Analyzing Onset of Non-Linearity of a Fractal Colloidal Gel in the Neighborhood of Critical Point

A colloidal dispersion of Laponite exhibits all the rheological features of a sol-gel transition. While undergoing gelation, Laponite dispersion passes through the critical state stress characterized by a percolated space-spanning fractal network for which the relaxation modulus shows a time dependent power law decay in the linear regime. When subjected to step strain in the non-linear regime, relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated by use of a strain dependent damping function. We also perform creep-recovery, startup shear and large amplitude oscillatory shear (LAOS) experiments on the Laponite dispersion at the critical gel state and record deviation in the response as flow becomes nonlinear. We also develop a quasi-linear integral model with relaxation modulus weighted by damping function to account for the effect of non-linear strain. Remarkably the proposed quasi-linear integral model predicts the deviation from linearity in the creep-recovery, startup shear and LAOS very well, leading to a simple formulation to analyze the nonlinear rheological behavior of fractal gels.