Accurate modeling of blood flow in a micro-channel as a non-homogeneous mixture using continuum approach-based diffusive flux model

Abstract

This paper presents a continuum approach for the blood flow simulation, inside the micro-channel of the few micrometers characteristics dimension, within the context of the finite volume method on unstructured grids. The velocity and pressure fields, for the blood flow, are obtained here by solving the Navier–Stokes equations. A particle transport equation, based on the diffusive flux model, provides the hematocrit distribution (i.e., the red blood cells volume-fraction). The momentum conservation equation for a non-Newtonian fluid model is coupled with the particle transport equation through the constitutive blood viscosity model, and this blood viscosity is dependent on hematocrit and shear rate. The continuum approach for blood flow inside the micro-channel of the length scale of a few micrometers to a few hundred micrometers is expected to break down. Interestingly, the present approach provides meaningful insights into biophysics with less computational cost and shows a good match with the experiments and mesoscale simulation with a maximum average deviation of 11% even at the characteristic dimensions of 10–300 μm. A correlation is proposed for additional-local shear rate in terms of the hematocrit and the ratio of red blood cells diameter to the channel diameter, which helps us to demonstrate an increase in the accuracy and also eliminates the issues of unphysical hematocrit reported in the earlier studies available in the literature. The study is extended to provide new results inside a square and rectangular cross section micro-channels, under a range of inlet parameters.