Grain-scale modelling of swelling granular materials; application to super absorbent polymers

Abstract

Swelling is an important process in many natural materials and industrial products, such as swelling clays, paper, and Super Absorbent Polymer (SAP) particles in hygienic products. SAP particles are capable to absorb large amounts of fluid. Each grain of SAP can absorb water 30 to 1000 times its initial mass, depending on the water composition. To gain insight in the swelling behaviour of a bed of SAP particles, we have developed a grain-scale model and have tested it by comparing it to experiments. The grain-scale model is based on a combination of the Discrete Element Method (DEM) and the Pore Finite Volume (PFV) method, which we have extended to account for the swelling of individual SAP particles. Using this model, we can simulate the behaviour of individual particles inside a water-saturated bed of swelling SAP particles while taking into account the hydro-mechanical effect arising from the presence of pore water. The model input includes physical parameters such as particle stiffness and friction angle, which were found in the literature, as well as particle size distribution and diffusion coefficients, which were measured experimentally. A swelling rate equation was developed to simulate the swelling of individual particles based on water diffusion into a spherical particle. We performed experiments to measure the rise of the surface of a bed of initially dry SAP particles, which were put inside a glass beaker that contained sufficient amount of water for the SAP particles to swell and to remain saturated at all times. We used our model to simulate the swelling of that SAP particle bed as a function of time. Simulations show that the numerical model is in accordance with the experimental data. We have also verified the model with Terzaghi's analytical solution for a small swelling event. Finally, a sensitivity analysis was performed to study the effects of main grain-scale parameters on the larger-scale behaviour of a bed of particles.