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

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.

💡 Research Summary

The paper presents a comprehensive analytical and numerical investigation of peristaltic transport of blood in micro‑circulatory vessels whose cross‑section varies along the axial direction. Blood is modeled as a Herschel‑Bulkley fluid, incorporating a yield stress (τ₀), a consistency index (k) and a power‑law index (n) to capture its non‑Newtonian, shear‑thinning or shear‑thickening behavior. The peristaltic wave is assumed sinusoidal, described by amplitude a, wavelength λ and wave speed c, while the vessel radius is expressed as R(z)=R₀