2.2. GENERAL DESCRIPTION OF THE MODEL

Simulation of the diffusion processes of migrant and simulant occurring in packaging layers can be reduced to the analysis of a single layer (see Fig. 2.1).

Fig.2.1: Scheme of the packaging.

The simulation of the whole packaging reduces to the analysis of a single layer and can then be extended from layer to layer.

Considering one layer inside the packaging, it can be demonstrated that the mass of the layer which is taken for calculation of the diffusion of both migrant and simulant can be treated as an ‘infinite’ surface of thickness ‘d’ (i.e. ‘infinite’ in two directions and of wall thickness ‘d’ in the third, see eqs. 3.7, 3.8). To calculate the amount of the migrating substance that reaches the food after a certain time all package geometries are reduced to a simple case: a plane of several sheets with only one surface in contact with the food. It can be assumed that diffusion obeys Fick’s law and that the diffusion of the species in the y and z direction is negligible as compared to x direction. The presented model enables calculations of the concentration gradients using finite element methods, considering the diffusion progresses of both species (migrant and simulant) in the multi-layers. The Arrhenius and Piringer equations can be applied in order to evaluate a magnitude for the diffusion coefficient in the different layers. The equations have been developed using coordinates (x and t) where the whole surface of the packaging will be derived from the different packaging shapes.