The literature reveals other disinfection formulas. These include Chick's law for contact time, modifications of Chick's law, and relationship between concentration of disinfectant and concentration of microorganisms reduced in a given percentage kill. Chick's law and its modification called the Chick-Watson model, however, are not useful formulas, because they do not incorporate either the concentration of the disinfectant that is needed to kill the microorganisms or the incorporation of the concentration is incorrect. The relationship of the concentration of disinfectant and the concentration of the microorganisms is also not a useful formula, since it does not incorporate the contact time required to kill the microorganisms. It must be noted that for a formula to be useful, it must incorporate both the concentration (intensity) of the disinfectant and the contact time corresponding to this concentration effecting a given percentage kill. For these reasons, these other disinfection formulas are not discussed in this book.
The Chick-Watson model needs to be addressed further. Watson explicitly expressed the constant k in Chick's law in terms of the concentration of disinfectant C as aCn, where a is an activation constant and n is another constant termed the constant of dilution. Chick's Law, thus, became dN/dt = -aCndt, where N is the concentration of microorganisms and t is time. Note that C is a function of time. When this equation was integrated, however, it was assumed constant, thus producing the famous Chick-Watson model,
No where No is the initial concentration of microorganisms. Because the concentration C was assumed constant with time during integration, this equation is incorrect and, therefore, not used in this book.
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