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be used to calculate estimates of
F
C (noted C
0
for multilayers) or
max
0
P Fo
C
=
. The proposed physical
approximations are an extension of the ones for monolayer materials.

Thus, as for monolayer materials (see Equation (29)), the contamination from multilayer
materials can be decomposed between a time independent and a time dependent contribution:
{ }
{ }
{ }
{ }
{
}
{ }
{ }
{ }
{ }
{
}
=
=
=
=
=
=
=
=
=
=
=
=
=
0..
0..
0..
0..
0
0..
0..
0..
0..
0..
0
0..
, ,
,
,
,
,
*
0
, ,
,
,
,
,
tim e ind ep en dent con tribu tion
tim e d ep en dent con tribu tion
j
j
j
j
j
j
n
j
n
j
n
j
n
t
j
n
j
j
j
j
j
j
n
j
n
j
n
j
n
t
j
n
F t h D
k
l
C
eq
t h D
k
l
C
C
C
v






(31)

with
0 eq
C
defined by Equation (19) and
*
0
1
v
.
Two approximations are particularly relevant:
*
1
v
(time independent)
*
1
v
(time dependent)
4.4.2 Scheme for the overestimation of the time independent contribution:
0 eq
C
If the problem is not time dependent, the contamination does not depend on the
arrangement/order of layers and Equation 19 can be partitioned between layers, which present a
higher chemical affinity for the migrating substance than for food (i.e.
{ }
0
0
i
i n
k
k
<
), and layers,
which present a lower chemical affinity (i.e.
{ }
0
0
i
i n
k
k
<
>
). By noting both partitions H and L, a
worst-case scenario but nevertheless not too much pessimistic is obtained by choosing:
{ }
0
i
i H
k
k
and
{ }
i
i L
k
. As a result, an overestimate of Equation (19) for multilayer
materials is obtained:
=
=
=
=
=
+
+
+
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
eq
n
n
j
j
j
j
j
j
t
t
j
j
eq
j
j
j
j
j
j
j
j
j H
j L
j H
C
l
l
C
C
l
l
C
l
l
l
k
k
l
k
l
k
l
(32)
If the partition H is empty, the scenario defined by Inequality (32) corresponds to scenario A
defined for monolayer materials. Otherwise, Inequality (32) is intermediate between previous
scenarios A and B. The estimation can be refined by introducing sub-partitions of H or L with
more reliable estimates of
{ }
0
.
i
i n
k
<
It is worth to notice that the overestimation defined by Equation (32) by assuming
*
1
v
seems
particularly useful to estimate the maximum contribution to the contamination of food by
specialty resins (adhesives, inks...) whose typical thickness is very low.