# Nanoparticle diffusion in sheared cellular blood flow

## TL;DR

This study calculates the complete nanoparticle diffusion tensor in sheared blood flow, revealing anisotropic behaviors, nonlinear shear-rate dependence, and the influence of red blood cell deformation, aiding in improved biotransport modeling.

## Contribution

It provides the first comprehensive calculation of the nanoparticle diffusion tensor in sheared blood flow, including the effects of shear rate and haematocrit, with empirical correlations for modeling.

## Key findings

- Nanoparticle diffusion exhibits high anisotropy under shear.
- A critical shear rate (~100 s^{-1}) marks a change from linear to nonlinear diffusivity dependence.
- Red blood cell deformation significantly influences nanoparticle diffusion behavior.

## Abstract

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.