MODELING THE LOWER AND THE UPPER REGIME OF THE BLOOD UNIDIRECTIONAL FLOW IN MICRO-VESSELS

Abstract

There is a formation of a cell-depleted layer adjacent to micro-vessel walls during blood flow in regime of creeping flow. This biological layer is of vital importance in the transport of oxygen-saturated red cells to the unsaturated tissues. In this work, we first discuss the physical mechanisms in this creeping flow which lead to the formation of a cell-depleted layer. The main non-dimensional physical parameter governing the layer formation are presented from a simple model of predicting the layer thickness in steady state. In particular, we study the blood flow in two different scales (i.e. lower and upper bound limit) of the in vitromicrocirculation. For this end we examine the capillary core flow solution in which the inner fluid is considered a non-Newtonian one facing a small annular gap of a Newtonian plasma. This model is a good approximation for the blood flow occurring in the length scales of venules and arterioles diameters. In addition, we also propose a model for smaller vessels, like capillaries with diameter of few micrometers. In this lower bound limit we consider a periodic configuration of lined up paraboloidal cells moving in a flow under regime of lubrication approximation. So, the boundary condition in this lower flow limit considers the cell velocity and a numerical integration is used to solve the volumetric flux as a function of the pressure drop inside the capillary. The effect of the cell volume fraction in terms of the depleted layer thickness and cell aggregations is also investigated with this model. The influence of the wall irregularities on the flow is studied by using a simple sinusoidal model for the wall. Finally, an intrinsic viscosity of the blood is predicted theoretically for both the lower and upper bound regimes as a function of the non-dimensional vessel diameter, in good agreement with previous experimental works. We compare our theoretical predictions with experimental data and obtain a qualitative good for the classic Fahraeus-Lindqvist effect. A possible application of this work could be in illness diagnosis by evaluating of changes in the intrinsic viscosity due to blood abnormalities. Keywords: blood, hydrodynamic diffusion, non-Newtonian, rheology, cell-depleted layer