Mathematical model of manganese ion catalyzed microwave deactivation of Enterococcus faecalis, Staphylococcus aureus and Escherichia coli.

Enterococcus faecalis, Staphylococcus aureus and Escherichia coli survival was investigated using microwave irradiation (power 130 W) both in a water control and in the presence of a 1 microM manganese ion solution. Measured survival dependencies had "bell" shape form with maximum bacterial viability between 1-2 min of microwave heating. Additional heating revealed bacteria survival decreasing up to 3 min of microwave heating when viability became insignificantly small. The total deactivation time of bacteria in the presence of manganese ions was significantly smaller then that of bacteria irradiated in the microwave without manganese ions present (4-5 min). One possible explanation for the rapid reduction of bacterial survival during microwave irradiation in the presence of manganese ions is that increasing manganese ion penetration into bacteria along with microwave irradiation related to an increase of kinetic energy of ions, and damaging of bacteria by metal ions. The proposed mathematical model for microwave heating took into account "growth" and "death" factors of bacteria. It assumes that rates of bacterial growth and decay are linear functions of water temperature, and rate of bacterial decay that relates with metal concentration into water is also linear, which influenced the differential equation for the dependence between number of survival bacteria and temperature water. By using proportionality between the time of microwave heating and water temperature we derived the differential equation, between bacterial viability and time of microwave irradiation which was used as mathematical model for microwave heating in the presence of metal ions. This model had forms of second-degree polynomial functions. We received good relationships (with coefficient of correlation 0.92-0.99) between proposed mathematical model and experimental data for all bacterial deactivation.