3.1. GENERALIZED MASS BALANCE OVER A LAYER VOLUME ELEMENT

In order to consider the change of the concentration of the migrant (and/or simulant) diffusing inside the layer (see Fig. 3.1), a mass balance over a volume element can be made as follows:
Fig.3.1: Generalized mass balance over a layer volume element.

Input = Output + Accumulation +Reaction

with		(3.1)
		(3.2)
		(3.3)
where		(3.4)
		(3.5)
with		(3.6)
		(3.7)
without chemical reaction		(3.8)
and		(3.9)
the mass balance for a migrant ‘M’ reads:		(3.10)
Similarly, the mass balance for a simulant S’ reads:		(3.11)
The initial concentration of the migrant has to be set for each layer. If a layer is isolated on its left or right side, boundary condition (I, see Fig. 2.1) is derived from the symmetrical properties of the concentration distribution at the wall surface. The other boundary conditions (II, Fig. 2.1) are derived from comparison of fluxes at the interface between the different layers, between the layer and gas phase, and between the layer and the food. We have for a migrant ‘M’: - Boundary (I): Symmetry axis (if perfect insulation):		(3.12)
- Boundary (II): Considering the ‘left’ and ‘right’ side of one interface, we can write between 2 layers:		(3.13)
		(3.14)