Yielding in a strongly aggregated colloidal gel. Part II: Theory

Abstract

We derive a constitutive relation to describe the deformation of a two-dimensional strongly aggregated colloidal system by incorporating the interparticle colloidal forces and contact dynamics. The theory accounts for the plastic events that occur in the form of rolling/sliding during the deformation along with elastic deformation. The theory predicts a yield stress that is a function of volume fraction of the colloidal packing, the coordination number, the interparticle potential, coefficient of friction, and the normal and the tangential stiffness coefficients. The predicted yield strain was independent of the particle volume fraction although the compressive yield stress exhibited a power-law relation with the volume fraction. The power-law exponent, however, was lower than that obtained from simulations reported in a paper by Roy and Tirumkudulu [“Yielding in a strongly aggregated colloidal gel. Part I: 2D simulations,” J. Rheol. 60(4), 559–574 (2016)]. The cause for the discrepancy was identified to be the nonaffine deformation of the network. To account for such effects, a constitutive relation based on a simple fractal model was developed that predicts yield stress profile close to those obtained from simulations.