the handbook of food engineering practice crc press chapter 10 ...

k i = f (T,a w ,pH, P O2 , P CO2 ...) (42)
the values of which are in turn time dependent:
T=T(t), a w = a w (t), pH=pH(t), P O2 = P O2 (t), P CO2 = P CO2 (t) (43)
The functions of (32) incorporate the effects of storage conditions, packaging
method and materials and biological activity of the system. Thus for variable conditions
the rate constant is overall a function of time, i.e. k i =k i (t). In that case the quality function
value at certain time is given by the expression
t
Q i (A i ) = ⌡ ⌠k i dt (44)
0
If the lower acceptable value of the quality parameter A i , noted as A m is known
then at time t the consumed quality fraction, Φc i , and the remaining quality fraction, Φr i ,
are defined as:
Φc i = Q i(A i )-Q i (A o )
Q i (A m )-Q i (A i ) (45)
Φr i = Q i(A m )-Q i (A i )
Q i (A m )-Q i (A o ) (46)
Knoweledge of the value of Φr i for the different deterioration modes allows the calculation
of the remaining shelf life of the food, θ r , from the expression
θ r = min [ Φr i /k i ] (47)
where the rate constants k i are calculated for an assumed set of "remaining" constant
conditions.
The above analysis sets the foundations of shelf life prediction of a complex
system under variable conditions. The major tasks in a scheme like this, is recognition of
the major deterioration modes, determination of the corresponding quality functions and
estimation of Eq.(42) i.e. the effects of different factors on the rate constant. The latter is a
difficult task for real food systems. Most actual studies concern the effect of temperature
42