various approaches: analytical, numerical, and computational. Throughout the review, the author clarifies the importance of these different aspects and how the shape of the vessel and dimensionality of the approach markedly determine the flow dynamics, viscous thinning, surface shear stress, and the shear pressure gradient. The author comments on the vital shift from basic 2D representations to more elaborate 3D models that accurately depict physiological conditions, though this advancement varies greatly depending on the shape involved. The article notes a particularly concerning gap in the literature on fully 3D studies of Carreau fluid mechanics in cylindrical shapes a basic yet necessary configuration.