Study of blood flow in several benchmark micro-channels using a two-fluid approach

Abstract

It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs.

Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms

“…where T f and T s represent the Cauchy stress tensors for the plasma and the RBCs, respectively, b f and b s are the body forces, and f I stands for the interaction forces (exchange of momentum) between the components, (for more information about the derivation operator, see [22]). The balance of the angular momentum implies that, in the absence of couple stresses, the total Cauchy stress tensor is symmetric.…”

“…It is noted that Equations (9a,b) imply that when the hematocrit approaches zero the viscosity of RBCs reduces to zero. One of the outstanding advantages of the current viscosity model is that we use a larger set of experimental data, where the hematocrit ranges from 8.6% to 70.2%; therefore, this correlation is, in a sense, more general and better suited for studying problems when the local hematocrit varies heavily in the flow region [22]. Similar to the plasma, the term β 20 φ + φ 2 trD s disappears automatically, because we consider the RBC component to be incompressible.…”

“…Experimental data is by Brooks [29]. The figure is reused with permission from [22], Copyright Elsevier, 2015.…”

“…We assume that ( ) has the following properties: (1) ( ) must be a monotonic increasing function of , so that the platelets are always excluded by the RBCs and diffuse to a region with lower volume fraction of the RBCs; (2) When = 0, ( ) = 0, which means that when there is no RBC, the RBCs-induced Experimental data is by Brooks [29]. The figure is reused with permission from [22], Copyright Elsevier, 2015.…”

“…Therefore, in the present study, a continuum multicomponent model is applied. The multicomponent model was previously developed by our group [21,22], in which the flow of the plasma and RBCs are modeled by mixture theory and the platelets transport is modeled by a convection-diffusion equation. The advantage of this continuum approach is its economical computational cost compared with the mesoscale simulations; therefore, it can be potentially applied to very large-scale problems with complex geometries.…”