A good way to graph concentrations that may change over several orders of magnitude is to use logarithms. When data for disinfection are presented as logarithm of N versus time, actual systems may not produce good straight lines. There are several explanations-mixtures of different organisms with varying susceptibilities to the killing agent would not be expected to obey Chick's law. However, pure cultures of microorganisms may also exhibit non-linear death curves. Mysterious lag effects have been postulated, but one proposed mechanism that makes sense is that there is a sequence of reactions:
X ----> Xs ----> Xd
where X is the number of unaffected organisms, Xs is the number of organisms that have encountered the killing agent but can still recover, and Xd is the number of dead organisms.
The figures (same as above) show arithmetic and logarithmic plots for the sequential mechanism. Increasing the concentration of the killing agent increases the rate coefficients. Rates would also increase with temperature. The graphs reinforce the concept that killing depends on time and on concentration. Although a fraction of an organism per unit volume makes no sense, low numbers can be converted to the volume that would be required to have one living organism. When the concentration of organisms is very low, the material is assumed to be sterile. In a practical sense, microorganisms in a sample may be too few to cause spoilage within the holding time for milk, water, or other material. Furthermore, natural defense mechanisms of the body can overcome small numbers of disease organisms.