A Modified Suspension-Balance Model for Deformable Particle Suspensions: Application to Blood Flows with Cell-Free Layer

We propose a modified suspension balance model (SBM) for the flow of red blood cells (RBCs) and other deformable particle suspensions in confined geometries. Specifically, the method includes the hydrodynamic lift force generated by deformable particles interacting with walls leading to a cell-free layer. The lift force is added to the SBM to drive RBCs migrating away from the wall. Using the modified SBM (MSBM), we simulate blood flows through microvascular channels and tubes. The method is able to capture the transient development of the cell-free layer (CFL) and the corresponding hematocrit and velocity profiles with the development of the CFL. The CFL thickness and hemorheological hallmarks in microcirculation, such as the Fahraeus Effect and the Fahraeus-Linqvist Effect, are captured in good agreement with existing experimental and direct numerical results of blood flows. This work establishes a novel continuum computational framework that can efficiently capture the microstructural heterogeneity and non-Newtonian flow behavior of concentrated deformable particle suspensions under confinement.

💡 Research Summary

In this paper the authors introduce a Modified Suspension‑Balance Model (MSBM) that augments the classical suspension‑balance framework with a wall‑induced hydrodynamic lift force to capture the migration of deformable particles such as red blood cells (RBCs) away from solid boundaries. The conventional suspension‑balance model (SBM) accounts for particle‑particle interactions through a particle‑phase stress tensor and a hindered‑settling drag term, but it neglects the non‑inertial lift that arises when deformable capsules interact with a wall. By adding a volume‑averaged lift term (L_{\perp}) to the inter‑phase force balance, the authors obtain a new governing equation for the particle migration flux: \