Estimation of diffusion coefficients of essential oil of Pimenta dioica in edible films formulated with Aloe vera and gelatin, using Levenberg-Marquardt method

We performed the study of the diffusion of the essential oil of pimento (Pimenta dioica L. Merrill) from an edible film formulated with Aloe vera, gelatin and glycerol. The analysis was done for three concentrations of essential oil (0.5, 1.0 and 1.5% w/w) and at two temperatures (5 ° C and 25 ° C) for a period of 180 hours, taking samples at various times to measure the concentration of the essential oil whose eugenol is the main component. The governing equations were obtained from Fick´s second law. The predictions of the eugenol concentration were compared with the experimental values using a least squares scheme, where the diffusion coefficient and the mass transfer coefficient were estimated using Levenberg-Marquardt method. The effective diffusivity of eugenol is between 7.0529∙10-12 to 5.3586∙10-11 m²/h at 5 °C, while at 25 °C, the effective diffusivity values ​​are between 3.7980∙10-11 to 5.2578∙10-10 m²/h. These values ​​are in agreement with those reported for other similar systems and indicate that the diffusive transport of the essential oil through the edible film studied is a slow process, a required condition to increase the shelf life of foods where these films can be used as coatings in meat products and cheeses.

Keywords: parameter estimation, diffusion coefficient, essential oil, Pimenta dioica, orthogonal collocation, Levenberg-Marquardt method.