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

semi-empirical kinetic/mathematical model that effectively represents the experimental data.
Preferably the model would still have the general form of the quality function of eq.(14),
where Q(A) can obtain any form other than the typical ones of Table 1. The steps for
building such a model are described by Saguy and Karel (1980). Multivariable linear
models, polynomial equations or nonlinear models can be defined and their fit to the data
can be tested with computer aided multiple linear, polynomial or nonlinear regressions.
Empirical equations modeling the effect of different composition or process parameters can
be derived from statistical experimental designs, like the surface response methods
(Thompson, 1983).
A special category of reactions, the enzymatic reactions, important in foods are
usually modeled by the Michaelis-Menten equation. This is a reaction rate function based
on the steady-state enzyme kinetics approach (Engel, 1981). For an enzymatic system,
with no inhibition, the rate equation has the form:
r A =
k [A]
K m + [A] (16)
where A is the substrate, k=k o [e] is proportional to the enzyme (e) concentration (k is
usually called v max in biochemical terminology) and K m is a constant (r A = 0.5 k for [A] =
K m ). When [A]>>K m , the equation reduces to a zero order reaction, r A =k. This is often
the case in foods with uniformly distributed substrate in excess and small amounts of
enzyme, e.g., lipolysis of milk fat. When K m >>[A], the equation reduces to first order,
r A =(k/K m ) [A]. This occurs in foods where the enzymes are highly compartmentalized
and have limited access to the substrate or where generally the substrate limits the reaction,
e.g., browning of fruit and vegetable tissue due to polyphenolase activity. Thus, a large
portion of enzymatic reactions in foods can be handled as zero or first order systems.
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