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4.4.3 Schemes for the overestimation of the time dependent contribution:
Effect of the arrangement of layers
The estimation
v depends strongly on the arrangement of the layers. By comparison to
monolayer materials with similar initial content and whole thickness, two mechanisms may delay
the desorption kinetics:
a barrier effect (an initially virgin layer is intercalated between the layer formulated with
the substance of interest and the food product);
a reservoir effect (the layer formulated with the substance of interest is located between
the food product and an initially virgin layer).

These effects are illustrated on Figure 7 on bilayer structures. These results are subsequently used
to define general rules to simulate mass transport in multilayer materials in presence of
uncertainty on Henry-like coefficients: k

In Figure 7, all layers have the same thickness and diffusion coefficient. The dilution factor
between the whole packaging material and the food product is 1/25, k
is set to 1, and Bi
The different tested conditions are detailed in Table 2. It is worth to notice that all tested
configurations present a same initial amount of substance but do not yield exactly the same
concentration in F at equilibrium. For each configuration,
v is calculated by the ratio
The barrier effect introduces a typical delay at the beginning of the kinetic: that is an initial
period with zero flux at the interface F-P. The delay is in itself not affected by the chemical
affinity of the substance for the crossed layer (effect of barrier of diffusion). Only the mass flux
at the interface between layers 1 and 2 is affected by the chemical affinity. Thus, increasing k
reduces the desorption rate (effect of barrier of solubility).
By contrast, the reservoir effect appears to be significant only after a certain time. This time is
required to "fill" the reservoir before to "empty" it. Since the reservoir is located farther from the
exchange surface, the reservoir effect acts mainly by increasing the dimension characteristic of
the mass transfer. Its effect varies significantly according to the thickness and the affinity of the
substance for the reservoir layer.
Proposed approximations to overestimate
According to simulated results of Figure 7 and as first approximations, it is stated that the
contamination from the bilayer material coded [0 1]-[>1 1] (diffusion and solubility barrier) is
overestimated by assuming either:
a monolayer material equivalent to [0.5 0.5]-[1 1];
a bilayer material equivalent to [0 1]-[1 1].
The first approximation cannot however be generalized, since it works well only when both
layers have similar D values. From this point of view the second approximation, which removes
the "solubility barrier" seems more satisfactory.
The situation [0 1]-[<1 1] (diffusion barrier but no solubility barrier) requires a particular
treatment. Since k
is expected to be smaller than k
, a worst-case assumption consists in taking
0 so that the equivalent mass transport in 1
(see Equation (22)). This assumption is
equivalent to a material 1 of zero thickness and zero capacity (see Equation (23)), as the layer did