Study of Anomalous Behavior of blood flow in Capillary Surrounded by tissue

Abstract

A Mathematical model for the two phase flow of blood in a narrow capillary surrounded by the tissue has been presented in this paper. We have developed the earlier two phase models of blood flow in capillaries into a model of capillary-tissue fluid exchange system by including porous tissue enclosing the capillary. Blood is not a homogeneous fluid, It is a suspension. The suspended blood cells accumulate at the axis in response to flow, resulting in a blunting of the velocity profile near the axis in contrast to the parabolic profile observed in homogeneous fluids. Earlier models have not included the effect of fluid exchange in between the capillary and the tissue while microtubes or capillaries are surrounded by tissue. Therefore, our aim is to include effects of permeability of the tissue with two phase flow of blood in narrow tubes. The model consists of a core region of suspension of all erythrocytes and a peripheral layer of plasma surrounding the core. The governing partial differential equations have been solved by using mathematical and computational techniques. Analytical results, in the proposed model for apparent viscosity, Bluntness and ratio of capillary hematocrit with discharge hematocrit values have been presented and discussed through graphs for various values of parameters and with their axial variations.