Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

TL;DR

This paper presents a theoretical analysis of non-Newtonian blood flow in micro-vessels, highlighting how vessel shape and blood properties influence flow characteristics like velocity and shear stress.

Contribution

It introduces a generalized model for non-Newtonian peristaltic blood flow in micro-vessels with variable cross-section, considering Herschel-Bulkley fluids and SSD wave propagation.

Findings

Flow behavior is significantly affected by vessel non-uniformity.

Amplitude ratio and fluid index strongly influence velocity and shear stress.

Peristaltic transport differs notably between channel and circular vessel geometries.

Abstract

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of the blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.