Inertial migration of red blood cells under a Newtonian fluid in a circular channel

TL;DR

This study numerically investigates how red blood cells migrate laterally in a circular channel under various flow conditions, revealing bistable flow modes and their impact on equilibrium positions and energy dissipation.

Contribution

It introduces a detailed numerical model of RBC inertial migration considering membrane properties, initial orientations, and flow modes, highlighting the bistability and energy aspects of RBC dynamics.

Findings

RBCs exhibit bistable rolling and tumbling motions.

Tumbling RBCs are farther from the channel center than rolling ones.

Membrane deformation energy depends on flow mode and viscosity ratio.

Abstract

We present a numerical analysis of the lateral movement and equilibrium radial positions of red blood cells (RBCs) with major diameter of 8 $\mu$m under a Newtonian fluid in a circular channel with 50-$\mu$m diameter. Each RBC, modelled as a biconcave capsule whose membrane satisfies strain-hardening characteristics, is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$, the latter of which indicate the ratio of the fluid viscous force to the membrane elastic force. The effects of initial orientation angles and positions on the equilibrium radial position of an RBC centroid are also investigated. The numerical results show that depending on their initial orientations, RBCs have bistable flow modes, so-called rolling and tumbling motions. Most RBCs have a rolling motion. These stable modes are accompanied by different equilibrium radial positions, where tumbling RBCs are further away from the channel axis than rolling ones. The inertial migration of RBCs is achieved by alternating orientation angles, which are primarily affected by the initial orientation angles. Then the RBCs assume the aforementioned bistable modes during the migration, followed by further migration to the equilibrium radial position at much longer time periods. The power (or energy dissipation) associated with membrane deformations is introduced to quantify the state of membrane loads. The energy expenditures rely on stable flow modes, the equilibrium radial position of RBC centroids, and the viscosity ratio between the internal and external fluids.