International Scientific Journal


The migration of chemicals from packaging materials into food is predictable by various mathematical models. However, the loss of chemicals makes the predictions more complicated. In this article, a mathematical model considering chemical instability is developed to quantify the release of chemicals through double-layer packaging films based on Fick's diffusion and first order reaction. At the same time, two different loading modes are considered in the loss function. The release model is solved numerically to elucidate the effects of diffusivity value, distribution of chemical and mass transfer at the interface of material and food on the migration process, and the loss of the chemicals in food is also elucidated.
PAPER REVISED: 2019-04-13
PAPER ACCEPTED: 2019-06-21
CITATION EXPORT: view in browser or download as text file
  1. Lin, Q. B., et al., Analysis of Isothiazolinone Biocides in Paper for Food Packaging by Ultra-High-Performance Liquid Chromatography-Tandem Mass Spectrometry, Food Additives and Contaminants, 27 (2010), 12, pp. 1775-178
  2. Zhu, X., et al., Release Property and Antioxidant Effectiveness of Tocopherol-Incorporated LDPE/PP Blend Films, Food Additives and Contaminants, 29 (2012), 3, pp. 461-468
  3. Huang, X. L., et al., Factors Affecting Migration of Contaminants from Paper through Polymer Coating into Food Simulants, Packaging Technology and Science, 26 (2013), Suppl. 1, pp. S23-S31
  4. Gemili, S., et al., Develop-Ment of Cellulose Acetate Based Antimicrobial Food Packaging Materials for Controlled Release of Lysozyme, Journal of Food Engineering, 90 (2009), 4, pp. 453-462
  5. Pires, C., et al., Hake Proteins Edibile Films Incorporated with Essential Oils: Physical Mechanical, Anti-oxidant and Antibacterial Properties, Food Hydrocolloids, 30 (2013), 1, pp. 224-231
  6. Chen, X., et al., Release Kinetics of Tocopherol and Quercetin from Binary Antioxidant Controlled-Release Packaging Films, Journal of Agriculture and Food Chemistry, 60 (2012), 13, pp. 3492-3497
  7. Bierhalz, A., et al., Natamycin Release from Alginate/Pectin Films for Food Packaging Applications, Journal of Food Engineering, 110 (2012), 1, pp. 118-125
  8. Wang, Z. W., et al., A Systematic Study on the Stability of UV Ink Photoinitiators in Food Simulants Us-ing GC, Packaging Technology and Science, 22 (2009), 3, pp. 151-159
  9. Huang, X. L., et al., Modeling Release of Chemicals from Multilayer Materials into Food, Thermal Science, 20 (2016), 3, pp. 839-843
  10. Han, J. K., et al., Application of a computer Model to Evaluate the Ability of Plastics to Act as Functional Barriers, Packaging Technology and Science, 16 (2003), 3, pp. 107-118
  11. Franz, R., et al., Presentation and Experimental Verification of a Physicomathematical Model Describing the Migration Across Functional Barrier Layers into Foodstuffs, Food Additives and Contaminants, 14 (1997), 6, pp. 627-640
  12. Perou, A. L., et al., Model for Transfer of Contaminant During the Coextrusion of Three-Layer Food Package with a Recycled Polymer, Effect on the Time of Protection of the Food of the Relative Thick-ness of the Layers, Journal of Applied Polymer Science, 73 (1999), 10, pp. 1938-1948
  13. Helmroth, E., et al., Stochastic Modelling of Migration from Polyolefins, Journal of the Science of Food and Agriculture, 85 (2005), 6, pp. 909-916
  14. Monteiro, M., et al., Migration of Tinuvin P, a UV Stabilizer, from PET Bottles into Fatty-Food Simu-lats, Packaging Technology and Science, 12 (1999), 5, pp. 241-248
  15. Philo, M. R., et al., Measurement of Styrene Oxide in Polysty-Renes, Estimation of Migration to Foods, and Reaction Kinetics and Products in Food Simulants, Food and Chemical Toxicology, 35 (1997), 8, pp. 821-826
  16. Monteiro, M., et al., Migration of Tinuvin P, a UV Stabilizer, from PET Bottles into Fatty-Food Simu-lats, Packaging Technology and Science, 12 (1999), 5, pp. 241-248
  17. Ortuoste, N., et al., Hydrolytic Stability and Hydrolysis Reaction Mechanism of bis (2,4-di-tert-butyl) pentaerythritol diphosphite (Alkanox p-24), Polymer Degradation and Stability, 91 (2006), 1, pp. 195-211
  18. Liu, H. Y., et al., A Fractional Nonlinear System for Release Oscillation of Silver Ions from Hollow Fibers, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2018), 1, pp. 88-92
  19. Liu, H. Y., et al., A Fractal Rate Model for Adsorption Kinetics at Solid/Solution Interface, Thermal Science, 23 (2019), 4, pp. 2477-2480
  20. Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250
  21. He, J. H., et al., A New Fractional Derivative and Its Application to Explanation of Polar Bear Hairs, Journal of King Saud Universe Science, 28 (2016), 2, pp. 190-192
  22. He, J. H., Li, Z. B. A Fractional Model for Dye Removal, Journal of King Saud Universe Science, 28 (2016), 1, pp. 14-16
  23. Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear hairs, Fractals, 26 (2018), 6, 1850086
  24. Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs (vol. 26, 1850086,2018), Fractals, 27 (2019), 5, 1992001
  25. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals,
  26. He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565F25

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence