MATHEMATICAL MODEL AND NUMERICAL SIMULATION OF OXYGEN TRANSPORT IN MULTILAYER FOOD PACKAGING: A SEMI-ANALYTICAL APPROACH
The purpose of this work was to develop a numerical simulation methodology using a free software capable of predicting the behavior of oxygen in multilayer polymeric systems to optimize packaging configurations with a greater barrier to O2. The Laplace Transform method was used to solve partial differential equations, with numerical inversion by the Stehfest algorithm together with the Gauss-Sidel method. It was possible to simulate the oxygen concentration profile in packaging systems containing two or three materials in the configuration. For some systems, the increase in the simulation time caused a numerical fluctuation at the material interface, especially if oxygen diffused from a material with greater diffusivity to one with lower diffusivity. The numerically simulated oxygen concentration profile can be associated with results from the literature, experimentally validated. The results showed to be promising for application in diffusion problems of multilayer systems, and the methodology can be used to describe systems with more layers. Mathematical modeling and numerical simulation have been allies to predict the behavior of oxygen in different materials and layer configurations, and it is relevant to provide a better understanding of the oxygen transport fundamentals involved and shorten product development cycle time and cost, contributing to the economy and new product development.