# A Numerical Investigation on the Effect of Size and Volume Fraction of Red Blood Cells in a Microchannel with Sudden Expansion

## TL;DR

This study uses numerical simulations to explore how red blood cell size and concentration affect their distribution and pressure in microchannels with sudden expansions.

## Contribution

The study introduces a parabolic correlation for predicting pressure drop based on hematocrit with high accuracy.

## Key findings

- RBC migration and distribution are strongly influenced by RBC size and hematocrit.
- Pressure drop is primarily affected by hematocrit, with a minimum at a hematocrit of 0.3.
- A parabolic correlation predicts pressure drop with a maximum relative error of 1.13%.

## Abstract

This study numerically investigates the effects of red blood cell (RBC) volume fraction (hematocrit) and RBC diameter on cell distribution, cell-free layer (CFL) thickness and pressure drop in a microchannel with sudden expansion. Hematocrit levels of 0.2, 0.3, 0.4 and 0.5, together with RBC diameters of 4, 8 and 11 µm, are considered, where deviations from the physiological diameter of 8 μm represent pathological conditions. An Euler–Euler approach is employed to model the multiphase flow, treating RBCs as rigid spherical particles, while the non-Newtonian viscosity of blood is represented using a modified Carreau–Yasuda model. The numerical predictions are validated against existing experimental and numerical data. The effect of volumetric flow rate on RBC distribution is found to be limited; therefore, a representative flow rate of 100 μL/min is adopted for the subsequent analysis. The results show that RBC migration and the resulting cell distribution are strongly governed by RBC size and hematocrit. The pressure drop is primarily influenced by hematocrit, while the effect of RBC size is relatively weak. A minimum value for pressure drop is observed at a hematocrit of 0.3, indicating an optimal hematocrit level for minimizing flow resistance. A parabolic correlation is proposed for predicting the pressure drop as a function of hematocrit, with a maximum relative error of 1.13%. This study contributes to the understanding of pathological RBC size variations and their impact on microscale hemodynamics.