Reference ID: MET-2BE2 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The migration of chemical substances from polymeric packaging into food is a critical safety concern in Process Engineering. Regulatory frameworks, such as EU 10/2011 and FDA 21 CFR, mandate that the concentration of migrants in food must remain below established Specific Migration Limits (SML). This calculation provides a first-tier screening tool to predict the mass transfer of a migrant from a planar membrane into an acidic food simulant. It is typically used during the material development phase to ensure that packaging formulations meet safety compliance before proceeding to expensive, time-consuming laboratory migration testing.
Methodology & Formulas
The migration process is modeled as unsteady-state diffusion governed by Fick’s Second Law. For a planar membrane of thickness L with an initial uniform concentration C0, the mass transfer is calculated based on the contact time t and the diffusion coefficient D. When the contact time is sufficiently short relative to the membrane thickness, the system is treated as a semi-infinite medium.
The characteristic time for diffusion is defined as:
\[ \tau = \frac{L^{2}}{D} \]
The cumulative mass of the migrant M (in kg) transferred across the contact area A (in m2) is calculated using the short-time approximation:
\[ M = A \cdot 2 \cdot C_{0} \cdot \sqrt{\frac{D \cdot t}{\pi}} \]
To determine the specific migration in mg/kg, the mass is converted to milligrams and normalized by the standard food-contact ratio (6 dm2 of surface area per 1 kg of food):
To ensure compliance, process engineers must verify the material against regional regulatory frameworks. Follow these steps:
Identify the specific regulatory body governing your region, such as FDA 21 CFR in the United States or EU 1935/2004 in the European Union.
Obtain a Declaration of Compliance (DoC) from the raw material supplier.
Review the migration testing data to ensure that chemical substances do not transfer into food at levels exceeding safety thresholds.
Confirm that the material is listed on the positive list of authorized substances for the intended temperature and food type.
Maintaining a robust audit trail is critical for regulatory inspections. You should keep the following documents on file:
A signed Declaration of Compliance (DoC) for every material in the process stream.
Technical data sheets specifying the chemical composition and grade of the material.
Migration test reports conducted under worst-case scenario conditions.
Records of Good Manufacturing Practice (GMP) implementation as required by EC 2023/2006.
Compliance is not static and depends heavily on the operational parameters of your process. Consider these factors:
Temperature: High-heat processes may cause degradation or increased migration rates that exceed safety limits.
Contact Time: Extended exposure to food products increases the risk of chemical leaching.
Food Type: Acidic or fatty food products can react differently with polymers or metals compared to aqueous solutions.
Cleaning Cycles: Harsh Clean-in-Place (CIP) chemicals can degrade material surfaces, potentially compromising their food-safe status over time.
Worked Example: Migration from Polymeric Membrane into Acidic Food Simulant
A 1-mm thick polypropylene film containing 5 wt% DINP plasticizer is in contact with 3% acetic acid food simulant under stirred conditions. A worst-case diffusion coefficient (1×10−10 m²/s) is assumed for a quick screening, and the contact time is set to 50 seconds. The goal is to compute the specific migration and compare it with the EU Specific Migration Limit (SML) for DINP (9.0 mg/kg).
Knowns:
Film thickness: L = 0.001 m
Initial migrant concentration in polymer: C0 = 50.0 kg/m³
Diffusion coefficient: D = 1×10−10 m²/s
Contact time: t = 50.0 s
Contact area: Adm² = 1.0 dm²
Specific Migration Limit (SML): 9.0 mg/kg
EU standard ratio: 6 dm² contact area per kg food
Step-by-Step Calculation:
Area conversion. The contact area in square meters: Am² = Adm² / 100 = 1.0 / 100 = 0.01 m².
Characteristic diffusion time.τ = L2 / D = (0.001)2 / (1 × 10−10) = 1×10−6 / 1×10−10 = 10000 s.
