A non-homogeneous constitutive model for human blood: Part II. Asymptotic solution for large Péclet numbers

In tube flow of healthy human blood the formed elements typically migrate away from vessel walls, leaving a plasma-rich, cell-depleted region there. In larger tubes (corresponding in size to arteries, for example) and at physiologically realistic flow rates, very thin wall boundary layers may develop which, nonetheless, have an impact upon the bulk flow properties. In this paper the non-homogeneous blood model of Moyers-Gonzalez et al. [M. Moyers-Gonzalez, R.G. Owens and J. Fang, A non-homogeneous constitutive model for human blood. Part I. Model derivation and steady flow, submitted for publication] is used in combination with a novel matched asymptotic method, to study the boundary layer behaviour of the steady tube flow of blood at high Péclet numbers Pe$Pe$ and in vessels of diameters corresponding to those of small arteries. A boundary layer thickness of O(Pe^−1/2)$O(P{\text{e}}^{-1/2})$ is predicted. In the absence of stress diffusion (the homogeneous case, with Pe=∞$Pe=\infty$) no cell migration takes place and the size and number density of red cell aggregates along the axis of symmetry remains constant at all flow rates. In the non-homogeneous case, however, even at very high values of Pe$Pe$, particles migrate, introducing a thin apparent slip layer next to the wall and affecting the aggregate distribution throughout the flow, even on the axis of symmetry.