Laminar Flow and Blood Oxygenation in Channels With Boundary Irregularities

Abstract

To understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in a channel with irregular surfaces where the spread of the surface roughness is large compared to the mean width of the channel. The hydrodynamic solution is then used to obtain the effects of wall roughness upon the blood oxygenation in a membrane oxygenator. The effects of various pertinent parameters upon the flow field, energy loss, and oxygen concentration, and possible occurrence of separation and reattachment are examined for symmetric and nonsymmetric channels with sinusoidal variation. It is found that when the blood is assumed to behave like a homogeneous fluid the wall irregularity has a strong effect on local oxygen concentration distribution, but has little effect on the saturation length. The saturation length is found to be of the order of 3/2 (1 + FS0/P0)ReScd for a channel with, or without, wall irregularity. Therefore, the secondary flows induced by the cell-plasma and cell-cell interaction is more likely the primary mechanism for a vast increase in oxygenation efficiency using wavy channels reported by Kolobow, et al.