In one set of modified-atmosphere (MA) packages of cut broccoli (Brassica oleracea L., Italica Group), O2 partial pressures ranged from 1.2 to 3.6 kPa at 0C [88 packages, 0.00268-cm-thick low-density polyethylene (LDPE) film, 600-cm2 film area, 40±0.5 g cut broccoli], and in another set (94 packages, same film and area as before, 25±0.5 g cut broccoli) they ranged from 5.0 to 9.2 kPa. For characterizing O2 uptake as a function of O2 partial pressure and determining anaerobic fermentation induction point at 0C, a range of steady-state package O2 partial pressures was generated by placing different amounts of cut broccoli (10 to 160 g) in LDPE packages. Oxygen uptake was modeled using a Michaelis-Menten-type equation. The maximum rate of product O2 uptake when O2 partial pressure was nonlimiting and the package O2 partial pressure corresponding to half-maximum O2 uptake were estimated as 147±3 nmol·kg-1·s-1 and 0.26±0.025 kPa, respectively. Respiratory quotient and head space ethanol increased sharply below package O2 partial pressures of 0.15 kPa, indicating stimulation of fermentation within the packages. The frequency distributions of CO2 production rates were measured for 80 samples of 100 g each of cut broccoli at two O2 partial pressures (21.0 kPa and 1.3 kPa) using a flow-through method. The average coefficient of variation of the CO2 production rate was ≈5%. Frequency distributions of O2 partial pressures were modeled as a function of product-to-product variation in O2 uptake and package-to-package variation in film permeability using the estimated O2 uptake characteristics and coefficient of variation. The model was used to predict the target O2 partial pressures for the design of cut broccoli MA packages. It was predicted that the packages for cut broccoli at 0C should be designed for a target O2 partial pressure of 2.54 kPa to have actual package O2 partial pressures ≥1.0 kPa at 0.0001% probability level. Film specifications for MA packaging of cut broccoli at 0C were calculated based on the predicted target O2 partial pressures.
Total pressure generally decreases in a sealed rigid package containing respiring produce, whereas total pressure is essentially constant and free volume decreases in a flexible package. We found that predicted O 2 , CO 2 , and N 2 partial pressures were different for similarly designed (same surface area, thickness, film permeabilities and produce mass) flexible and rigid packages at ''quasi steady state'' and steady state, respectively. Predicted O 2 and CO 2 partial pressures were slightly higher in a flexible package than in a rigid package and were a function of the film permeability ratio of N 2 to O 2 and of CO 2 to O 2 . They also related to the ratio of product CO 2 production rate to O 2 uptake rate, target steadystate O 2 partial pressure, and respiration characteristics. Differences were slight for films such as low-density polyethylene.
To investigate free-volume changes in flexible, sealed packages containing respiring fruits and vegetables, a simple method based on the dilution of an injected gas (ethane) in the package was developed. Free-volume decreased steadily at Ϸ3 cm 3 /day after an initial transient period in lowdensity polyethylene packages (29-µm-thick film; 600-cm 2 surface area; initial free volume Ϸ285 cm 3 ) containing 40g of cut broccoli held at 0ЊC. A general transient model was developed that showed that freevolume changes in flexible packages were a function of differential film O 2 , CO 2 , and N 2 permeabilities and differential product O 2 uptake and CO 2 production rates. The model predicted that flushing packages with low permeative gases would decrease free-volume depletion rate, whereas flushing with highly permeative gases, such as CO 2 , would increase the initial rate considerably.
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