  Using a multiscale blood flow solver, the complete diffusion tensor of
nanoparticle (NP) in sheared cellular blood flow is calculated over a wide
range of shear rate and haematocrit. In the short-time regime, NPs exhibit
anomalous dispersive behaviors under high shear and high haematocrit due to the
transient elongation and alignment of the red blood cells (RBCs). In the
long-time regime, the NP diffusion tensor features high anisotropy.
Particularly, there exists a critical shear rate ($\sim$100 $s^{-1}$) around
which the shear-rate dependence of the diffusivity tensor changes from linear
to nonlinear scale. Above the critical shear rate, the cross-stream diffusivity
terms vary sublinearly with shear rate, while the longitudinal term varies
superlinearly. The dependence on haematocrit is linear in general except at
high shear rates, where a sublinear scale is found for the vorticity term and a
quadratic scale for the longitudinal term. Through analysis of the suspension
microstructure and numerical experiments, the nonlinear hemorheological
dependence of the NP diffusion tensor is attributed to the streamwise
elongation and cross-stream contraction of RBCs under high shear, quantified by
a Capillary number. The RBC size is shown to be the characteristic length scale
affecting the RBC-enhanced shear-induced diffusion (RESID), while the NP size
at submicron exhibits negligible influence on the RESID. Based on the observed
scaling behaviors, empirical correlations are proposed to bridge the NP
diffusion tensor to specific shear rate and haematocrit. The characterized NP
diffusion tensor provides a constitutive relation that can lead to more
effective continuum models to tackle large-scale NP biotransport applications.
