A Simple Approach to Characterize Sorption and Release Kinetics in Polymeric Materials with Planar, Cylindrical or Spherical Geometries

This study presents a theoretical framework for modeling sorption and release kinetics of substances in polymeric materials with planar, cylindrical, and spherical geometries. Fick's second law was expressed in dimensionless variables and solved numerically using a finite-difference approach to generate universal profiles for mass transfer. These profiles were fitted with double-exponential equations, yielding explicit expressions that allow for straightforward estimation of diffusion coefficients from experimental data. The method was validated using literature data for films, fibers, and microspheres, showing excellent agreement with reported values. Unlike classical analytical solutions, which are limited to planar systems under ideal conditions, the proposed approach is applicable to diverse geometries commonly employed in packaging, biomedical devices, controlled-release formulations, and environmental technologies.