Red blood cell migration in microvessels

Red blood cell (RBC) migration effects and RBC-plasma interactions occurring in microvessel blood flow have been investigated numerically using a shear-induced particle migration model. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced RBC migration in concentrated suspensions. The model couples a non-Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the viscosity is dependent on the haematocrit and the shear rate (Quemada model). The focus of this paper is on the determination of the two phenomenological parameters, Kc and Kmu, in a diffusive flux model when using the non-Newtonian Quemada model and assuming deformable particles. Previous use of the diffusive flux model has assumed constant values for the diffusion coefficients which serve as tuning parameters in the phenomenological equation. Here, previous data [Biophys. J. 92 (2007), 1858-1877; J. Fluid Mech. 557 (2006), 297-306] is used to develop a new model in which the diffusion coefficients depend upon the tube haematocrit and the dimensionless vessel radius for initially uniform suspensions. This model is validated through previous publications and close agreement is obtained.