Development of a two-dimensional model of blood microcirculation flows

Abstract

This thesis presents the development of a dimensionless blood microcirculation model for the study of blood microcirculation flows. It is a two dimensional, axially symmetric, incompressible, Newtonian-flow, Krogh cylinder model subjected to axially periodic boundary conditions. This model formulation allows for the use of the streamfunction-vorticity formulation of the Navier-Stokes equation, which offers simplification to boundary conditions and also allows for the use of a non-uniform, collocated mesh. A streamfunction vorticity formulation of the Immersed Boundary Method is also developed, specifically for the boundary conditions along the immersed boundary (red blood cell membrane). Periodic boundary conditions are used, with the assumption of fully-developed flow, in order to focus on the effects of the transient diffusion of oxygen into the surrounding tissue, orthogonal to the capillary flow direction.