Peristaltic Pumping of Blood Through Small Vessels of Varying Cross-section

TL;DR

This study analyzes how peristaltic motion influences blood flow in small, variably shaped vessels, considering blood as a Herschel-Bulkley fluid, and examines the effects of various parameters on flow characteristics.

Contribution

It provides an analytical and numerical investigation of blood flow in non-uniform vessels considering Herschel-Bulkley fluid properties and sinusoidal peristaltic waves, which is novel.

Findings

Velocity and wall shear stress are significantly affected by vessel geometry.

Flow characteristics are highly sensitive to amplitude ratio and fluid index.

Non-uniform vessel geometry influences blood flow and shear stress patterns.

Abstract

The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, streamline pattern and wall shear stress. On the basis of the derived analytical expression, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the non-uniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.