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

objective is to model the change of the concentrations of constituents connected to food
quality, as functions of time. Molecular, irreversible reactions are typically expressed as
µ 1 A 1 + µ 2 A 2 + µ 3 A 3 + .... + µ m A m → k f
P (2)
where A i are the reactant species, µ j the respective stoichiometric coefficients (j=1,2...m), P
the products and k f the forward reaction rate constant. For such a scheme the reaction rate,
r, is given (Hills and Grieger-Block, 1980) by:
r = - 1 µ j
d[A j ]
dt = k f [A 1 ] n 1
[A 2 ] n 2 ...... [Am ] n m
(3)
where n j is the order of the reaction with respect to species A j . For a true molecular
reaction, it holds that: n j = µ j . More often than not, the degradation of important
components to undesirable products is a complex, multistep reaction for which the limiting
reaction and intermediate products are difficult to identify. A lot of reactions are actually
reversible having the form:
α A + β B ←
→ k f
γ C + δ D (4)
k b
In this case A reacts with B to form products C and D which can back react with a rate
constant of k b . The reaction rate in this case would be:
r = -d[A]
α dt
= -d[B]
β dt
= +d[C]
γ dt
= +d[D]
δ dt
= k f [A] α [B] β - k b [C] γ [D] δ (5)
For the majority of food degradation systems either k b is negligible compared to k f , or for
the time period of practical interest they are distant from equilibrium, i.e.[C] and [D] are
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