Poiseuille flow of a fluid with couple stress with applications to blood flow

Abstract

In this paper, the Poiseuille flow of blood is studied. Blood is assumed to be a fluid with couple stress. In order to verify that the rheological properties of blood can be explained in terms of the linear couple stress theory, we compare the velocity profiles of theoretical solutions with the ones obtained experimentally. Very good agreement is observed by choosing the appropriate values for the couple stress parameters $\overline{\mathit{\alpha }}$ and $\overline{\mathit{\eta }}$ for different concentration factors of erythrocytes. The effects of the concentration factor on the velocity profile as well as on the values of the velocity are also discussed. We conclude that as far as Poiseuille flow is concerned blood flow characteristics can be explained in terms of the linear couple stress theory.