An order parameter equation for the dynamic yield stress in dense colloidal suspensions

TL;DR

This paper derives an order parameter equation for the dynamic yield stress in dense colloidal suspensions, linking the onset of yield stress to a bifurcation in the pair distribution function and phase transition theory.

Contribution

It introduces a novel amplitude equation approach to describe the emergence of yield stress, connecting colloidal rheology with phase transition concepts.

Findings

Derives an amplitude equation analogous to phase transition order parameters.

Identifies a shear thinning exponent of 2/3.

Links the critical behavior to the mean field Ising model.

Abstract

We study the dynamic yield stress in dense colloidal suspensions by analyzing the time evolution of the pair distribution function for colloidal particles interacting through a Lennard-Jones potential. We find that the equilibrium pair distribution function is unstable with respect to a certain anisotropic perturbation in the regime of low temperature and high density. By applying a bifurcation analysis to a system near the critical state at which the stability changes, we derive an amplitude equation for the critical mode. This equation is analogous to order parameter equations used to describe phase transitions. It is found that this amplitude equation describes the appearance of the dynamic yield stress, and it gives a value of 2/3 for the shear thinning exponent. This value is related to the mean field value of the critical exponent $\delta$ in the Ising model.