A model for diffusion of water into a swelling particle with a free boundary: Application to a super absorbent polymer particle

In this work, a model is developed for describing the swelling of an individual particle, made of Super Absorbent Polymers (SAP). Governing equations for the water uptake at the particle surface, diffusion of water into the particle and the subsequent swelling of the particle are developed for an irregularly shaped particle. The modelling domain is assumed to have a free and moving boundary, thus a moving particle surface, to account for the increase in particle size. In addition, the entrance of water through the particle surface is modelled as a first-order kinetic process. The proposed model is then simplified for a spherical particle, made dimensionless, projected onto a fixed grid, and solved using an explicit numerical scheme. A dimensionless number is defined as the ratio of kinetics of water uptake at the particle surface to the water diffusivity. Using this dimensionless number, three regimes of swelling kinetics can be identified: (i) diffusion is limiting, (ii) water uptake is limiting, or (iii) both processes are limiting. Numerical results indicate that experimental data from literature can be reproduced when assuming water uptake kinetics at the particle surface to be very fast; i.e. instantaneous, thus diffusion being the controlling mechanism. Of course, for SAP particles having a different composition, the particle surface may slow down the swelling kinetics. Our model is compared to three other models found in the literature. They all give a similar result but with different diffusive coefficients.