Numerical analysis of suspension rheology of red blood cells under oscillatory shear flow

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. Our numerical results show that the deformations of RBCs weakly depend on the shear frequency, and the normal stress differences, the membrane tension and the amplitude of the shear stress are reduced by the oscillations. The frequency-dependent complex viscosity is nevertheless partially consistent with the classical behaviour of non-Newtonian fluids, where the real part of the complex viscosity η' decreases as the frequency increases, and the imaginary part η" exhibits a maximum value at an intermediate frequency. Such local maximum frequency is the same in both dense and dilute conditions. The effect of the viscosity ratio between the cytoplasm and plasma and of the capillary number are also assessed.