Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

Abstract

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R = 0 to r/R = 1 and it follows a concave pattern when we move from r/R = 0 to r/R = −1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

Analysis of dynamics variation against thixotropic parameter’s preferential range

“…Also, it is noted that pressure gradient decreases with increase in λ-values. Additionally, we observe that the change in pressure gradient corresponding to the change in yield stress for Thixotropic model for λ = 0.1 tends to match with the results in the case of Herschel-Bulkley's model [38] but for our choice of consistency index value. Thus, we have deduced that parameter λ influences the arterial flow and plays its role in causing changes in dynamics in addition to the role of varying yield stress of fluid.…”

“…On the basis of the pattern of red blood cell aggregation in the form of rouleaux structure and its disintegration due to flow, the suitability of Casson and Herschel-Bulkley models was discussed in detail in [35][36][37]. Working on the subject of blood flow through a stenosed artery, Priyadharshini et al discussed the dynamics of flow in the context of movement of the artery wall and the factor of dilation using Herschel-Bulkley model [38]. The role of time parameter in the dynamics of blood flow due to bifurcating movements of vessels was investigated in [39][40][41].…”

Herschel-Bulkley Magnetized Blood Flow Model for an Inclined Tapered Artery for an Accelerated Body

“…Similarly, one can expand the shear stress ̅̅̅̅̅( , , ), the plug core radius ( , ), the plug core velocity ( , ),and the plug core shear stress ̅̅̅( , ), in terms of ̅̅̅ 2 . Substituting the perturbation series expansions of and in [9] and then equating the constant term and ̅̅̅̅̅ 2 terms respectively one can obtain the first approximation and the second approximation as,…”

“…Priyadharshini et.al. [9] has analysed that the blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of Abstract: Analytical investigation of Herschel-Bulkley model for axisymmetric pulsatile blood flow through an inclined stenosed artery of a periodically accelerated body under the influence of a magnetic field has been done.…”

Role of a structural parameter in modelling blood flow through a tapering channel

“…However, limitation of Casson model in a complete description of blood flow dynamics was brought up by Blair and Spanner [38]. The use of Herschel-Bulkley model to include many physiological characteristics of blood flow was adopted by Priyadharshini and Ponalgusamy [39,40]. The factors of timed movement of channel due to peristaltic flow and tapering of the channel wall were studied by Mandal, Manton and Whitemore [41][42][43].…”