Mathematical modeling of swelling in high moisture whey protein gels

Gels prepared from whey proteins can be used for controlled release of nutrients or active ingredients in food systems. The objective of this study was to characterize the water uptake by these hydrophilic gels to aid in the design of release systems. Whey protein isolate (WPI) gels (17% w/w protein) of different aspect ratios were submersed in aqueous solution at pH 7.0. Modeling of mass uptake is presented in terms of Case I (Fickian diffusion) and Case II (kinetic) models. Due to the extent of swelling, the Fickian diffusion with moving boundaries provided the most realistic reflection of the physics. An optimization routine provided the best fit values for the diffusivity. The average diffusivity for the smaller gels (with an initial radius of 6.7 mm) was 1.40 × 10−10 m2/s. The average diffusivity of the larger gels (with an initial radius of 8.5 mm) was 0.79 × 10−10 m2/s. The average diffusivities differed due to the slight variation in the composition of the gels. The model also yielded instantaneous values of the radius and sample length. The functionality of moisture uptake and total surface area was linear. The Fickian diffusion with moving boundary model can be extended to evaluate different geometries for controlled release systems.