The Einstein viscosity with fluid elasticity

Abstract

We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to $O(\varphi {\mathrm{Wi}}^2)$ in the Weissenberg number $\mathrm{Wi}=\dot{\gamma }\lambda$, where $\dot{\gamma }$ is the typical magnitude of the suspension velocity gradient, and $\lambda$ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain hot spots near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at $O(\varphi \mathrm{Wi})$, and find dramatic strain-rate thickening at $O(\varphi {\mathrm{Wi}}^2)$. We validate our theory with fully resolved numerical simulations.

In review

References in corpus (1)

• Spherical particle sedimenting in weakly viscoelastic shear flow

Cited by in corpus (4)

• Force moments of an active particle in a complex fluid
• Prediction of shear-thickening of particle suspensions in viscoelastic fluids by direct numerical simulation
• Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid
• Correlation between the rheology of 2D-inks precursors and the droplet size generated from a capillary nozzle in dripping regime