Abstract
Mathematical modeling of the blood flow with a resolved description of biological cells mechanics such as red blood cell (RBC) has been a challenge in the past decades as it involves physical complexities and demands high computational costs. In the present study, we propose an approach for efficient simulation of blood flow with several suspended RBCs. In this approach, we employ our previously proposed reduced-order model for deformable particles (Nair et al. in Comput Part Mech 7:593–601, 2020) to mimic the mechanical behavior of an individual RBC as a cluster of overlapping spheres interconnected by flexible mathematical bonds. This discrete element method-based model is then coupled with a fluid flow solver using the immersed boundary method with continuous forcing in the context of computational fluid dynamics-discrete element method (CFD-DEM) coupling. The present computational method is tested with a couple of validation cases in which the single RBC dynamics, as well as the blood flow with several RBCs, were tested in comparison with existing literature date. First, the RBC deformation index in shear flow at different shear rates is studied with a good accuracy. Then, the blood flow in micro-tubes of different diameters and hematocrits was simulated. The key characteristics of blood flow such as cell-free layer (CFL) thickness, Fahraeus effect and the relative apparent viscosity are used as the validation metrics. The proposed approach can predict the formation of the migration of RBC toward the tube center-line and the CFL thickness in good agreement with previous measurement and simulations. Furthermore, the model is employed to study the CFL enhancement for plasma separation based on channel constriction. The simulation results compute the CFL thickness downstream of the channel constriction in good agreement with the experiments in a wide range of flow rates and constriction lengths. The original contribution of this study lies in proposing an efficient resolved CFD-DEM simulation method for blood flows with many RBCs which can be employed for numerical investigation of bio-microfluidic applications.
Highlights
Blood is an important physiological fluid which is vital for the transportation of oxygen and nutrients to various parts of the body
This red blood cell (RBC) model is coupled with a modified version of the resolved computational fluid dynamics-discrete element method (CFD-DEM) solver cfdemSolverIB from the libraries of the open-source software package CFDEMcoupling [22,44]
An approach for modeling blood flow with several suspended red blood cells is presented in the context of resolved computational fluid dynamics (CFD)-DEM
Summary
Blood is an important physiological fluid which is vital for the transportation of oxygen and nutrients to various parts of the body. [19] proposed a torus of overlapping colloidal particles connected using worm-like chain (WLC) springs to represent an RBC This model is coupled to a Dissipative Particle Dynamics (DPD) method and revealed a good degree of accuracy with a reduction in computational cost, and lacked some of the critical behaviors of RBC such as viscoelasticity and tank-treading behavior. From a mathematical modeling viewpoint, such a combination of different sub-models is common in the simulation of dispersed multiphase systems, e.g., particle-laden flows In this context, the coupling between computational fluid dynamics and discrete element method (CFD-DEM) is employed to model the interaction between suspended particles and the carrier fluids. Following the concept of model order reduction, we have recently introduced a reduced-order model for deformable particles in the frame of DEM [21] In this model, a single RBC consists of several constituent spheres with their centroids interconnected by mathematical elastic bonds.
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