Abstract
Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.
Highlights
The analysis of blood flow through stenosed arteries is very important because of the fact that the cause and development of many arterial diseases leading to the malfunction of the cardiovascular system are, to a great extent, related to the flow characteristics of blood together with the geometry of the blood vessels
We study a two-phase fluid model for pulsatile flow of blood through stenosed narrow arteries assuming the fluid in the core region as a Herschel-Bulkley fluid while the fluid in the peripheral region is represented by a Newtonian fluid
When R1 R, the present model reduces to the single fluid model Herschel-Bulkley fluid model and in such case, the expressions obtained in the present model for velocity uH, shear stress τH,wall shear stress τw, flow rate Q, and plug core radius RP are in good agreement with those of Sankar and Hemalatha 2
Summary
The analysis of blood flow through stenosed arteries is very important because of the fact that the cause and development of many arterial diseases leading to the malfunction of the cardiovascular system are, to a great extent, related to the flow characteristics of blood together with the geometry of the blood vessels. Bugliarello and Sevilla and Cokelet have shown experimentally that for blood flowing through narrow blood vessels, there is an outer phase peripheral layer of plasma Newtonian fluid and an inner phase core region of suspension of all the erythrocytes as a nonNewtonian fluid. Srivastava and Saxena 25 have analyzed a two-phase fluid model for blood flow through stenosed arteries treating the suspension of all the erythrocytes in the core region inner phase as a Casson fluid and the plasma in the peripheral layer outer phase is represented by a Newtonian fluid. In this paper, we study a two-phase fluid model for blood flow through mild stenosed narrow arteries of diameter 0.02 mm–0.1 mm at low-shear rates γ < 10/sec treating the fluid in the core region inner phase as a Herschel-Bulkley fluid and the plasma in the peripheral region outer phase as a Newtonian fluid. The estimates of wall shear stress increase factor and the increase in resistance to flow factor are calculated for the two-phase Herschel-bulkley fluid model and single-phase fluid model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
