Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction

TL;DR

This study uses numerical simulations to show that the viscosity of suspensions of viscoelastic spheres depends on an effective volume fraction, revealing a universal rheological behavior similar to rigid sphere suspensions, with implications for blood flow modeling.

Contribution

It introduces a universal rheological function for deformable sphere suspensions by defining an effective volume fraction, linking viscoelasticity to suspension viscosity.

Findings

Viscosity increases with volume fraction and decreases with sphere elasticity.

The viscosity function collapses to a universal form akin to rigid sphere suspensions.

Results offer new insights into blood rheology modeling.

Abstract

We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in plane Couette geometry, by means of direct numerical simulations. We find that in the limit of vanishing inertia the effective viscosity $\mu$ of the suspension increases as the volume-fraction occupied by the spheres $\Phi$ increases and decreases as the elastic modulus of the spheres $G$ decreases; the function $\mu(\Phi,G)$ collapses to an universal function, $\mu(\Phi_e)$, with a reduced effective volume fraction $\Phi_e(\Phi,G)$. Remarkably, the function $\mu(\Phi_e)$ is the well-known Eilers fit that describes the rheology of suspension of rigid spheres at all $\Phi$. Our results suggest new ways to interpret macro-rheology of blood.