A new numerical approach using the VOF method to model the two-layered Herschel-Bulkley blood flow in microvessels

Abstract

In this paper, we propose a novel numerical approach to model the complex blood flow in microvessels using a two-layered fluid representation. The model considers blood flow as two layers of homogeneous, immiscible fluid with different viscosities: a core layer, rich in erythrocytes (red blood cells, RBCs), occupying the central region of the vessel, and a peripheral cell-free plasma layer (CFL) near the vessel walls. The Herschel-Bulkley constitutive model governs the core layer as a non-Newtonian viscoplastic fluid, accounting for its yield stress and shear-thinning behavior. We model the plasma layer as a Newtonian fluid with constant viscosity. We numerically solve the governing equations for fluid motion in an axisymmetric tube geometry to account for unsteady, incompressible flow. We employ the Volume of Fluid (VOF) method to accurately model the interaction between two immiscible fluids. Comparisons with the analytical one-dimensional Herschel-Bulkley model for single-layer fluid flow, two-layered fluid flow, and with the experimental data have shown that the two-layer model is valid and that the proposed method can accurately predict the dynamic behavior of blood flow in microvessels. Furthermore, numerical results reveal the presence of a plug flow region at the centerline of the vessel. The rheological properties of the core fluid, particularly the hematocrit level and yield stress values, significantly influence the thickness of the cell-free layer (CFL) and the plug flow radius. As both hematocrit and yield stress increase, the CFL thickness decreases while the plug flow radius expands. We also observe that the Reynolds number has a minimal impact on the characteristics of the CFL and the plug flow region. These results show that the two-layered numerical approach is a good way to accurately predict how blood flow moves in microvessels.