A Mathematical Approach For The Evaluation Of Critical Concentration/ Critical Time For Inactivation Of Bacteria Systems With Special Reference To Ozone/Escherichia Coli System In Water

Author(s): W.J.N.Fernando

Many waters and wastewaters require disinfection of microorganisms which involves transfer of an active disinfectant component into individual bacteria sites or colonies and thereafter making them to become inactive individually and collectively. Here, the active disinfectant component reacts with bacteria at rates determined by the concentrations of the disinfectant and bacteria and the respective rate constants leading to decay/death of bacteria and shrinkage of colonies. Design of disinfection processes require the disinfection to be achieved within a determined time. The time required for a desired degree of disinfection is a function of the colony strength and the initial disinfectant concentration. This paper develops and presents general mathematical co-relations for the determination of the initial concentration of the disinfectant(termed critical concentration c*) required to achieve a given degree of inactivation of a colony of a given initial size, at the end of a specified time(termed as critical time t*). A case study based on experimental data already available for the Ozone/ Escherichia coli system in water is used to develop a simplified equation for the critical concentration for the system. Application of the data in the co-relations demonstrates satisfactory applicability of the co-relations.

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