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If $\delta =0$, then $\epsilon =0$, the cell-rich material fills the gap, andIf $\delta =h$, then the core disappears andFor the physical ordering ${\mu }_w<\mu$, increasing the cell-free layer thickness monotonically lowers ${\mu }_{\mathrm{eff}}$ between these limits, exactly as intuition and the Fahraeus--Lindqvist effect suggest.

The Fahraeus--Lindqvist effect is the decrease of blood's apparent or effective viscosity as a microvessel narrows through much of the physiological small-vessel range. Deformable red blood cells migrate away from the wall and concentrate near the centre, creating a cell-free layer of relatively low-viscosity plasma beside the vessel wall. Because the largest shear occurs near the wall, replacing cell-rich blood there by plasma reduces hydraulic resistance particularly effectively. At diameters comparable with a red blood cell, confinement eventually invalidates this decreasing trend.