MIGRATION FROM MONOLAYER MATERIALS

What is migration?

Migration is the macroscopic process associated the net displacements of "contaminants" or 'migrants" from one compartment to another one without consideration of the physical nature of the displacements (through the solid, liquid, gas phase; the considered temperature and history of mass transfer).

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Example of of migrants: $i$

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Dimensionless time and migration kinetics

Property	description	SI units
$t$	contact time	$s$
$D_{i,P}$	diffusion coefficient (in the polymer)	$m^2\cdot s^{-1}$
$l_p$	wall thickness	$m$

All migration kinetics are homothetic to dimensionless time or Fourier time:

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Migration can occurs at any time.

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1D approximation and dimensionless mass balance

Property	description	SI units
$L_{P/F}=\frac{V_P}{V_F}=\frac{l_P}{l_F}$	dilution ratio or polymer-to-food ratio; ratio of thicknesses in 1D approximation description of mass transfer with implicit food	$-$
$K_{i,F/P}=\frac{C_{i,F}^{eq}}{C_{i,P}^{eq}}$	partition coefficient (food-to-polymer) with concentrations in food ($F$) and in the polymer ($P$) expressed in $kg\cdot m^{-3}$ or in $mol\cdot m^{-3}$	$-$
$V_P=\frac{m_P}{\rho_P}$	volume of the packaging estimated from the mass of the polymer $m_P$ and the polymer density $\rho_P$	$m^3$
$V_F=\frac{m_F}{\rho_F}$	volume of the food (as read on specifications, by filling it with water, etc.)	$m^3$
$l_F=\frac{V_F}{A}$	equivalent food dimension	$m$
$C_{i,F}$	concentrations in the food ($F$)	$kg\cdot m^{-3}$
$C_{i,P}$	concentrations in thepolymer ($P$)	$kg\cdot m^{-3}$

Total migration and large partition coefficient $K_{i,F/P}=50$

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Limited migration in food $K_{i,F/P}=\frac{1}{50}$

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Maximum concentration in food: $C_{i,F}^t\leq C_{i,F}^{eq}$