Application of inverse problems in diffusivity coefficient estimation of polymeric packaging materials and food shelf-life determination

An effective analysis method with multiple accelerant factors is needed for rapid shelf-life determination for foods. This study aimed to investigate the effect of environmental oxygen pressure on oxygen diffusivity in polyethylene terephthalate (PET), high-density polyethylene (HDPE) and polypropylene (PP) bottles. The bottles were placed in custom-made high-pressure (10–30 psig) chambers with a 100% oxygen environment after filled with water and flushed with nitrogen to reduce the internal oxygen level below 2%. Bottles were subjected to three pressure levels and the accumulation of headspace and dissolved oxygen was used to estimate the diffusivity with the inverse problems approach. Modelling of diffusion was performed by numerically solving Fick's law and the sequential estimation of the diffusion coefficient was performed based on the Gauss minimization method. The oxygen diffusion coefficient of PET, HDPE and PP was in the range of 0.78−1.16x10⁻¹³ m²s⁻¹, 0.14−0.46x10⁻¹³ m²s⁻¹ and 0.59−14.09x10⁻¹⁶ m²s⁻¹, respectively. The application of oxygen pressure significantly increased the rate of oxygen transfer for all packaging materials compared to the control samples at ambient pressure. The application of inverse problems enabled the determination of the diffusion coefficient of oxygen with minimal errors and small confidence intervals. The use of elevated pressure and temperature as accelerants has potential application in rapid shelf-life determination of foods.