6. Created by:
Migration Models: Deterministic
6
Bi>100
No Resistance
h is not
infinitive
Diffusion
coefficient
Interaction
effects
Swelling of the packaging materials -> Swelling layer
E.g. Olive oil into PP
(Poças, Oliveira, Oliveira, & Hogg, 2008)
8. Created by:
Migration Models: Probabilistic
Variability in migration model outputs as a result of the uncertainty in model inputs
Mixed effect models with deterministic models
Probability distribution of the diffusion coefficient using Molecular mass
Distribution of outputs
Monte Carlo sampling
Fourier Amplitude Sensitivity Test (FAST)
Latin hypercube sampling
Capturing lack of knowledge
• Temperature fluctuations
• Time of contact
• Non-systematic errors
Uoverall Migration = 2 mg/dm2 or 12 mg/kg
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Editor's Notes
Chemical partitioning from packaging material into the food systems : Migration
Worst case scenario: 100% migration
Models can at least partially replace experiments
Functional barrier (virgin polymer) effectiveness in laminated or coextruded structures
SML = specific migration limits
Therefore, the majority of the scientific literature on migration modeling is dedicated to the deterministic approach. In many cases, migration is governed by a mass transfer process called diffusion that can be described by FICK’s LAW
Two constants partition coefficient and alpha at equilibrium
Low Mw no longer homogenously distributed at the interface
No transfer at the outer surface if migrant has lower volatility
2-3 orders of magnitude difference, this is explained by molecular size and shape. The higher, the lower the D
Both of these models can be applied accurately to polyolefins
Monte Carlo sampling based on random sampling
Model output is the distribution of values
PET, PEN, PS, PA are lower than polyolefins
Polyolefins modeling more sensitive and faster results due to high migration rates : E.g. antioxidants modeling in polyolefins
Paper migration is higher / faster
To food and to atmosphere
The retention behaviour of the substance in the paper matrix depends also on its interaction with fibres surface and, as mentioned before, the cellulose fibres have an overall negative charge due to carboxyl groups from the carbohydrates and the hydroxyl groups of the lignins. Thus, substances rich in electrons, such as naphthalene, tend to be repelled and are not retained by the fibre. As a consequence, these substances are less absorbed by the paper
Tau system time parameter, Beta shape parameters
Weibull model: Simple and flexible in determining mass transfer ptocessess where diffusion theories cannot explain.
Migratest :Piringer’s model -> Designed to overestimate
AKTS: Monolayers (freeware version), Up to 10 layers (licensed version)
SMEWISE: Freeware
Several orders of magnitude overestimation
Values had a large margin of uncertainty
Photoinitiator study has 20% m ore than actual values