Mathematical Modeling of Hydrogels Swelling Based on the Finite Element Method

Abstract

In recent years, hydrogels have been introduced as new materials suitable for applications in areas such as biomedical engineering, agriculture, etc. The rate and degree of hydrogel swelling are important parameters that control the diffusion of drugs or solvents inside a polymer network. Therefore, the description of the dynamic swelling process of the hydrogels is very important in applications that require precise control of the absorption of solvents inside the hydrogel structure. To date, most of the numerical models developed for describing the swelling process are based in the finite difference methods. Even though numerical models supported in finite differences can be easily implemented, their use is limited to samples with very simple shapes. In this paper, a new model based on the finite element method is proposed. The diffusion equation is solved in a time-deformable grid. An original procedure is proposed to numerically solve the non-linear algebraic equation system that permits computing a new grid for each time-step. Hydrogel samples of different shapes were prepared in order to conduct experimental tests to validate the numerical proposed model. Numerical results show that the new model is able to describe the mass and shape changes in the hydrogel samples in time. An application of the numerical model to determine the relation between diffusion coefficients and density in Poly-acrylamide samples allows verifying the versatility of the model.