Shear-thinning in dense colloidal suspensions and its effect on elastic instabilities: from the microscopic equations of motion to an approximation of the macroscopic rheology

TL;DR

This paper develops a simplified theoretical model to understand how shear-thinning affects flow stability in dense colloidal suspensions near the glass transition, explaining the absence of observed elastic instabilities.

Contribution

It extends a first-principles approach to inhomogeneous flow and derives a White-Metzner type constitutive model fitted to experimental rheology data.

Findings

Shear-thinning stabilizes flow in dense colloidal suspensions.

The model captures shear-thinning behavior but is not fully quantitative.

Flow instabilities are suppressed in the studied geometry due to shear-thinning.

Abstract

In the vicinity of their glass transition, dense colloidal suspensions acquire elastic properties over experimental timescales. We investigate the possibility of a visco-elastic flow instability in curved geometry for such materials. To this end, we first present a general strategy extending a first-principles approach based on projections onto slow variables (so far restricted to strictly homogeneous flow) in order to handle inhomogeneities. In particular, we separate the advection of the microstructure by the flow, at the origin of a fluctuation advection term, from the intrinsic dynamics. On account of the complexity of the involved equations, we then opt for a drastic simplification of the theory, in order to establish its potential to describe instabilities. These very strong approximations lead to a constitutive equation of the White-Metzner class, whose parameters are fitted with experimental measurements of the macroscopic rheology of a glass-forming colloidal dispersion. The model properly accounts for the shear-thinning properties of the dispersions, but, owing to the approximations, the description is not fully quantitative. Finally, we perform a linear stability analysis of the flow in the experimentally relevant cylindrical (Taylor-Couette) geometry and provide evidence that shear-thinning strongly stabilises the flow, which can explain why visco-elastic instabilities are not observed in dense colloidal suspensions.