A micropolar fluid model of blood flow through a tapered artery with a stenosis

Abstract

IntroductionStenosis is one of the most frequent anomalies in blood circulation. It is known as a partial occlusion of the blood vessels due to the accumulation of cholesterols, fats and smooth muscle cells. The occlusion makes the walls thickened and hardened which may reduce the volume of the blood that travels through the arteries. This leads to a reduction in the amount of oxygen and nutrients transported to the peripheral organs. The study by Moayeri and Zendehboodi [1] noted that once the occlusion is formed, the blood flow is significantly altered and fluid dynamical factors play important roles as the stenosis continues to enlarge leading to the development of cardiovascular diseases, such as heart attack and stroke. Thus, the study of blood flow through a stenosed artery is very important due to the fact that the development of diseases is related to the nature of blood movement and the mechanical behaviour of the blood vessel walls.Cavalcanti [2] considered a mild stenosis with 2% area reduction. The study used a thin-rigid wall model, along with the continuity and axial component of the Navier-Stokes equations to obtain an approximate analytical solution to the physiological flow of blood. A nonlinear two-dimensional flow of blood in a mild stenosed flexible artery was investigated by Chakravarty et al. [3] by treating the arterial wall as an anisotropic, linear viscoelastic and an incompressible circular cylindrical membrane shell. Chakravarty and Mandal [4] extended the work by considering the bifurcated arteries with a mild stenosis. The vascular wall deformability is taken to be elastic whereas the flowing blood is treated to be Newtonian.Most of the above-mentioned studies characterized blood as a Newtonian fluid and little attention has been given to its suspension nature. It is well known that blood is a suspension of red and white cells together with other small particles in electrolytic aqueous solution of plasma. The non-Newtonian behaviour is attributed to the particulate suspension nature of blood, for which the Newtonian model is inadequate to describe.Micropolar fluid, a non-Newtonian fluid, considers the suspension of naturally buoyant blood particles in a viscous fluid where the individuality of the substructures affects the flow. Charya [5] modelled the steady blood motion as a micropolar fluid to account for the microspin of the particles in a suspension. The study examined the blood flow through a nonsymmetric channel with continuous constricted boundaries. The rheological blood properties together with the shape and size of the stenosis become

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

“…Kumari and Nath [5] presented an unsteady boundary layer flow of a micropolar fluid at a stagnation point. Abdullah and Amin [6] treated the flow of blood as a micropolar fluid through a tapered artery with a stenosis. Seddeek [7] examined the flow of a micropolar fluid over the continuous moving plate.…”

Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery

“…The micropolar fluid model is a common choice to account for the suspension nature of blood in fluid dynamical studies on blood flow through stenotic arteries. This model has been successfully used by Abdullah and Amin 15 and Abdullah et al 16 to investigate the characteristics of blood through a tapered stenotic artery. The shear-thinning nature of blood in hemodynamical studies is mostly captured by the use of Generalized Newtonian Fluid (GNF) models.…”

Numerical Investigation of Pulsatile Blood Flow in Stenosed Artery

“…The governing equations for the axisymmetric micropolar flow in the cylindrical polar coordinate system may be written in nondimensional forms as follows [1,12]:…”

“…The theory can be used to explain the flow of colloid fluids, liquid crystals, animals blood, etc. The classical NavierStokes equations are incapable of explain the microrotations or particles' spin of suspensions [1,12]. Micropolar fluid takes care of the rotation of fluid particles by means of spin vector, so using these fluids for blood stream is more appropriate than other non-Newtonian fluids [17].…”

“…Abdullaha and Amin [1] presented a nonlinear two-dimensional mathematical model for the blood flow in a tapered artery with a single stenosis. They assumed that the blood flow as a single-layered micropolar fluid and concluded that the increase in the value of the taper angle leads to an increase in the axial velocity and the flow rate and a decrease in the radial velocity and the resistance to flow.…”