ANALYSIS OF MATHEMATICAL MODELS TO DESCRIBE THE MIGRATION OF ADDITIVES FROM PACKAGING PLASTICS TO FOODS

The mathematical modeling of migration of additives from plastics to food simulants was studied using experimental data published in the literature, following two routes: the conventional approach using the solution of Fick's 2nd law, and a kinetic model based on the Weibull distribution function. The objective of this comparison was to permit using a mathematically simpler model equally able to describe migration data, and that could have a generally wider applicability by describing situations more complex than those that simple diffusional phenomena can describe. The relationship between the parameters of the two models was analyzed by regression of data generated by Fick's law using the Weibull model. The results show that the time constant parameter is related to the diffusion coefficient and the material thickness. It depends on temperature and on the molecular weight of the migrant in a similar manner to the diffusion coefficient. The activation energy presented values from 72 to 125 kJ/mol. The shape parameter is a function of the contribution of the mass transfer resistance at the interface. It was independent of temperature and of the migrant, assuming a global constant value of 0.67, for the systems and conditions studied. The results indicate that the Weibull model can be used to describe and analyze the migration of additives from plastics to foods with a meaning of the parameters in terms of the underlying physical phenomena. PRACTICAL APPLICATIONS The Weibull model can be used to describe the migration from packaging to foods with the advantage of significant simplicity of calculation compared to Fick's 2nd law. The model can be applied in packaging systems with mass transfer processes more complex than those that simple diffusional phenomena can describe. In the migration of components from paper-based materials (instead of plastics) into solid foods, mass transfer occurs in a heterogeneous medium of paper fibers and air. Migration curves commonly present an initial lag phase for heavier migrants. The sigmoidal-shape of the migration curves are not adequately described by the established models based in Fick's 2nd law solutions, and the Weibull model is a good alternative. Additionally, this simple model can potentially be used in probabilistic approaches for exposure assessments of consumers to migrants originating from packaging materials.