Mathematical Modelling of Drying of Hydrogels via Finite Element Method and Texture Analysis

Abstract

Hydrogels are polymeric materials with specific mechanical handling and encapsulation properties. Despite their widespread application, the modelling of the drying behaviour of hydrogels, particularly the evolution of texture stiffness with moisture loss, requires further development. This work aimed to develop numerical models to predict the moisture and deformation of cornstarch–alginate hydrogels under convective drying at 60 °C and 0.5 m/s. Cylindrical solids were used, and a transient three-dimensional FEM model predicted drying profiles via diffusion–convection mass transport. Texture analysis evaluating the hyperelastic coefficients of the hydrogels was performed for moisture contents ranging from 0.91 to 0.55 kg∙kg−1 w.b., yielding Young’s modulus values from 24 to 147 kPa. A dimensionless relationship between the moisture ratio and elastic modulus produced a stiffness coefficient, used to adjust the moving boundary velocity and predict volumetric deformation. The model fitting returned an R2 higher than 0.95 and an RMSE lower than 0.04. The FEM model simulated hydrogel shrinkage by assessing the molar flux of water and mesh deformation at the boundaries, with mass diffusivity ranging from 2.38 to 5.46 × 10−10 m2∙s−1. Shrinkage reduced the surface area of solids during drying, revealing a pseudo-constant rate period in the drying profiles. The developed models effectively describe the drying of food materials with high shrinkage ratios.