Abstract

Mathematical modeling allows a shift away from expensive and time consuming migration analysis. The primary aim of this study was to compare two alternative expressions, Fick’s law and Fokker-Planck’s law, and gain insight of the diffusive flux migration profiles of lead (Pb) from polyethylene bags (of 30 µ) to Matooke at distances of 0 to 1.5, 1.6 to 3.0 and 3.1 to 4.5 cm, was measured at cooking times of 1, 2 and 3 h under three holding temperatures of 65, 90 and 100°C. The tendency of Fick’s law and Fokker-Planck’s law to over predict the actual Pb migration was checked using the migration estimation model. In general, it was noted that lead flux is higher at 100°C for cooking time of 3 h and also, the predicted Pb concentration is less than the measured Pb concentration, indicating that the migrant estimation model is not overestimating the Pb migration. Herein, the study makes three conclusions. First, the performance of both the Fickian model and Fokker- Planckian model is comparable under the conditions investigated. Second, high temperature and long exposure time combinations are synonymous with higher lead concentration migration when compared to low temperature and long exposure time scenarios. Third, lead concentrations are higher at surfaces in contact with the black polyethylene bags and lower at the centroid of the food. Future works should focus on model validation to test model robustness.

Key words: Modeling, migration, food safety, lead contamination, matooke, polyethylene bags, temperature.