Simulation of release of additives from mono- and multilayer packaging

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Simulation of release of additives from mono- and
multilayer packaging
Training Course The use of diffusion modelling to
predict migration offered by the Community
Reference Laboratory on Food Contact
Materials for National Reference Laboratories on
Food Contact Materials 7-8 November 2006, JRC,
Ispra, Italy

• B. Roduit(1) , Ch. Borgeat(1), S. Cavin(2) ,
• C. Fragnière(2) and V. Dudler(2)

(1)
Advanced Kinetics and Technology Solutions
http//www.akts.com/sml.html
(2)
Swiss Federal Office of Public Health, Division
of Food Science
http//www.bag.admin.ch
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Overview

• Actual limitation in simulation
• Description of model
• Importance of temperature control
• Relevance of the partition coefficient
• Mathematical verification
• Experimental validation
• Conclusions

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Kinetics of diffusion in polymer
Ficks 2nd law of diffusion
The description of the migration in a polymer
requires an analytical solution of this partial
differential equation
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Diffusion out of a plane sheet
Mt
time
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Constraints
C
Migrant M
X
0
L
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Consequences

• Analytical solutions of Ficks law are restricted
  to simple cases
• Single layer package
• Simple initial and boundary conditions during
  migration
• Homogeneous distribution of migrant
• Migration under isothermal condition
• Complex, modern packaging requires numerical
  approximation

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Numerical approximations

• Monte-Carlo
• Variational methods
• Finite Element Analysis
• Finite Differences

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FEA is the application of the Finite Element
Method. In it, the object or system is
represented by a geometrically similar model
consisting of multiple, linked, simplified
representations of discrete regions i.e., finite
elements. The analysis is therefore done by
modelling an object into thousands of small
pieces (finite elements). The finite elements are
used for solving partial differential equations
(PDE) approximately.
computational
physical
f
t
Discretization
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• Finite Element Analysis is written as a set of
  communicating elements
• Organization of an object in a (virtual) mesh

?

• Grid generation in time and in space

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Considering one layer inside the packaging, it
can be demonstrated that the mass of the layer
which is taken for calculation of the diffusion
of both migrant and simulant can be treated as an
infinite surface of thickness d (i.e.
infinite in two directions and of wall
thickness d in the third).
and
gt Ficks 2nd law of diffusion
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Model assumptions

• the migration follows a diffusive process (Ficks
  law) and is not controlled by other kinetic steps
  
• D f (T) Piringers model, Arrhenius
  relationship or customized equation
• the equilibrium solubility of the migrant in the
  different layers of the structure and in the food
  is governed by the partition coefficients, K,
  between the layers of the multilayer structure
  and between the contact layer and food,
  respectively.
• the food is in intimate contact with all the
  package surfaces (no void space)
• the transfer of migrant at the interface
  material-food is rapid and the migrant is
  homogeneously distributed in the food.
• the transfer of migrant at the interface
  package-air is nil

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Diffusion in a multilayer structure
PP
migration
FOOD
PE
additive
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Example with partition coefficientCylindrical
package, height of 25 cm and diameter of 4 cm
K2,3 1
K4,5 1
solubility in food 4.3 mg/kg
partition coefficient K3,4 0.7
K1,2 1
partition coefficient K5,Food 100
functional barrier gt time lag 5 days
Simulated migration experiment in a five-layers
laminate film. (A) Concentration profiles of the
migrant in the multilayer material at different
times 0 (a), 0.5 (b), 5 (c), 20 (d) and 70 days
(e). (B) Corresponding migration curve.
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Importance of temperature control
HDPE film d 250 µm Additive MW
350g/mol Conc.1000 ppm
1000cm3

• Migration conditions
• 10 days, temperature 20 10C, 24 hours
  modulation
• 10 days, isothermal temperature 20C

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Importance of temperature control
T isothermal 20C
T modulation 20 10C, 24 hours period
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Real climatic variation
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Real climatic variations
T isothermal 20C
T modulation 20 10C, 24 hours period
Barcelona climate November
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Programme validation

• Mathematical verification
• 2. Experimental validation

?to assess the accuracy and stability of the
algorithm
?measure of the migrant distribution inside
multilayer structures
?migration tests with temperature variation
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Mass conservation
Iterative, repetitive calculation can bring
rounding calculation error ?
concentration
C
Diffusion until equilibrium
C/6
error lt 5 10-5
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Strategy of mathematical validation

• Design a multilayer structure comparable to a
  single layer
• Calculate the migration by FEA approximation and
  with the true analytical solution
• Determine the accuracy at different Mt/M? of the
  migration

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Strategy of mathematical validation

• Determine the accuracy at different Mt/M? of the
  migration

TRUE (Analytical solution) 1 Layer
FEA (Numerical solution) 10 Layers
C
Diffusion comparison
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Strategy of mathematical validation

• Determine the accuracy at different Mt/M? of the
  migration

TRUE (Analytical solution) 1 Layer
FEA (Numerical solution) 10 Layers
C
Diffusion comparison
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Strategy of mathematical validation

• Vary parameters and repeat experiment
• Thickness of multilayer structure 1-1000
  µmNumber of layers 1-10Minimal layer
  thickness 1 µmMigrant concentration 100-1000
  mg/kg
• Diffusion coefficient 10-15 10-7
  cm2/sMigration time 10 min 100 years

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Distribution of relative error
Number of tests 1200 Average error -0.4 Std.
Deviation 0.6
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Diffusion experiment in multilayer
experimental conditions Multilayer
LDPE/LDPE/PP with one PE layer saturated with
additive Total thickness 1100 µm Diffusion
both external surfaces are insulated Temperature
60C Analysis IR-microspectrometry
Benzophenone
PE
PP
additive
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time 0
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time 51 min
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time 84 min
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time 154 min
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Migration with temperature variation
experimental conditions Polymer LDPE, 800 µm
thick film with 5 additive Simulant
hexane Migration one side T-variation step or
ramp Analysis GC
HP 136 C-radical scavenger (Ciba Specialty
Chemicals)
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Migration profile with a T-step
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Migration profile with a T-step
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Migration Profile with a double T-step
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Migration Profile with a double T-step
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Migration profile with a T-ramp
1C/min
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Migration profile with a T-ramp
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Conclusions

• Simulation of migration from multilayer laminate
  by numerical analysis is possible
• Temperature variation can be taken into account
• Possible implementation of partition coefficients
  in the model up to 10 multilayer films
• Trade-off between the complexity of use and the
  programme capability

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• For more information
• See publication in
• FOOD ADDITIVES AND CONTAMINANTS
• October 2005
• Or
• http//www.akts.com/sml.html