The effective viscosity of blood in minute vessels highly depends on the vessel radii because of the presence of red blood cell (RBCs), known as the Fåhræus-Lindqvist effect. A single-file flow pattern forms in the narrowest capillaries, with vessel radii below $5\mu \mathrm{m}$, whereas a double-file flow pattern, in which RBCs flow alternately, emerges in wider vessels. Our interest here is to understand how vessel curvature influences these flow patterns, since curved vessels frequently appear both in vivo bodies and in microfluidic devices. We performed direct numerical simulations of pressure-driven RBC flows in toroidal vessels with constant curvature. Our analysis reveals that the transition from single-file to double-file flow is promoted as the effect of vessel curvature increases. The effective viscosity in the double-file regime is higher than in the single-file regime, because wall shear stress is amplified as the gap between RBCs and the vessel wall is reduced. We also show that internal energy dissipation within RBCs is small in single-file flow due to limited membrane rotation, whereas double-file flow exhibits pronounced energy dissipation by enhanced membrane rotations. In contrast, dissipation in the surrounding fluid and in the entire system shows the opposite trend, since the total dissipation is closely related to the flow rate. We further investigate the effects of RBC swelling, which is associated with diseases such as malaria. Our results indicate swollen RBCs are more likely to maintain a single-file arrangement, and that the flow pattern itself—rather than the swelling ratio—is the dominant factor governing the effective viscosity. These findings provide fundamental insights for the design of microfluidic devices.

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• Blood flow
• Capsule & cell dynamics
• Haemodynamics