A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

The earlier constitutive model of Fang & Owens ( Biorheology , vol. 43, 2006, p. 637) and Owens ( J. Non-Newtonian Fluid Mech . vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus–Lindqvist effect whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in sufficiently small vessels. That this is due to the development of a slippage layer of cell-depleted fluid near the vessel walls and a decrease in the tube haematocrit is demonstrated from the numerical results. Although clearly influential, the reduction in tube haematocrit observed in small-vessel blood flow (the so-called Fåhraeus effect) does not therefore entirely explain the Fåhraeus–Lindqvist effect.