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Simulation of release of additives from mono- and multilayer packaging

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

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Simulation of release of additives from mono- and multilayer packaging

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  1. 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

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

  3. Kinetics of diffusion in polymer Fick’s 2nd law of diffusion The description of the migration in a polymer requires an analytical solution of this partial differential equation

  4. Diffusion out of a plane sheet Mt time

  5. Initial conditionst = 0 C = C0 C0 Ct • Boundary conditionst > 0 X = L C = 0 • The diffusivity D is constant Constraints C Migrant M X 0 L

  6. Analytical solutions of Fick’s 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 Consequences

  7. Monte-Carlo Variational methods Finite Element Analysis Finite Differences… Numerical approximations

  8. Elements 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

  9. Structured Grids: uniform regular rectilinear • 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

  10. 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 => Fick’s 2nd law of diffusion

  11. Model assumptions • the migration follows a diffusive process (Fick’s law) and is not controlled by other kinetic steps • D = f (T) [Piringer’s 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

  12. Diffusion in a multilayer structure PP migration FOOD PE additive

  13. 0 days 2 days 5 days food 40 days 70 days

  14. Example with partition coefficient:Cylindrical package, height of 25 cm and diameter of 4 cm K4,5 = 1 K2,3 = 1 solubility in food = 4.3 mg/kg partition coefficient K3,4 = 0.7 K1,2 = 1 partition coefficient K5,Food = 100 functional barrier => 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.

  15. Importance of temperature control HDPE film d: 250 µm Additive MW: 350g/mol Conc.:1000 ppm 1000cm3 • Migration conditions • 10 days, temperature 20± 10°C, 24 hours modulation • 10 days, isothermal temperature 20°C

  16. 12% Importance of temperature control T isothermal 20°C T modulation 20 ± 10°C, 24 hours period

  17. Real climatic variation

  18. Real climatic variations T isothermal 20°C T modulation 20 ± 10°C, 24 hours period Barcelona climate November

  19. Mathematical verification 2. Experimental validation Programme validation to assess the accuracy and stability of the algorithm measure of the migrant distribution inside multilayer structures migration tests with temperature variation

  20. Mass conservation Iterative, repetitive calculation can bring rounding calculation error ? concentration C Diffusion until equilibrium C/6 error < 5 10-5

  21. 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 Strategy of mathematical validation

  22. 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

  23. 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

  24. 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 Strategy of mathematical validation

  25. Distribution of relative error Number of tests 1200 Average error-0.4% Std. Deviation ± 0.6%

  26. 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: 60°C Analysis: IR-microspectrometry Benzophenone PE PP additive

  27. time = 0

  28. time = 51 min

  29. time = 84 min

  30. time = 154 min

  31. 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)

  32. Migration profile with a T-step

  33. Migration profile with a T-step

  34. Migration Profile with a double T-step

  35. Migration Profile with a double T-step

  36. Migration profile with a T-ramp 1°C/min

  37. Migration profile with a T-ramp

  38. 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 Conclusions

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

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