Simulation of the diffusion processes of migrant and simulant occurring in packaging multi layers can be reduced to the analysis of a single layer.

Fig. 1 – Scheme of the simulation of the migrant concentration in packaging

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). To calculate the amount of the migrant that reaches the food after a certain time all package geometries are reduced to a simple case: a plane of several sheets with only one surface in contact with the food. It can be assumed that diffusion obeys Fick’s law and that the diffusion of the species in the y and z direction is negligible as compared to x direction. The presented model enables calculations of the concentration gradients using numerical analysis methods, considering the diffusion progresses of both species (migrant and simulant) in the multi-layers. The Arrhenius, Piringer and Brandsch equations can be applied in order to evaluate a magnitude for the diffusion coefficient in the different layers. The equations have been developed using coordinates (x and t) where the whole surface of the packaging will be derived from the different packaging shapes.

 

Concentration distribution in the layers

Generalized mass balance over a layer volume element

In order to consider the change of the concentration of the migrant (and/or simulant) diffusing inside the layer, a mass balance over a volume element can be made as following:

Fig. 2 – Generalized mass balance over a layer volume element

Input = Output + Accumulation + Reaction

(2.1)

(2.2)

(2.3)

(2.4)

 

where

(2.5)

(2.6)

 

Considering cylindrical coordinates and generalizing the above equation we can write for a recipient

(2.7)

(2.8)

where J is a geometry factor which is dependent on the type of recipient:

J=0 for the infinite plate
J=1 for the infinite cylinder
J=2 for the sphere

Without chemical reaction

(2.9)

the mass balance for a migrant ‘M’ reads for an infinite plate:

(2.10)

Similarly, the mass balance for a simulant S’ reads:

(2.11)

with the following possible boundary conditions:

– Boundary (I): Symmetry axis (if perfect insulation):

(2.12)

If a layer is insulated on its left or right side, the boundary condition is derived from the symmetrical properties of the concentration distribution at the wall surface of a layer U.

– Boundary (II): Considering the “left” and “right” sides of one interface, we can write at the interface between two layers U and U+1.

(2.13)

This boundary condition is derived from comparison of fluxes at the interface between the different layers.

In the above scheme, the initial concentration of the migrant and solubility have to be set for each layer. To solve the problem we essentially apply the equation (2.8) under consideration of the boundary conditions. The solubility in each layer to “control” the effect of the partition coefficient at the interface between two layers is also considered in the calculation procedure. A mass balance can be established similarly for both, migrant and/or simulant.

 

Discretization of the layer domain

The packaging mass which is taken for the diffusion expressions can be treated as an “infinite” surface of thickness “d” (i.e. infinite in two directions -y, z directions- and of layer thickness “d” in the third -x direction-).

Using the generalized mass balance eq. 2.8 over one layer element in the packaging wall, we can relate the diffusion of e.g. a migrant ‘M’ in each layer. The scheme of the grid-point distribution applied for calculating the concentration distribution in each layer is presented below.

Fig. 3 – Description of a Layer “Domain”. The grid-point distribution is chosen with variable step lengths in the diffusion direction x as well as in time

 

The functions of the mass balance (eq. 2.8) are singular at the interface of the different layers and at the beginning of the diffusion process (times around 0). Therefore the grid-point distribution must be chosen with variable step lengths (see Fig. 2.3). The generation of adaptive meshes allows the achievement of a desired resolution in localized regions and decreases by orders of magnitude the calculation time. Grid points are added in regions of high gradients to generate a denser mesh in that region and subtracted from regions where the solution is decaying or flattening out.

The Fig. 4 illustrates the discretization of the governing partial differential eq. 2.8 describing the diffusion processes occurring inside the layer. The layers can be divided into a series of N mesh planes each having IxJ elements. The position of the mesh planes is moved along the time-axis allowing the calculation of the concentrations of both species (migrant and stimulant) at each location for every x, t grid points of each layer.

Discretization: Let us choose “n” for satisfying following conditions:

(2.14)

(2.15)

where λ = 1
e.g. λ = 1

describes with arbitrary units the length of a desired thickness inside one layer. After computing a series expansion of the above equations with respect to the variable “k”, we obtain:

(2.16)

(2.17)

Taking the natural logarithm, we can solve the inequality 2.17 for “n” and round the obtained value to the nearest integers towards minus infinity:

(2.18)

The concentration profile for the migrant may now be expressed by substituting finite-difference approximations. Taylor series expansions of the second derivates are computed, with respect to the variable x, up to the order three. The series data structure represents an expression as a truncated series in one indeterminate node, expanded about the particular point (i ,j) (see Fig. 2.3). The more detailed presentation of analysis is upon the scope of this help.

 

Programming

Using the boundary conditions expressed by eqs. 2.12-13 and eq. 2.8 which describes the diffusion in the bulk, the concentration distribution inside all layers can be computed for both migrant and the simulant. The initial concentrations of the migrant (in mg/kg units) have to be introduced for all layers at t = 0. The strong internal gradients are calculated very precisely due to the variable step lengths.

Software Basics

The use of AKTS-SML software can be described in four steps:

Fig. 4 – Applications of SML-Software from packaging definition to legislation conformity.

1. Define the package by creating the different articles of the package and introducing their properties.
2. Predict the migration using different temperature profiles (iso, non-iso, worldwide climate, etc.).
3. Analyze the calculated outputs.
4. Check the conformity of the results with corresponding legislations.

 

Package Structure

A package is a group of different articles, each having different layers properties. For instance a bottle can be treated as two articles: the bottle cap and the bottle body.

Fig. 5 – A package can be composed of multiple articles.

An article is composed of one or more layers of different sizes and properties.

Fig. 6 – An article is composed of multiple layers and Fig. 3.4 : Migrants can be found in all layers.

Chemicals can be found in one or more layers.

 

Creating packages and articles

The package details will be displayed by clicking on New Package.

The Package Properties tab allows changing the geometry and the size of the package. The surface, shape and size of each article can be defined in the grid.

The Wizard

When creating an article, many information and properties have to be implemented. The role of the Article Creation Wizard is to help introducing all this information step by step.

1. Surface: The surface of the article has to be entered first.
2. Layers: Then enter the number of layers and give the information for each of them.
3. Migrants: Enter the number of chemicals and fill the information for each of them.
4. Data: First specify the concentration of each migrant in each layer, then the diffusion coefficients and finally the partition coefficient.

When the package data are fully implemented, it is possible to start calculating predictions by clicking on the Run Prediction button

Note: the Wizard is optional.

 

Article Properties

The article grid.

In the Article Grid it is possible to customize the concentration, the diffusion coefficient and the partition coefficient for all migrants and layers.

The button Add Layer adds a new layer displayed as a column in the grid.
The button Add Migrant(s) adds a new chemical displayed in a row in the grid.

See more about:

• The layer properties;
• The migrant(s) properties;
• The data (concentration and coefficients).

When all the properties of the article are introduced click on Run Prediction to start a calculation process. See the Predictions chapter for more information.

 

Layers

The layer properties panel allows defining the properties of the current selected layer.
Type (of layer) defines if the layer is a contact medium (typically food) or a polymer.

Fig. 12 – Considered Properties of Polymer Type Layer.

Database allows browsing for a known polymer.

Fig. 13 – Layer Material(s) Database.

 

Contact medium

 

When all properties of an article are introduced, it is possible to proceed with prediction calculations by clicking on the Run Prediction button.

Fig. 20 – The run prediction button

The predictions can be performed for different temperature profiles:

• Isothermal
• Non-Isothermal
• Stepwise
• Modulated
• Shock
• Worldwide
• STANAG
• Customized

 

Isothermal

In the isothermal conditions mode, it is possible to set a number of isotherms and the temperature difference (ΔT) between each isotherm.

Fig. 21 – Isothermal conditions

 

Non-Isothermal

In the non-isothermal conditions, the starting temperature and different heating rates can be defined.

Fig. 22 – Non-Isothermal conditions

 

Stepwise

The stepwise conditions are a combination between isothermal and non-isothermal temperature modes. A number of cycles can be defined.

Fig. 23 – Stepwise conditions

 

Modulated

In the modulated conditions, it is possible to set an oscillatory temperature mode as e.g. a day/night cycle

Fig. 24 – Modulated conditions

 

Shock

The shock temperature conditions simulate a rapid temperature raise. The frequency of the temperature shocks can be also defined.

 

 

The output window shows the results of the prediction calculations. The window is divided as following:

• The results grid;
• The c(t) chart;
• The c(x, t) chart;
• Comparison Output;
• Sum Output

Moving the mouse pointer over the c(t) chart will update the results grid and the c(x, t) chart based on the time pointed on the c(t) chart.

 

The results grid

Fig. 29 – The Results Grid c(t)

The grid shows the values of the concentration, the diffusion coefficients and the partition coefficients for all migrants in all layers.

 

The c(t) chart

Fig. 30 – The c(t) chart

 

The c(t) chart shows the dependence of the concentration of the migrant as a function of time. The chemicals and layers to be displayed can be selected by using the checkboxes in the results grid.

Exportation and importation of c(t) and c(x,t) dependences for comparison can be done by a right-click on the calculated results as presented in the next figure.

 

Fig. 31– Import / Export of c (t) Chart

 

The c(x, t) chart

Fig. 32 – The c(x, t) chart

 

The c(x, t) chart shows the spatial concentration of the migrant in the different layers.

Exportation and importation of c(t) and c(x,t) curves for comparison can be done by a right-click on the calculated results as presented in the next figure.

 

Fig. 33 – Import / Export of c (x, t) Chart

 

Comparison Output

The comparison output window allows comparing the calculation results of different outputs. To add an output to the comparison, drag and drop the output from the list on the left to the dedicated zone in the comparison output window.

Fig. 34 – The comparison output window

 

Sum Output

The sum output window allows adding the calculation results presented in different outputs of same migrants. To add an output to the comparison, drag and drop the output from the list on the left to the dedicated zone in the comparison output window.

Fig. 35 – The sum output window

In the last years migration modelling became more and more accepted and it was introduced in legislation for plastic food contact materials and articles allowing for compliance assessment with applicable specific migration limits stipulated by legislation.

Legislation conformity check: Compliance evaluation for substances with specific migration limit (SML) listed in the Plastics Regulation (EU) No 10/2011 and generation of compliance certificates.

Fig. 36 – Legislation and compliance report (calculated migration values)

 
 

Fig. 37 – Legislation and compliance report (migration limits)

Introduction

Sensitivity analysis studies allow estimating how the uncertainties in the model inputs (X1;X2;…;Xk) affect the model’s response Y, which (for simplicity) we assume to be a scalar:

Y = f(X1;X2;…;Xk);

where f describes the implemented model.

A sensitivity analysis attempts to provide a ranking of the model’s input assumptions with respect to their contribution to model output variability or uncertainty. The difficulty of a sensitivity analysis increases when the underlying model is nonlinear, nonmonotonic or when the input parameters range over several orders of magnitude. Many sensitivity analysis methods have been proposed. For example, the partial rank correlation coefficient and standardized rank regression coefficient have been found to be useful. Scatter plots of the output for each of the model inputs can be a very effective tool for identifying sensitivities, especially when the relationships are nonlinear. In a broader sense, the sensitivity analysis can show how conclusions may change if models, data, or assessment assumptions are changed, see [1] for more details on the subject.

The analysis methods available in SML software are:

• Monte Carlo
• Fourier Amplitude Sensitivity Test (FAST)
• Sobol

Monte Carlo Simulation (MCS)

Monte Carlo Simulation (MCS) is a widely used method applied for uncertainty or sensitivity analysis. It involves random sampling from the distribution of inputs and successive model runs until the desired accuracy of the outputs is reached. Not only the means and variances but also the distributions of input parameters are required to run the MCS. In the present version of SML Software only Gaussian (normal) distribution has been implemented for the different input parameters.

Fig. 38 – Random sampling from the distribution of inputs (Gaussian (normal) distribution).

The main advantage of the MCS is its general applicability. MCS suffers for its computational requirements since thousands of repetitive runs of a model are required to reach convergence. High-speed personal computers have minimized the computational challenges. Another limitation of MCS is the need for user-specified rules for determining the number of simulations required, see [2-4] for more information and recommendation on the subject.

Fig. 39 – Quantification of the amount of variance that each input factor Xi (all variables of the articles) contributes with on the unconditional variance of the output V (Y).

Sensitivity measures based on the MCS approach include regression-based measures applying Standardized Regression Coefficients (SRC), Partial Correlation Coefficients (PCC), Standardized Rank Regression Coefficients (SRRC), Partial Rank Correlation Coefficients (PRCC). Some of them have been implemented in the present version of SML and are described below.

Correlation coefficient (CC) and partial correlation coefficients (PCC)

The correlation coefficient (CC) usually known as Pearson’s product moment correlation coefficients, provides a measure of the strength of the linear relationship between two variables x and y and is denoted as corr(x; y), see for example [5] for more information on the definition of CC.
The correlation coefficient measures the extent to which y can be approximated by a linear function of x, and vice versa. In particular if exactly y = a + bx, then corr(x; y) = 1, if b = 1 and corr(x; y) = -1, if b = -1. CC only measures the linear relationship between two variables without considering the effect that other possible variables might have. When more than one input factor is under consideration, as it usually is, the partial correlation coefficients (PCCs) can be used instead to provide a measure of the linear relationships between two variables when all linear effects of other variables are removed. PCC between an individual variable xi and y can be written in terms of correlation coefficients, see for example [5]. It is denoted by pcc(xi; y). PCC characterizes the strength of the linear relationship between two variables after a correction has been made for the linear effects of the other variables in the analyses.

Fig. 40 – Correlation coefficients (CC) providing a measure of the strength of the linear relationship between two variables x (variable parameters in the article) and y (migration).

 

Fig. 41 – Scatter plots illustrating relationships between the input factor Xi (variable parameters in the article) and the output Y (migration).

 

A scatter plot of the points [Xij ; Yj ] for j = 1; 2;…;N can reveal nonlinear or other unexpected relationships between the input factor Xi and the output Y. Scatter plots are undoubtedly the simplest sensitivity analysis technique and their applications is a natural starting point in the analysis of a complex model. It facilitates the understanding of model behavior and the planning of more sophisticated sensitivity analysis.

 

Rank correlation coefficient (RCC) and partial rank correlation coefficients (PRCC)

Since the use of the correlation coefficient and partial rank correlation coefficient methods is based on the assumption of linear relationships between the input-output factors, they will perform poorly if the relationships are nonlinear. The SML-Software allows applying the rank transformation of the data. This concept can be used to transform a nonlinear but monotonic relationship to a linear relationship. When using rank transformation the data are replaced with their corresponding ranks. The usual correlation procedures are then performed on the ranks instead of the original data. Spearman rank correlation coefficient (RCC) is the corresponding CC calculated on ranks and partial rank correlation coefficients (PRCC) is the PCC calculated on ranks.

Rank transformed statistics is more robust, and provides a useful solution in the presence of long tailed input-output distributions. A rank transformed model is not only more linear, it is also more additive. Thus the relative weight of the first-order terms is increased on the expense of higher-order terms and interactions, see for example [5].

 

Variance based methods for sensitivity analysis

The main idea of the variance-based methods is to quantify the amount of variance that each input factor Xi contributes with on the unconditional variance of the output V (Y).

We are considering the model function: Y = f(X), where Y is the output and X = (X1;X2;…;Xk) are k independent input factors, each one varying over its own probability density function. The values of the input parameters are not exactly known. We assume that this uncertainty can be handled by using random variables Xj , j = 1;…; k of known distributions. Then the model output is also a random variable Y = f(X1; : : : ;Xk).

The first order effect for the input factor j is the fraction of the variance of the output Y which can be attributed to the input Xj and is denoted by Sj , see for example [5].

To estimate the value of Sj we require realizations of the input distributions and the associated model evaluations. The ratio Si was named as a first order sensitivity index by Sobol [6]. The first order sensitivity index measures only the main effect contribution of each input parameter on the output variance. It doesn’t take into account the interactions between input factors. Two factors are said to interact if their total effect on the output isn’t the sum of their first order effects. The effect of the interaction between two orthogonal factors Xi and Xj on the output Y can be computed (see for more details [5]) and is known as the second order effect. Higher-order effects can as well be computed, see for example [5].

A model without interactions is said to be additive, for example a linear one. The first order indices sums up to one in an additive model with orthogonal inputs. For additive models, the first order indices coincide with what can be obtained with regression methods. For non-additive models we would like to know information from all interactions as well as the first order effect. For non-linear models the sum of all first order indices can be very low.

The sum of all the order effects that a factor accounts for is called the ‘total’ effect [7]. So for an input Xi, the total sensitivity index STi is defined as the sum of all indices relating to Xi (first and higher order).

There are different techniques to obtain these sensitivity indices, such as Sobol’s indices, Jansen’s Winding Stairs technique, (Extended) Fourier Amplitude Sensitivity Test ((E)FAST).

In the present software, two methods are implemented, the FAST method and the Sobol’s indices based on Jansen’s Winding Stairs technique.

 

Fourier Amplitude Sensitivity Test (FAST)

The Fourier Amplitude Sensitivity Test (FAST) was proposed already in the 70’s [8-10] and was since this time successfully applied to chemical reaction systems involving sets of coupled, nonlinear rate equations.

FAST is a sensitivity analysis method which does not use a Gaussian distribution. Rotating vectors are assigned to each variable, and each has a unique frequency and the amplitude of the “mean”. A lot of input sets are generated, making the variables oscillating. A Fourier analysis is then applied on the results. The number of runs depends only on the number of variables.

Note that the graphs displaying the results obtained by the FAST method are the same as the graphs presenting results obtained with Sobol, approach except that FAST shows only the local sensitivity.

Fig. 42 –  Quantification based on FAST analysis of the amount of variance that each input factor Xi (all variables of the articles) contributes with on the unconditional variance of the output V (Y).

 

Fig. 43 – FAST analysis results. Sensitivity S(v) of each variable (influence of each examined variable on the migration results)

 

Sobol’s indices via Winding Stairs

Chan, Saltelli and Tarantola [11] proposed the use of a new sampling scheme to compute both first and total order sensitivity indices in only N x k model evaluations. The sampling method used to measure the main effect was called Winding Stairs, developed by Jansen, Rossing and Deemen in 1994 [12].

A first set of variables simply comes from the Gaussian distribution. Then a lot of other set of input of variables are generated from the first set and used in complex mathematics analysis afterward (For example: if one enters 10 runs and has one migrant with four variables, it will run the simulations (4+1)*10 times)

Fig. 44 – Sobol analysis results. Total sensitivity St(v) of the variables (influence of all variables on the migration results)

The above figures illustrate the total sensitivity St(v) of the variables (influence of all variables on the migration results) and the evolution of the total sensitivity as a function of time. In some cases there are “unexplained” values. This situation can happen when the calculation is not fully completed. Two cases are possible:

• The number of runs chosen to perform the calculations is not sufficient;
• Not enough variables are chosen to apply the method correctly.

Comments about our example :

All methods clearly demonstrate for our examined article that the initial concentration of the migrant (OCTADECYL 3-(3,5-DI-tert-BUTYL-4-HYDROXYPHENYL) PROPIONATE) plays the most important role concerning its migration from the article to the contact medium. The other parameters such as the thickness of both layers and the solubility of migrant in the contact medium have in comparison a negligible influence on the migration.

[1] A. Saltelli, K. Chan, M. Scott (Eds.). Sensitivity Analysis Probability and Statistics Series, John Wiley and Sons, 2000.
[2] J. C. Helton, F. J. Davis. Sampling Based Methods. Chapter 6 in Mathematical and Statistical Methods for Sensitivity Analysis of Model Output. Edited by A. Saltelli, K. Chan, and M. Scott, John Wiley and Sons, 2000.
[3] Helton J. C. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering and System Safety, 42, 327 – 367, 1993.
[4] http://www.epa.gov/reg3hwmd/risk/human/info/guide1.htm
[5] P.-A. Ekström A simulation toolbox for sensitivity analysis, degree project, 2005.
[6] I. M. Sobol’. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment, 1, 407 – 414, 1993.
[7] T. Homma and A. Saltelli. Importance measure in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety, 52, 1 – 7, 1996.
[8] R. I. Cukier, C. M. Fortuin, Kurt E. Shuler, A. G. Petschek, and J. H. Schaibly. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I theory. The Journal of Chemical Physics, 59, 3873 – 3878, 1973.
[9] J. H. Schaibly and Kurt E. Shuler. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II applications. The Journal of Chemical Physics, 59, 3879 – 3888, 1973.
[10] R. I. Cukier, J. H. Schaibly, and Kurt E. Shuler. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. III analysis of the approximations. The Journal of Chemical Physics, 63, 1140 – 1149, 1975.
[11] Karen Chan, Andrea Saltelli, and Stefano Tarantola. Winding stairs: A sampling tool to compute sensitivity indices. Statistics and Computing, 10, 187 – 196, 2000.
[12] M.J.W. Jansen, W.A.H. Rossing, and R.A. Daamen. Monte Carlo estimation of uncertainty contributions from several independent multivariate sources. Predictability and Nonlinear Modelling in Natural Sciences and Economics, 334 – 343, 1994.

Introduction

Single use food contact materials like food packaging are in the focus of the food contact legislation. Repeated use food contact materials like kitchen utensils, drinking bottles, food processing equipment, etc. are as important. Generally, migration will reduce upon successive uses because the migration is determined by diffusion. Occasionally the migration may increase upon successive uses, e.g. migration of formaldehyde from phenol-formaldehyde or melamine-formaldehyde articles may increase due to hydrolysis in addition to diffusion. Therefore, migration from repeated use articles e.g. a food storage box or a bowl or plate should be assessed in three successive contact periods, using a new portion of food simulant for each contact period. Conventionally the migration found in the third migration experiments shall comply with the relevant specific migration limit.

Determination of the migration from a repeated use article does not deviate from the procedure followed for single use articles. However, establishing the right contact conditions of time and temperature as well as actual surface to volume ratio may be more complex. More details can be found in the guidelines of the EU Commission and the Joint Research Center:

Fig.45 – Guidelines on testing conditions for articles in contact with foodstuffs. Technical guidelines for compliance testing.

 

More complex repeated use scenarios are relevant for plastic materials in contact with drinking water. The migration simulation follows the testing requirements given in DIN EN 12873-1 and 2 and the KTW Guideline of the German UBA:

• cold water: 1 + 3 x 3 days;
• warm water: 1 + 3 x 1 + 3 + 3 x 1 days;
• hot water: 1 + 3 x 1 + 3 + 3 x 1 days.

According to the KTW Guideline of the German UBA extended testing cycles up to 31 days by repeating the above 10 days test cycles is optional but compulsory for multilayer materials.

The above-mentioned test cycles are implemented as predefined cycles in the SML 6 software:

Fig. 46 – Predefined cycles in the predictions window.

or can be customized by user by e.g. extending of testing scheme for 31 days = 4 x [4 x 1 + 3] + 3 x 1 d

Fig. 47 – Set up of an advanced repeated use function.

Example

The application of the the repeated use function implemented in the SML 5.3 software is illustrated for the composite drinking water pipe with the layered structure HDPE/Aluminium/PE-Xb:

Fig. 48 – Composite drinking water pipe.

It is assumed that the adhesive layer between the plastic (HDPE and PE-Xb) and the Aluminum layers contains a residual amount of 5000 ppm maleic acid.

 

Repeated use simulation

The migration simulations during the contact of the pipe with cold (23°C) and warm water (60°C) were carried out according to the specific migration assessment requirement of the KTW Guideline. The figure (a) presents the initial spatial concentration profile C(x,t) of the migrant (maleic acid) at 23°C. The figure below (b) shows the spatial concentration of the migrant (maleic acid) C(x,t) after a period of 10 days at 23°C.

Fig. 49 – Initial spatial concentration profile C(x,t) of the migrant (maleic acid), essentially contained in the two adhesive layers.

 

Fig. 50 – Spatial concentration profile C(x,t) of the migrant (maleic acid) after 10 days at 23°C

At 23°C the PE-Xb layer acts as a functional barrier and no migration of maleic acid from the pipe to drinking water is observed after 10 days. The migrant concentration profile C(x,t) in figure (b) clearly confirms that the maleic acid present in the adhesive layer penetrates only slightly through the PE-Xb layer. The same result, i.e. no migration of maleic acid from the pipe to drinking water is observed for the extended test cycle of 31 days.

The following figures shows the migration of maleic acid from the pipe to drinking water during 35 days at 60°C (test applied for the warm water: 1 + 3 x 1 + 3 + 3 x 1 days): the figure (a) presents the initial spatial concentration profile C(x,t) of the migrant (maleic acid), the figure (b) shows the spatial concentration of migrant C(x,t) in the pipe after 35 days, figure (c) presents the concentration of maleic acid C(t) in water as a function of time.

 

Introduction

During production and processing food contact materials and articles are stored often on the reel or in the stack where the inner food contact layer of the material or article comes into contact with the next outer layer. In such situation the transfer of migrants from the outer layer (such as e.g. printing ink) to the food contact layer (e.g. sealing layer) may occur. The set-off function is an in-built functionality which simulates migration in the reel or in the stack during storage when the material or article is brought into contact with food or food simulant and the specific migration is simulated according to the conditions of use or testing.

Example

Conical aluminum tubes with an inside placed protective coating containing the authorized migrants and a decorative printing placed outside containing ‘permitted’ migrants (based on risk assessment).

 

Set-off during storage

The conical tubes are stored in the stack prior to filling during which set-off, i.e. transfer of migrants from the decorative printing to the protective coating occurs as displayed in the picture :

 

Fig. 54 – Conical tubes stored in the stack prior to filling.

Summary

In the European Union, the safety evaluation of a PET recycling process is performed by comparing the residual concentration of each contaminant in recycled PET (Cres) to a modelled concentration (Cmod) in PET [1]. This Cmod is calculated using generally recognized conservative migration models and it corresponds to a migration which cannot give rise to an unsafe dietary exposure.

This application note describes how to apply the fitting model in AKTS-SML software to calculate Cmod for a contaminant used in a challenge test performed for the determination of the cleaning efficiency.

[1] EFSA Panel on on food contact materials, enzymes, flavourings and processing aids (CEF); Scientific Opinion on the criteria to be used for safety evaluation of a mechanical recycling process to produce recycled PET intended to be used for manufacture of materials and articles in contact with food. EFSA Journal 2011;9(7):2184. [25 pp.] doi:10.2903/j.efsa.2011.2184.

 

Evaluation principles

Migration criterion

In the safety evaluation, EFSA considers that a contaminant present in recycled PET should not give rise to a migration in food which could result in a dietary exposure higher than 0.025 µg/ kg bw/day.

Three exposure scenarios are considered. For the infants, the population group the most at risk, the exposure limit is respected if the concentration in water is lower or equal at 0.1 µg/ kg (modelling over-estimation factor of 5 included).

Cmod is the concentration in recycled PET that leads to a migration equal to 0.1 µg/kg food, using migration modelling.

 

Evaluation principles

Modelling parameters

For the Cmod calculation (infant scenario), EFSA requires the following parameters to be applied in the modelling:

Contact time: 12 months
Contact temperature: 25°C
Thickness of PET package: 300 µm
Density of PET material: 1.375 g/cm3
Packaging geometry: EU-cube (V=1l, S=6dm2)
Diffusion coefficient, D: estimated with Piringer model (Ap’ = 3.1, Tau = 1577, worst case for T ≤ 70°C )
Partition coefficient, Kp/F 1.0 (good solubility)

 

Solving problem step by step

1. Create the traditional “EU cube” package (volume of 1 l, surface of 600 cm2), one layer PET of 300 µm

 

2. Define the characteristics of the PET layer in the tab “set to User Defined” (alternatively, material type can be selected and assigned using the database)

 

3. Select one migrant using the database (note: benzophenone is a common surrogate in challenge test of PET recycling process)

 

4. Assign an initial concentration of benzophenone in the PET material

Note: the initial concentration of the contaminant is not important as it will be fitted backwards.

 

5. Select the Piringer model for the estimation of the diffusion coefficient, then define the partition coefficient Kp/f equal to 1.0

 

6. Enter the density of the contact medium (water)

 

7. Run a prediction of the diffusion for the benzophenone

 

8. Then import the migration criterion from a predefined file (migration infant scenario.txt)

 

9. Switch the package in fitting mode…

 

10. …and chose to optimize the initial concentration in PET

Note: if the difference between the migration criterion and the predicted migration is too large, the fitting module may have difficulty optimising the Cmod value. The value of the initial concentration must then be adapted.

 

Final remarks

This calculation can be adapted to fit different scenarios (i.e. EFSA scenarios for toddler or adult) or to calculate Cmod of other surrogates used in challenge test of PET recycling process: use the prepared package “Cmod_calculation” and enter the parameters of the desired migrant.

Also, the contact time or the temperature of the articles can be modified to evaluate packaging other than bottles.

Summary

Flavoured milks, packed in a multilayer package are contaminated by different photoinitiators. The contamination occurs during the storage time of the printed material, by set-off, when the food contact layer stays in contact with the external layer.

The migration of photoinitiators into food simulant is measured to determine the real values diffusion coefficients.

This application note shows how to extract the different diffusion coefficients of each photoinitiator from the experimental data and to how to find the initial concentration in the food layer with the fitting mode.

 

Experimental

Material

The package is a multilayer cardboard/aluminium/LDPE with the cardboard surface printed (offset printing with UV-curing). The LDPE layer is 40 µm thick and is in contact with the food.

 

The three photoinitiators used to cure the ink are:

 

Experimental setup and conditions

The migration of photoinitiators from the LDPE layer into ethanol 95% (food simulant) is measured at 20°C. A one-side diffusion cell with a contact surface of 1dm2 and a volume of 100ml is used for the test. The initial concentration of photoinitiators in the LDPE, after set-off, is not measured and is unknown.

 

Measured data

The concentration measured during the experiments are indicated in the table below.

 

Solving problem step by step

1. Define the package corresponding to the experimental diffusion cell by using the surface/volume ratio geometry.

 

2. Define the characteristics of the layers (only two are necessary, as the aluminium layer acts as a barrier layer). Material type can be selected using the database.

 

…repeat step 2 for the contact medium layer

 

3. Add the migrants using the database The initial concentration of the photoinitiators was not assessed and is unknown. As the concentration in the ink layer is high (5%), the concentration in the LDPE can be high as well. Use a first estimate of 5 mg/kg (0.01% set-off).

 

…repeat step 3 for all migrants

 

4. Estimate the diffusion coefficients of the photoinitiator using the Piringer model.

 

5. Define the partition coefficients between the LDPE layer and the food simulant as 1 (worst case).

 

6. Duplicate this package twice to get one package per photoinitiator. Rename each article for one photoinitiator and delete the other two migrants.

 

7. Run a prediction for the first photoinitiator (ITX)

 

8. Then import the experimental data from a predefined file (migration ITX_20C.txt)

 

9. Switch the package in fitting mode…

 

10. …and optimize the initial concentration

 

11. Unselect the optimisation of the concentration and optimize the diffusion coefficient

 

12. Select to optimise both the concentration and the diffusion together and launch the fitting process again.

 

13. Repeat this process from step 7 on the two other packages and optimize the initial concentration and the diffusion coefficient for the two other photoinitiators

Expected results

 

14. Results for EHA

 

15. Results for PBzP