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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 CourseThe use of diffusion modelling to predict migration

offered by theCommunity Reference Laboratory on Food Contact Materials

for National Reference Laboratories on Food Contact Materials7-8 November 2006, JRC, Ispra, Italy



(1)

(2)



Overview

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



Kinetics of diffusion in polymer

2

2

x

CD

t

C

Fick’s 2nd law of diffusion

The description of the migration in a polymer requires an analytical solution of this partial differential equation



Diffusion out of a plane sheet

02

22

22 4

)12(exp

)12(

18

nt L

tDn

nMM

time

Mt

M



Constraints

Migrant M

0 L

C

X

C01. Initial conditions

t = 0 C = C0Ct

2. Boundary conditions

t > 0 X = L C = 0

3. The diffusivity D is constant



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



Numerical approximations

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



computationalphysical

ft

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.



• Finite Element Analysis is written as a set of communicating elements• Organization of an object in a (virtual) mesh

uniform regular

Structured Grids:

rectilinear

• Grid generation in time and in space

?



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).

2

2

2

2

z

c

x

c

z

c

x

c

2

2

2

2

y

c

x

c

y

c

x

c

and

2

2

x

CD

t

C=> Fick’s 2nd law of diffusion



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



Diffusion in a multilayer structure

additive

PP

FO

ODmigration

0 100 200 300 400th ickness [µm ]

0

200

400

600

800co

nce

ntra

tion

[pp

m]

layer 1 layer 3 layer 4 layer 5layer 2

PE







0 days

2 days

5 days

40 days

70 days

0 100 200 300 400th ickness [µm ]

0

200

400

600

800co

nce

ntra

tion

[pp

m]


food



0 20 40 60 80 100m igration tim e [days]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

con

cen

tra

tion

in fo

od

[mg

/kg

]

(B)

solubility in food = 4.3 mg/kg

functional barrier => time lag 5 days

0 100 200 300th ickness [µm]

0

200

400

600

800

con

cen

tra

tion

[p

pm

]


(a)

(b)

(c)

(d)

(e)

(A)

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 coefficientK3,4 = 0.7

partition coefficientK5,Food = 100

K1,2 = 1

K2,3 = 1 K4,5 = 1

Example with partition coefficient:Cylindrical package, height of 25 cm and diameter of 4 cm



Importance of temperature control

HDPE filmd: 250 µmAdditive MW: 350g/molConc.:1000 ppm

1000cm3

Migration conditions

a) 10 days, temperature 20± 10°C, 24 hours modulation

a) 10 days, isothermal temperature 20°C



Importance of temperature control

T isothermal20°C

T modulation20 ± 10°C,24 hours period

0 2 4 6 8 10m igration tim e [day]

0

2

4

6

8

mig

rant

con

cent

ratio

n [m

g/k

g] 12%



Real climatic variation



Real climatic variations

0 2 4 6 8 10m igration tim e [day]

0

2

4

6

8

mig

rant

con

cent

ratio

n [m

g/kg

]

T isothermal20°C

T modulation20 ± 10°C,24 hours period

Barcelona climateNovember



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



Mass conservation

Diffusion until equilibrium

concentration

C

C/6

error < 5 10-5

Iterative, repetitive calculation can bring rounding calculation error ?



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




Diffusion comparison

FEA (Numerical solution)10 Layers

‘TRUE’ (Analytical solution)1 Layer

C





Diffusion comparison

FEA (Numerical solution)10 Layers

‘TRUE’ (Analytical solution)1 Layer

C





• Vary parameters and repeat experimentThickness 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



Distribution of relative error

-5 -4 -3 -2 -1 0 1 2 3 4 5relative error [% ]

0

100

200

300

400

500

Fre

quen

cy

Number of tests1200

Average error -0.4%

Std. Deviation ± 0.6%



Diffusion experiment in multilayer

o

Benzophenone

experimental conditions

Multilayer: LDPE/LDPE/PPwith one PE layer saturated with additive Total thickness: 1100 µmDiffusion: both external surfaces are insulatedTemperature: 60°CAnalysis: IR-microspectrometryPE

PP

additive



0 250 500 750 1000 1250th ickness [µm ]

0

10

20

30

40

50

60

con

cent

ratio

n [a

.u]

LD PE LD PE PP

time = 0



0 250 500 750 1000 1250th ickness [µm ]

0

10

20

30

40

50

60

conc

ent

ratio

n [a

.u]

LD PE LD PE PP

time = 51 min



0 250 500 750 1000 1250th ickness [µm ]

0

10

20

30

40

50

60

conc

ent

ratio

n [a

.u]

LD PE LDPE PP

time = 84 min



0 250 500 750 1000 1250thickness [µm ]

0

10

20

30

40

50

60

conc

entr

atio

n [a

.u]

LD PE LD PE PP

time = 154 min



Migration with temperature variation

experimental conditions

Polymer: LDPE, 800 µm thick film with 5% additive

Simulant: hexaneMigration: one sideT-variation: step or rampAnalysis: GC

HP 136® C-radical scavenger(Ciba Specialty Chemicals)

o

o

H



Migration profile with a T-step



Migration profile with a T-step

0 20 40 60 80tim e [m in]

0

0.1

0.2

0.3

0.4co

ncen

trat

ion

in f

ood

sim

ulan

t [m

g/kg

]



Migration Profile with a double T-step



Migration Profile with a double T-step

0 10 20 30tim e [m in]

0

0.04

0.08

0.12

0.16

0.2co

ncen

trat

ion

in f

ood

sim

ulan

t [m

g/kg

]



Migration profile with a T-ramp

1°C/min



Migration profile with a T-ramp

0 10 20 30 40tim e [m in]

0

0.1

0.2

0.3

0.4co

ncen

trat

ion

in fo

od s

imul

ant

[mg/

kg]

serie 2serie 1



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



For more information

See publication in

‘FOOD ADDITIVES AND CONTAMINANTS’

October 2005

Or


Http:// http :// Simulation of release of additives from mono- and multilayer packaging B. Roduit (1), Ch. Borgeat.

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