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 η′ decreases as the frequency increases, and the imaginary
part η′′ 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