Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries

Abstract

The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model.

Two-fluid non-Newtonian models for blood flow in catheterized arteries — A comparative study

“…(11)-(16), one can obtain the following expressions for the shear stress and velocity distribution in the core region and the peripheral region. 25) are given in Sankar and Lee [20]. By the continuity of the velocity distribution throughout the flow field, we have the condition…”

“…Hence, for a more realistic description of blood flow, it is appropriate to treat the blood as a two-fluid model consisting of a core region containing all the erythrocytes as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid [17][18][19]. Sankar and Lee [20,21] have analyzed two-phase fluid models for blood flow through narrow arteries at low shear rates, by treating the fluid in the core region as (i) Casson model and (ii) HerschelBulkley (H-B) model, respectively. In both two-fluid models, the fluid in the peripheral layer is treated as Newtonian fluid.…”

“…Hence, in this paper, we have compared the effect of various parameters on the flow quantities of the two-fluid H-B model and two-fluid Casson model and brought out the advantages of two-fluid H-B model over the two-fluid Casson model for the flow of blood through catheterized arteries. The governing equations and the boundary conditions of both the two-fluid models, and the expressions obtained for the various flow quantities of these models by Sankar and Lee [20,21] are mentioned in brief in this study and are used to perform a comparative study.…”

Ferromagnetic effects for nanofluid venture through composite permeable stenosed arteries with different nanosize particles

“…3 Herschel Bulkely fluid in stenosed arteries has been examined by Sankar and Lee. 4 The mathematical modelling done by them was for pulsatile flow. They used regular perturbation technique and found analytical solutions.…”

Mathematical Model of Blood Flow in Small Blood Vessel in the Presence of Magnetic Field

“…They also reported the viscosity increases non-linearly with the hematocrit. Bugliarello and Sevilla [6], Cokelet [7] and [8][9][10] have reported that for blood flowing through narrow blood vessels, there is a peripheral layer of plasma and a core region of suspension of all the erythrocytes.…”