Haemorheology of dense suspension 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, oscillatory shear flow. The RBCs are modeled as biconcave capsules, whose membrane is an isotropic and hyperelastic material following the Skalak constitutive law, and the suspension examined for a wide range of applied frequencies. 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 deformations of RBCs wekaly depend on the shear frequency, and the normal stress differences, membrane tension and amplitude of the shear stress are reduced by the oscillations. The frequency-dependent complex viscosity is nevertheless consistent with the classical behavior of non-Newtonian fluids, where the real part of the complex viscosity $\eta^\prime$ decreases as the frequency increases, and the imaginary part $\eta^{\prime\prime}$ exhibit 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 ratios between the cytoplasm and plasma, volume fractions of RBCs, and oscillatory amplitudes represented by a capillary number on the complex viscosity are also assessed