Catching gas with droplets : modelling and simulation of a diffusion-reaction process

Abstract

The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial differential equations: a reaction-diffusion equation for the oxygen concentration and a reaction equation for the scavenger concentration. A probabilistic background of this model is given and different methods are used to get information from the model. Homogenization theory is used to describe the influence of the shape of the scavenger droplets on the oxygen flux, an argument using the Fourier number of the foil leads to insight into the dependency on the position of the scavenger and a method via conformal mappings is proposed to find out more about the role of the size of the droplet. Also simulations with Mathematica were done, leading to comparisons between different placements and shapes of the scavenger material in one- and two-dimensional foils