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

Table 5. Analytical expressions for calculation of Γ for different temperature functions.
Function Q 10 Approach Arrhenius Approach
Sine wave Γ=I o (a o b) Γ≈I o
E a a o
RT m T m +a o
Square wave Γ= 1 2 [ea ob +e
-a o b 1
] Γ= 2 exp[ E A a o
RT m (T m +a o ) ] +1 2 exp[
-E A a o
RT m (T m -a o ) ]
Spike wave
j=0
Random Γ=
e bT m
E A a o
Γ= ea ob -e
-a o b
exp[ RT m (T m +a o ) ] - exp[
-E A a o
RT m (T m -a o ) ]
2a o b Γ=
E A a o
2RT m (T m +a o )
n
n
∑
e bT j ∆t j
∑
exp( -EA ) ∆t j RTj
j=0
Γ=
exp( -EA ) RTm
I o (x) is a modified Bessel function of zero order. Its values can be calculated from an
infinite series expansion, I o (x)=1+ x2
2 2 + x4
2 2 4 2 + x 6
2 2 4 2 6 2 +..., or found in Mathematical
Handbooks (Tuma, 1988).
From Γ of a variable temperature distribution the effective reaction rate and
temperatures k eff andT eff and the value of the quality function for the particular
deterioration mode are calculated. Comparison of this value to the experimentally obtained
quality value, for variable temperature functions covering the range of practical interest is
the ultimate validation of the developed kinetic models. This methodology was applied by
Labuza and coworkers for various food reaction systems and agreement or deviation from
predicted kinetic behavior was assessed (Berquist and Labuza, 1983; Kamman and
Labuza,1981; Labuza et al. 1982; Riboh and Labuza, 1982; Saltmarch and Labuza,1982;
Taoukis and Labuza,1989).
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