Analysis of the Flow Dynamics of Blood Through Viscoelastic Constricted Artery

Abstract

In this paper, we focused on the flow through an axisymmetric constricted artery of the pulmonary region to study the condition of stenosis. Theory of dust particles suspended in gas is applied on blood flow through the artery, where the “particles” represent “cells” suspended in plasma. The flow is governed by two dimensional Navier–Stokes’ equations by including Darcy–Forchheimer drag force caused by non-Darcian effect. The material of the artery is approximated as a linear elastic and simplest rheological equation that includes viscosity and elasticity (considered lung as a Voigt body) is used. Effect of various parameters, such as Reynolds number (Re), Forchheimer number ($$F_s$$), Darcy number (Da), aspect ratio ($$\beta $$), shape factor ($$S_f$$), porosity ($$\epsilon $$), aerodynamic diameter ($$d_p$$), bulk compression ($$\phi $$) of elasticity, shear ($$\eta $$) and bulk ($$\zeta $$) coefficients of parenchymal viscosity are obtained on the radial and axial velocities of blood and particles graphically. We found that the fluid (blood) and particle (cells suspended in plasma) velocities along both the axes (axial and radial) increase by increasing Reynolds number, the pulsating amplitude, aspect ratio, and porosity of walls. While by increasing Forchheimer number, velocities of blood and particles in both the axes decreases gradually. The present analysis is also indicate that the viscoelasticity of walls are affected by the amplitude of pulsatile flow of blood and for a large value of amplitude, the viscoelastic effect decreases.