Pulsatile flow of particle-fluid suspension model of blood under periodic body acceleration

Abstract

A particle-fluid suspension model is applied to the problem of pulsatile blood flow through a circular tube under the influence of body acceleration. With the help of finite Hankel and Laplace transforms, analytic expressions for axial velocity for both fluid and particle phase, fluid acceleration, wall shear stress and instantaneous flow rate have been obtained. It is observed that the solutions can be used for all feasible values of pulsatile and body acceleration Reynolds numbers Rp and Rb. Using physiological data, the following qualitative and quantitative results have been obtained. The amplitude Qb of instantaneous flow rate due to body acceleration decreases as the tube radius decreases. The effect of the volume fraction of particle C on Qb is to increase it with increase of C in arteriole and to decrease Qb as C increases in coronary and femoral arteries. The maximum of the axial velocity and fluid acceleration shifts from the axis of the tube to the vicinity of the tube wall as the tube diameter increases. The effect of C on the velocity and acceleration are nonuniform. The wall shear amplitude \(\tau_b\) due to body acceleration increases as the tube diameter decreases from femoral to coronary and a further decrease in the tube diameter leads to a decrease in \(\tau_b\). The effects of C on \(\tau_b\) are again nonuniform.