Numerical simulation of blood flow modeled as a fluid- particulate mixture

Abstract

ABSTRACT A continuum model for the transport of red blood cells (RBC) inside arteries and capillaries of small diameters is proposed. The pressure and velocity fields are solved using the Navier-Stokes equations while the distribution of the RBC volume fraction, namely, hematocrit is obtained by solving the particle transport equation arising from the diffusive flux model. The momentum and hematocrit transport equations are coupled through a hematocrit-dependent blood viscosity model. The coupled equations are numerically solved using a 3D unstructured finite volume method. The proposed model predicts the shear induced diffusion of RBCs where RBCs migrate from the wall to the center of the blood vessel leading to a cell free layer (CFL) near the wall. Three geometries with sizes of the order of 40 µm have been considered for the present work. For flow inside a tube, results in terms of the concentration distribution and cell-free layer from the present continuum model show a good match with experiments and DPD simulations. For flow inside a tube with a constriction it is found that hematocrit depletion is greater downstream of the neck of the constriction. In addition, the effect of hematocrit loading on its distribution is correctly predicted. Finally, for a flow inside a tube with a bifurcation the average hematocrit concentration is found to be higher for the branch with the higher flow rate, thereby complying with the well-known bifurcation law.