Red blood cells transition from single-file to two-file induced by streamline curvature*

Red blood cells(RBCs) in narrow capillaries take parachute-like shape and flow in single-file. In wider vessels, RBCs take slipper-like shape and flow in two-file. Previous research on these phenomena is mainly focused on straight vessels, while actual flow in human body or microfluidic devices include curve or bifurcation. In this research, we investigated the effect of streamline curvature for blood flow by numerical simulation. The immersed boundary method was employed to calculate the motion of RBCs. Simulations were conducted in toroidal vessels and a straight vessel. Imposed pressure gradient and vessel radius were set to be the same. Initial distributions of RBCs were in single-file in both simulations. Transition from single-file to two-file was observed only in toroidal pipe. Additionally, the effective viscosity increased after the transition. In single-file flow, the gradient of angular velocity was small because flow rotates as if solid body. However, in two-file flow, the gradient of angular velocity increased because each RBCs can move separately. The effective viscosity increase is caused by the difference of red blood cells motions and energy dissipation between single-file flow and two-file flow.