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http ://www.akts.com/sml.html Simulation of release of additives from mono- and multilayer packaging B. Roduit (1), Ch. Borgeat.

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Presentation on theme: "http ://www.akts.com/sml.html Simulation of release of additives from mono- and multilayer packaging B. Roduit (1), Ch. Borgeat."— Presentation transcript:

1 http://www.bag.admin.ch http ://www.akts.com/sml.html Simulation of release of additives from mono- and multilayer packaging B. Roduit (1), Ch. Borgeat (1), S. Cavin (2), C. Fragnière (2) and V. Dudler (2) Swiss Federal Office of Public Health, Division of Food Science Advanced Kinetics and Technology Solutions 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 http://www.akts.com/sml.html http://www.bag.admin.ch (1) (2)

2 http://www.bag.admin.ch http ://www.akts.com/sml.html Overview Actual limitation in simulation Description of model Importance of temperature control Relevance of the partition coefficient Mathematical verification Experimental validation Conclusions

3 http://www.bag.admin.ch http ://www.akts.com/sml.html Kinetics of diffusion in polymer Fick’s 2 nd law of diffusion The description of the migration in a polymer requires an analytical solution of this partial differential equation

4 http://www.bag.admin.ch http ://www.akts.com/sml.html Diffusion out of a plane sheet time MtMt

5 http://www.bag.admin.ch http ://www.akts.com/sml.html Constraints Migrant M 0L C X C0C0 1.Initial conditions t = 0 C = C 0 CtCt 2.Boundary conditions t > 0 X = L C = 0 3.The diffusivity D is constant

6 http://www.bag.admin.ch http ://www.akts.com/sml.html Consequences 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

7 http://www.bag.admin.ch http ://www.akts.com/sml.html Numerical approximations Monte-Carlo Variational methods Finite Element Analysis Finite Differences…

8 http://www.bag.admin.ch http ://www.akts.com/sml.html computational physical f t Discretization 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.

9 http://www.bag.admin.ch http ://www.akts.com/sml.html Finite Element Analysis is written as a set of communicating elements Organization of an object in a (virtual) mesh uniformregular Structured Grids: rectilinear Grid generation in time and in space ?

10 http://www.bag.admin.ch http ://www.akts.com/sml.html 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 2 nd law of diffusion

11 http://www.bag.admin.ch http ://www.akts.com/sml.html 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 http://www.bag.admin.ch http ://www.akts.com/sml.html Diffusion in a multilayer structure additive PP FOOD migration PE

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15 http://www.bag.admin.ch http ://www.akts.com/sml.html 0 days 2 days 5 days 40 days 70 days food

16 http://www.bag.admin.ch http ://www.akts.com/sml.html solubility in food = 4.3 mg/kg 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. partition coefficient K 3,4 = 0.7 partition coefficient K 5,Food = 100 K 1,2 = 1 K 2,3 = 1 K 4,5 = 1 Example with partition coefficient: Cylindrical package, height of 25 cm and diameter of 4 cm

17 http://www.bag.admin.ch http ://www.akts.com/sml.html Importance of temperature control HDPE film d: 250 µm Additive MW: 350g/mol Conc.:1000 ppm 1000cm 3 Migration conditions a)10 days, temperature 20± 10°C, 24 hours modulation a)10 days, isothermal temperature 20°C

18 http://www.bag.admin.ch http ://www.akts.com/sml.html Importance of temperature control T isothermal 20°C T modulation 20 ± 10°C, 24 hours period 12%

19 http://www.bag.admin.ch http ://www.akts.com/sml.html Real climatic variation

20 http://www.bag.admin.ch http ://www.akts.com/sml.html Real climatic variations T isothermal 20°C T modulation 20 ± 10°C, 24 hours period Barcelona climate November

21 http://www.bag.admin.ch http ://www.akts.com/sml.html Programme validation 1.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

22 http://www.bag.admin.ch http ://www.akts.com/sml.html Mass conservation Diffusion until equilibrium concentration C C/6 error < 5 10 -5 Iterative, repetitive calculation can bring rounding calculation error ?

23 http://www.bag.admin.ch http ://www.akts.com/sml.html 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 M t /M  of the migration

24 http://www.bag.admin.ch http ://www.akts.com/sml.html Strategy of mathematical validation Diffusion comparison FEA (Numerical solution) 10 Layers ‘TRUE’ (Analytical solution) 1 Layer C Determine the accuracy at different Mt/M  of the migration

25 http://www.bag.admin.ch http ://www.akts.com/sml.html Strategy of mathematical validation Diffusion comparison FEA (Numerical solution) 10 Layers ‘TRUE’ (Analytical solution) 1 Layer C Determine the accuracy at different Mt/M  of the migration

26 http://www.bag.admin.ch http ://www.akts.com/sml.html Strategy of mathematical validation Vary parameters and repeat experiment Thickness of multilayer structure: 1-1000 µm Number of layers: 1-10 Minimal layer thickness: 1 µm Migrant concentration: 100-1000 mg/kg Diffusion coefficient: 10 -15 – 10 -7 cm 2 /s Migration time: 10 min – 100 years

27 http://www.bag.admin.ch http ://www.akts.com/sml.html Distribution of relative error Number of tests 1200 Average error -0.4% Std. Deviation ± 0.6%

28 http://www.bag.admin.ch http ://www.akts.com/sml.html Diffusion experiment in multilayer Benzophenone 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 PE PP additive

29 http://www.bag.admin.ch http ://www.akts.com/sml.html time = 0

30 http://www.bag.admin.ch http ://www.akts.com/sml.html time = 51 min

31 http://www.bag.admin.ch http ://www.akts.com/sml.html time = 84 min

32 http://www.bag.admin.ch http ://www.akts.com/sml.html time = 154 min

33 http://www.bag.admin.ch http ://www.akts.com/sml.html 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)

34 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration profile with a T-step

35 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration profile with a T-step

36 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration Profile with a double T-step

37 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration Profile with a double T-step

38 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration profile with a T-ramp 1°C/min

39 http://www.bag.admin.ch http ://www.akts.com/sml.html Migration profile with a T-ramp

40 http://www.bag.admin.ch http ://www.akts.com/sml.html 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

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

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