- Practical Guide -
Page 63 of 153
2.1
General scientific considerations
Theoretical specific migration estimations can only be accepted on a case by case basis using
scientific evidence. A useful model for many situations occurring in food contact material is
based on following general requirements.
1.
In most cases of practical relevance a plastic food contact material or article
(monolayer, homogenous) (P), can be regarded as a polymer film/sheet, of finite and
constant thickness (d
P
) being in contact with a food or food simulant (F), of finite
volume (V
F
).
2.
It is assumed that during the manufacturing process of P the migrant is distributed
homogeneously in P.
3.
It is assumed that there is no boundary resistance for the transfer of the migrant
between P and F.
4.
It is assumed that the interaction between P and F is negligible and no swelling of P by
uptake of F occurs during the migration process.
5.
A partition coefficient between food and polymer is assumed and defined as
K
c
c
P F
P
F
P
F
,
,
,
=
¥
¥
H
H
6.
The migrant is homogeneously distributed in F. The sum total amount of the migrant in
P and F is constant during the migration process.
7.
The diffusion equation - also known as Fick's 2nd equation - describing a migration
process corresponding to the general requirements 1 to 5 is /3/:
2
2
x
c
D
t
c
P
=
(1)
where: c is the concentration of migrant in the food contact material or article (P) at
time t at distance x from the origin of the x-axis and Dp is the constant
diffusion coefficient in the food contact material or article.
8.
With requirements from 1 to 5 the analytical solution of Eq (1) is Eq (2) /3/:
m
A
c
d
q
D t
q
d
F t
P
P P
n
P
n
P
n
,
,0
.
exp
=
+
æ
è
ç
ö
ø
÷ -
+
+ +
-
æ
è
ç
ç
ö
ø
÷
÷
å
é
ë
ê
ê
ù
û
ú
ú
=
¥
01
1
1
2 1
1
2 2
2
2
1
H
=
=
=
=
= =
(2)
where:
=
H
H
=
=
¥
¥
1
K
V
V
c
c
V
V
P F
F
P
F
P
F
P
F
P
,
,
,
K
c
c
P F
P
F
P
F
,
,
,
=
¥
¥
H
H