Linear stability analysis of blood flow in small vessels

We investigate the linear stability of unidirectional Poiseuille flow of blood modeling the fluid as a spatially inhomogeneous fluid in which viscosity depends on the red blood cell concentration (RBCs). We consider small vessels like arteries terminal branches, arterioles or venules, where the inhomo-geneity is due to the non uniform distribution of RBCs on the vessel cross section. The stability analysis is performed applying the classical normal-mode linear analysis which results in a fourth-order eigenvalue problem that is solved numerically. The results obtained indicates that the flow is unconditionally unstable. However, those patterns in which the RBCs concentration decreases towards the vessel walls show growth rates so small that the observability of the instability requires a very large time. Conversely, the growth rates associated to the profiles in which the RBCs concentration increases toward the vessel walls are at least three order of magnitude larger than the previous case. We therefore believe that those distributions in which the RBCs are more concentrated around the vessel center are to be considered more “stable” than those in which RBCs accumulate towards the vessel walls.