# Rheological investigation of gels formed by competing interactions: A numerical study

## TL;DR

This numerical study explores how competing short-range depletion and long-range electrostatic interactions influence the rheological behavior and yielding of colloidal gels, revealing a systematic dependence on inter-particle potentials and flow conditions.

## Contribution

It introduces a detailed numerical analysis of equilibrium and shear-induced states in gels with competing interactions, highlighting the impact of inter-particle potentials on rheological transitions.

## Key findings

- Single yielding event at fixed strain in stress-strain curves
- Stress overshoot follows a power-law with Péclet number, with a larger exponent than depletion gels
- Steady states with the same Péclet number exhibit identical structural and rheological properties

## Abstract

A transition from solid-like to liquid-like behavior occurs when colloidal gels are subjected to a prolonged exposure to a steady shear. This phenomenon, which is characterized by a yielding point, is found to be strongly dependent on the packing fraction. However, it is not yet known how the effective inter-particle potential affects this transition. To this aim, we present a numerical investigation of the rheology of equilibrium gels in which a short-range depletion is complemented by a long-range electrostatic interaction. We observe a single yielding event in the stress-strain curve, occurring at a fixed strain. The stress overshoot is found to follow a power-law dependence on the P\'eclet number, with an exponent larger than that found in depletion gels, suggesting that its value may depend systematically on the underlying colloid-colloid interactions. We also establish a mapping between equilibrium states and steady states under shear, which allows us to identify the structural modifications induced by the presence of the shear. Remarkably, we find that steady states corresponding to the same P\'eclet number, obtained by different combinations of shear rate and solvent viscosity, show identical structural and rheological properties. Our results highlight the importance of understanding the coupling between colloidal interactions, solvent effects, and flow to be able to describe the microscopic organization of colloidal particles under shear.