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Mathematical Modelling

Mathematical modelling of additive or monomer diffusion, particularly in multi-layer materials, can support the understanding of migration processes and help in demonstrating suitability and safety in different food-contact situations. Mathematical algorithms/methods can be used to quantify the diffusion of a substance within a multi-layer material and its migration from the material into a contacting material or medium. Compliance with the Plastics Regulation 10/2011 can in many cases be demonstrated using modelling software, with significant cost savings over standard analytical testing. The approach can also be used to examine migration into food from packaging "set-off".


Some examples of the use of mathematical modelling are shown below.


Figure 1. Predicted migration of Irganox PS 802 (0.18%) from polypropylene into olive oil at 40C (determined to be within the SML restriction of 5 mg/kg after 10 days single use contact, 6dm2/kg).


Figure 2. Distribution of benzophenone UV Initiator with time from a 3 micron print layer on 1mm polyethylene by diffusion and also set-off during long term storage at 25C.





Figure 3. Concentration profiles of benzophenone (1000 mg/kg initial concentration) diffusing from a 3 micron print coating (left), 12 equal time points, into a 80 micron layer of PET during 120 days storage at 25C highlighting that this thickness of PET acts as a functional barrier to migration as none diffuses into the adjacent material to the right.

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