background image
14/27
appear as horizontal lines since their results are independent of kinetic effects. Scenarios C and D
lead to increasing curves with
*
1 v
-
. Curves predicted by scenario C are always located below
the curve predicted by scenarios D. In all subplots in the upper position of Figure 5 (i.e. for
similar L and Bi values), scenarios C appear therefore as a single curve very close to the one
predicted by scenarios D when K=5. Reciprocally, in all subplots in the bottom position of Figure
5 (i.e. for similar K and L values), scenarios D appear as a single curve above all the others and
very close to the curve predicted by scenario C for Bi=10
4
.

Abacuses depicted in Figure 5 are particularly valuable to make an audit of a provider with the
objective to get a confirmation that a given substance is used in conditions, which ensures a
contamination of food lower than a SML. In the current EU regulation, about 400 of the 2750
substances listed in the synoptic document (EC, 2005) are subjected to a regulated SML. For
audit purposes or formulation optimization, this value can be replaced by a more severe value
(lower value).
In the discussion process with the provider, the objective is not to guess the true
0
P Fo
C
=
used in
the formulation process (which is confidential) but to guess a value,
max
0
P Fo
C
=
, confirmed by the
provider, so that
max
max
0
0
0
P
P
P
Fo
Fo
Fo
C
C
C
=
=
=
<
. With a knowledge poor approach as scenario A, the
risk is to get the inequality
max
max
0
0
0
P
P
P
Fo
Fo
Fo
C
C
C
=
=
=
<
<
of little use. The initiated iterative
discussion process with the provider consists in getting significant additional information
(molecular mass, polarity of the molecule...) to fulfill:
max
0
0
P
P
Fo
Fo
C
C
=
=
>
. To reach this goal, a
solution consists in precalculating an abacus as depicted in Figure 5 for a large range of
conditions before any discussion with the provider.

A software has been developed (Decision Tool for Compliance Testing) to generate first a
database based on the geometry of the food product and its packaging and on its expected shelf
life (Figure 6). Both the provider and the company that requires an audit can share the database
on line. The final calculations can thus be performed in real time as additional information is
provided (e.g. during a phone talk with the provider).
If the provider accepts to propose a priori a
max
0
P Fo
C
=
value, an alternative objective consist in
getting the confirmation that the ^
K and/or
*
v values derived from
max
0
P Fo
C
=
and abacuses are
possible overestimates of likely K and/or
*
v values.
4.4 Multilayer materials
4.4.1 Main physical approximations
Enumerating and classifying all combination of intervals on input parameters for multilayer
materials is a much difficult task than for monolayer materials. The objective of this section is to
show that a decomposition between known and poorly known is almost always possible and can