Methods for food shelf life determination and prediction - Oxidation in Foods and Beverages and Antioxidant Applications - page 203

9.5.1 Evaluation of shelf life under actual storage conditions
When there is no necessity to speed up shelf life testing, the latter can be carried
out under conditions simulating as closely as possible those actually experienced
by the product on the shelves. The basic requirement is that storage conditions
(e.g., temperature, moisture, oxygen concentration, light) during shelf life testing
are kept constant and equal to the conventional storage temperature of the
product. Data describing the changes of the oxidative indicator under conditions
simulating actual storage are submitted to modelling according to the
fundamental kinetic principles or by exploiting descriptive mathematical models.
According to the well-known fundamental kinetic principles, the rate of
changes of an oxidative indicator (I ox ) can be calculated by integrating the
general kinetic equation:
Z I ox Z t

dI ox
I ox

k dt 9:1

I ox 0 0

where k is the rate constant and n the reaction order. The general rate law can be
integrated to obtain the equations of the pseudo zero, first, second or n order
(Table 9.5). In experimental kinetic studies I ox , ln(I ox ), 1=I ox , 1=I ox nÿ1 values are
plotted versus time to estimate the reaction rate (k) by linear regression analysis.
A comprehensive discussion on kinetic modelling of reactions in food is reported
in the textbook Kinetics Modelling of Reactions in Foods (van Boekel, 2009).
By solving the integrated forms of equation 9.1 as a function of time, shelf
life at the actual storage conditions can be calculated:

Z I ox

dI ox
I ox
k

I ox 0

SL T const 9:2

Table 9.5 Zero, first, second and n order integrated kinetic and shelf life equations.
Kinetic rate constants have positive or negative values if the quality indicator increases or
decreases vs time

Reaction order Integrated rate law Shelf life equation

SL I ox ÿ I ox 0
k

n 0 I ox kt I ox o

SL ln I ox ÿ ln I ox 0
k

n 1 ln I ox kt ln I ox 0

I ox ÿ 1

1

I ox kt 1

1

I ox 0
k

n 2 SL

I ox 0

I ox nÿ1 ÿ 1

1

1
I ox nÿ1 ÿ

1
I ox 0 nÿ1 nÿ1kt

I ox 0 nÿ1
k

n 6 1 SL