Geometric percolation of colloids in shear flow

TL;DR

This paper develops a combined theoretical and simulation approach to understand how shear flow influences the percolation threshold of colloidal particles, revealing complex effects dependent on flow conditions and connection criteria.

Contribution

It introduces a novel heuristic theory integrated with Smoluchowski dynamics to predict shear flow effects on colloidal percolation thresholds, validated by molecular dynamics simulations.

Findings

Shear flow can both increase and decrease the percolation threshold.

The impact of shear flow depends on the connection criterion and Péclet number.

The approach enables prediction of percolation in non-equilibrium nanocomposite materials.

Abstract

We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the P\'{e}clet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.