  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.
