# Analyzing Onset of Nonlinearity of a Colloidal Gel at the Critical Point

## TL;DR

This study investigates the onset of nonlinear rheological behavior in a colloidal gel at the critical point, developing a model that accurately predicts deviations from linearity during deformation.

## Contribution

It introduces a quasi-linear integral model that captures nonlinear rheological responses of colloidal gels at the critical gel state, validated against experimental data.

## Key findings

- The model accurately predicts nonlinear deviations in creep-recovery and start-up shear tests.
- Nonlinear deformation leads to a vertical shift in the relaxation modulus.
- Energy dissipation analysis supports the Bailey criterion validation.

## Abstract

In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.

---
Source: https://tomesphere.com/paper/1904.13321