Micro-mechanical insights into the stress transmission in strongly aggregating colloidal gel

Predicting the mechanical response of soft gel materials under external deformation is of paramount importance in many areas, such as foods, pharmaceuticals, solid-liquid separations, cosmetics, aerogels, and drug delivery. Most of the understanding of the elasticity of gel materials is based on the concept of fractal scaling with very few microscopic insights. Previous experimental observations strongly suggest that the gel material loses the fractal correlations upon deformation and the range of packing fraction up to which the fractal scaling can be applied is very limited. In addition, correctly implementing the fractal modeling requires identifying the elastic backbone, which is a formidable task. So far, there is no clear understanding of the gel's elasticity at high packing fractions or the correct length scale that governs its mechanical response. In this work, we undertake extensive numerical simulations to elucidate the different aspects of stress transmission in gel materials. We observe the existence of two percolating networks of compressive and tensile normal forces close to the gel point. We also find that the probability distribution for the compressive and tensile parts normalized by their respective mean shows a universal behavior irrespective of various values of interaction potential and thermal energy and different particle size distributions. Interestingly, there are also a large number of contacts with zero normal force, and, consequently, a peak in the normal force distribution is observed at f_n ≈ 0 even at higher pressures. We also identify the critical internal state parameters, such as the mean normal force, force anisotropies, and the average coordination number, and propose simple constitutive relations that relate different components of stress to internal state parameters. The agreement between our model prediction and the simulation observation is excellent. It is shown that the anisotropy in the force networks gives rise to the normal stress difference in soft gel materials. Our results strongly demonstrate that the mechanical response of the gel system is governed mainly by the particle length scale phenomena, with a complex interplay between the compressive and tensile forces at the particle contact.