We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high con finement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.

We study the focusing of red blood cells and vesicles in pressure-driven flows in highly confined microchannels (10–30 um), identifying the control parameters that dictate the cell distribution along the channel. Our results show that an increase in the flow velocity leads to a sharper cell distribution in lateral position of the channel. This position depends on the channel width, with cells flowing at outer (closer to the walls) positions in thicker channels. We also study the relevance of the object shape, exploring the different behaviour of red blood cells and different vesicles. We also analyze the implications of these phenomena in the cell suspension rheology, highlighting the crucial role of the wall confinement in the rheological properties of the suspension.