MATHEMATICAL MODEL FOR PREDICTING OXYGEN CONCENTRATION GRADIENTS IN MUSKMELON FRUITS

A mathematical procedure for modeling diffusion of O₂ through whole fruits of two morphologically contrasting cultivars of muskmelon (Cucumis melo L.) was developed using the steady state solution to Fick's second law of gas diffusion. Input variables included diffusion coefficients and path lengths for peel, flesh, and seed region. Tissue components were assumed to be in series and to possess the characteristic of isotropy for diffusion of metabolic gases. Dependence of respiration rate on oxygen concentration was incorporated into the model and steady state oxygen concentration gradients were generated using an iterative procedure. Predictive power of the model was demonstrated by comparison with experimental data on internal O₂ concentrations. For individual fruits, the model demonstrated the need to incorporate statistical variation of input variables, particularly diffusion coefficient of peel, thickness of peel, and respiration rates of all components. The approach used will aid in the selection or synthesis of gas diffusion barriers (e.g., films) with the necessary diffusive characteristics to generate and maintain the optimum postharvest atmospheres for muskmelons and other commodities.