 - Practical Guide -
Page 64 of 153
and respectively
n
n
q
q
=
-
=
tan
(2*)
where: m
F,t
- mass of migrant from P into F after time t, (mg)
A
- area of P in contact with F , (dm
2
)
c
P,0
- initial concentration of migrant in P, (mg/kg)
r
P
- density of P, (g/cm
3
)
r
F
- density of F, (g/cm
3
)
D
p
- diffusion coefficient of migrant in P, (cm
2
/s)
t
- migration time, (s)
d
P
- thickness of P, (cm)
V
P
- volume of P, (cm
3
)
V
F
- volume of F, (cm
3
)
c
P,
¥
- equilibrium concentration of migrant in P (mg/kg)
c
F,
¥
- equilibrium concentration of migrant in F (mg/kg)
K
P/F
- the partition coefficient of the migrant between P and F
q
n
- the non-zero, positive roots of equation (2*)
(9) Equation (2) can be rearranged to give equation (3), which can be used to estimate the
maximum initial concentration of migrant (MIC) in the food contact material or article.
1
1
2
2
2
2
exp
1
1
2
1
1
100
-
¥
=
ï
þ
ï
ý
ü
ï
î
ï
í
ì
ú
û
ù
ê
ë
é
÷
÷
ø
ö
ç
ç
è
æ
-
+
+
+
-
÷
ø
ö
ç
è
æ
+
=
å
n
P
n
P
n
P
P
F
F
d
q
t
D
q
d
A
V
SML
MIC
=
=
=
=
=
=
H
H
(3)
where: all parameters as for equation (2) apply, except
SML - Specific Migration Limit, (mg/kg)
MIC - maximum initial concentration in P, (mg/kg).
2.2
Migration estimation
As mentioned above the key parameters necessary for migration modelling are the diffusion
coefficient of the migrant in the plastic, D
P
, as well as the partition coefficient of the migrant
between the plastic and the food (simulant), K
P,F
. Both parameters play a crucial role in
determining the level of migration in a real food packaging application /4, 5/. Due to a lack
of knowledge of the exact values in any specific case, it is recommended to establish these
values in more generalized and conservative way so that reliably worst case scenarios with
respect to migration are estimated which, in fact, is of primary interest from regulatory stand
point. To meet this requirement the described migration model has the two following
implications: