Viscoelasticity of suspension of red blood cells under oscillatory shear flow

TL;DR

This study numerically investigates the viscoelastic behavior of red blood cell suspensions under oscillatory shear flow, revealing how frequency influences complex viscosity and stress differences, with implications for understanding blood rheology.

Contribution

It introduces a detailed numerical model of RBC suspensions under oscillatory shear, highlighting the frequency-dependent viscoelastic properties and the roles of cell deformation and membrane interactions.

Findings

Complex viscosity weakly depends on individual RBC deformations.

Oscillatory shear reduces normal stress differences compared to steady shear.

Viscosity ratio and capillary number influence suspension rheology.

Abstract

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) for different volume fractions in a wall-bounded, effectively inertialess, small amplitude oscillatory shear (SAOS) flow for a wide range of applied frequencies. The RBCs are modeled as biconcave capsules, whose membrane is an isotropic and hyperelastic material following the Skalak constitutive law. The frequency-dependent viscoelasticity in the bulk suspension is quantified by the complex viscosity, defined by the amplitude of the particle shear stress and the phase difference between the stress and shear. SAOS flow basically impedes the deformation of individual RBCs as well as the magnitude of fluid-membrane interactions, resulting in a lower specific viscosity and first and second normal stress differences than in steady shear flow. Although it is known that the RBC deformation alone is sufficient to give rise to shear-thinning, our results show that the complex viscosity weakly depends on the frequency-modulated deformations or orientations of individual RBCs, but rather depends on combinations of the frequency-dependent amplitude and phase difference. The effect of the viscosity ratio between the cytoplasm and plasma and of the capillary number are also assessed.