Multiphase flow of blood through arteries with a branch capillary: A theoretical study

In this paper, we present a theoretical analysis of the problem of hematocrit reduction ( due to plasma skimming) in a capillary that emerges from an artery making an angle a with the parent artery. The analysis bears the potential to explore a variety of information regarding some phenomenological aspects of this important physiological problem. The flow is considered to consist of three distinct phases, viz., the peripheral plasma layer, the cell-depleted middle layer, and the core region which usually has a high concentration of erythrocytes. This study deals with both steady and pulsatile flow of blood, which is treated as a non-Newtonian fluid of Herschel-Bulkley type. A computational procedure is developed for a quantitative measure of the velocity profile, the volumetric flow rate, and the hematocrit of blood in a specific situation. The procedure also gives us an opportunity to examine the nature of variation of these important hemodynamic factors; this observation holds true irrespective of whether the flow of blood is steady or pulsatile. The study reveals that the velocity of blood in the parent artery reduces when the fluid index/yield stress increases. It is further revealed that the volumetric flow rate of blood in the capillary also decreases with an increase in the value of the fluid index/yield stress of blood.