where tB is the shelf life, day and 02max is the maximum allowable oxygen, cc 02. Equation 2 assumes that 02 permeation through the package is the major factor in limiting shelf life. This is the case for food packages of good oxygen barrier, in which the oxidative reaction rate of the food is greater than the oxygen transmission rate of the package.

Substituting equation 1 into equation 2 yields

This equation is useful for evaluating many what-if scenarios. For example, if the thickness is decreased by 25% and the surface area is increased by 20%, then the equation predicts that the shelf life will be decreased by 37.5%. Equation 3 also shows that shelf life depends on the variables determined by the food, the package, and the environment.

The variable determined by the food is 02max. Oxidation (especially lipid oxidation) is an important mode of deterioration for many foods (4). The incentive for studying oxidation is that it provides an objective measure of the food stability in addition to the subjective measure of sensory evaluation. The sensory acceptability of an oxygen-sensitive food can then be correlated to the extent of oxidation reaction. However, measuring the extent of oxidation reaction requires a great effort because it depends on the concentration and diffusion of oxygen in the food.

02max is sometimes used as an alternative measure of oxygen stability by the food packaging industry. It is the maximum amount of additional oxygen the food can absorb before becoming unacceptable. It is a simpler but less accurate measure of oxygen stability than the extent of oxidation reaction because 02max usually ignores the effects of concentration and diffusion of oxygen in the food. Reference values for 02max are available in the literature for some foods (3); for example, the 02max for instant coffee is reportedly between 1 and 5 ppm. If the upper limit of 5 ppm is assumed, 02max for a package containing 454 g of instant coffee = 454 (5 x 10"6) = 2.37 x 10"3 g. Nevertheless, it is often necessary to determine 02max experimentally, which involves correlating the food quality with the amount of oxygen absorbed in the food. 02max is the difference between the critical oxygen level (at which the food is no longer acceptable) and the initial oxygen level (which depends on the initial condition of the food).

The variables determined by the package are L, A, and P. L and A are specified by the dimensions of the package. The permeability P is a measure of the permeation of the gas through the packaging material—the lower the P, the better the gas barrier. The values of P depend on the packaging material, permeant gas, temperature, and sometimes relative humidity. For example, the 02 permeability of polyethylene terephthalate (PET) at 23°C is between 3 and 6 (cc • mil)/(100 in.2 • day • atm). The relative humidity is not specified because it has little effect on the permeability of PET. P and gas permeation are further discussed in Packaging: part iii—materials.

The variables determined by the environment are Pe and Pj. Pe is the partial 02 pressure in the external environment, which is about 0.21 atm for a normal storage environment. Pi is the partial 02 pressure in the headspace, which is sometimes deliberately reduced using the techniques of vacuum packaging or modified atmosphere packaging for shelf life extension. (In vacuum packaging, the air in the headspace is removed before sealing. In modified atmosphere packaging, the air in the headspace is replaced by an inert gas such as nitrogen before sealing.) An important environmental variable not explicitly stated in equation 3 is temperature. An increase in temperature causes increases in the oxidation rate of the food and the package permeability.

The term Pe — in equation 3 is often called the concentration driving force—the larger the driving force, the higher the permeation rate. If the food is packaged in air, the external environment and the headspace have the same oxygen concentration, the driving force is Pe — P4 = 0, and there is no net flow of oxygen. If the food is packaged in a reduced oxygen environment, the driving force is Pe — P; > 0. This causes a net flow of oxygen into the package, but at a slower rate as time passes, because Pe — P; continues to decrease.

Shelf Life of Moisture-Sensitive Packaged Foods

A more elaborate approach to predict the shelf life of moisture-sensitive packaged foods is described elsewhere (5). The approach requires the definition of critical limits of aw, above or below which (depending on whether the food gains or loses moisture) the food is no longer considered acceptable. The moisture gain or loss through the package depends on the H20 permeability and the temperature as well as the relative humidities in the headspace and the external environment.

Some foods are both oxygen and moisture sensitive. For example, potato chips can lose crispness because of moisture gain and become rancid because of oxygen absorption. In packaging these foods, oxygen and moisture protection are required. In packaging foods that are less sensitive to oxygen or moisture, physical protection is more important than gas barrier protection.

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