Flow of a Casson fluid in a narrow tube with a side branch

Abstract

Development of a mathematical model suitable for studying the mass-flux and hematocrit reduction due to plasma skimming in a capillary emerging from an artery making an angle α with the parent artery is of primary concern in the paper. The flow is considered to have three phases – the peripheral plasma layer, the cell depleted middle layer and the core region where the concentration of erythrocytes is highest. Both steady and pulsatile flow situation are studied. The analysis for pulsatile flow has been carried out by considering the pressure gradient as a periodic function of time and the inertial effects as negligibly small. A perturbation technique is employed to solve the resulting quasi-steady non-linear system of equations that are considered to govern the flow. Basing upon relevant experimental data available for coronary arteries as well as very small vessels of the circulatory system, the study has been performed by considering Womeresely parameter to be small (less than unity). The theoretical estimates computed under the purview of the present mathematical analysis reveal that hematocrit in the branch capillary decreases with an increase in the yield stress of blood, both in steady and pulsatile flows for any branching angle. Further, erythrocytes entrainment from the parent artery to the branch capillary is least when the branch is perpendicular to the parent artery.