Modelagem matemática e simulação numérica do transporte de oxigênio em filme multicamadas para uso em alimentos: uma abordagem semi-analítica

Abstract

The purpose of the present study was to develop a numerical simulation methodology capable of predicting the behavior of oxygen against multilayer polymeric systems, to optimize packaging configurations with a greater barrier to this gas. The Laplace Transform method was used to solve partial differential equations, with numerical inversion by the Stehfest algorithm with the Gauss-Sidel method, using Fortran 77 language and a free compiler. With this methodology, it was possible to simulate the oxygen concentration profile in front of packaging systems containing two or three materials in the configuration (ABA or ABC). For some systems, increasing the simulation time, the concentration function showed numerical fluctuation at the material interface, especially if oxygen diffused from a material with greater diffusivity to one with less diffusivity. The greater the difference between the order of magnitude of the diffusion coefficients, the greater the numerical fluctuation found. The numerically simulated oxygen concentration profile can be associated with results from the literature, experimentally validated. The results showed to be promissing for application in diffusion problems in multilayer systems and the methodology can be used to describe systems with a greater number of layers.