Mathematical models for Enterococcus faecalis recovery after microwave water disinfection.

Microwave water disinfection is a rapid purification technique which can give billions of people access to clean drinking water. However, better understanding of bacterial recovery after microwave heating over time is necessary to determine parameters such as delayed bacterial growth rates and maximum bacterial yields. Mathematical models for Enterococcus faecalis recovery after microwave treatment in optimum growth conditions were developed for times up to 5 minutes using an optical absorbance method. Microwave times below 3 minutes (2,450 MHz, 130W) showed that bacterial recovery maintained a time-dependent sigmoidal form which included a maximum value. At microwave times greater than three minutes, bacterial recovery, with a time-dependent exponential form, significantly decreased and did not reach the maximum value within the interval of observance (0-8 hours). No bacterial growth was found after 6 minutes of microwave treatment. The prepared mathematical models were produced by transforming the given variables to the logistic or exponential functions. We found that time-dependent maximum growth rates and lag times could be approximated with second order polynomial functions. The determined models can be used as a template to illustrate bacterial survival during water purification using microwave irradiation, in both commercial and industrial processes.

3-(2,6-Dioxopiperidin-3-yl)-3-aza-bicyclo-[3.2.0]heptane-2,4-dione.

The title mol-ecule, C(11)H(12)N(2)O(4), consists of a 3-aza-bicyclo-[3.2.0]heptane group containing a nearly planar cyclo-butane ring (r.m.s. deviation of fitted atoms is 0.0609 Å), fused to a pyrrolidine ring, bonded to a 2,6-dioxopiperidine ring at the 3-position. The angle between the mean planes of the cyclo-butane and fused pyrrolidine ring is 67.6 (6)°. The dihedral angles between the mean planes of the pyrrolidine and cyclo-butane rings and the dioxopiperidine ring are 73.9 (2) and 62.4 (4)°, respectively. The pyrrolidine and dioxopiperidine rings are twisted about the 3-yl group [torsion angles = -55.0 (1) and 115.0 (1)°] in a nearly perpendicular manner. Crystal packing is influenced by extensive inter-molecular C-H⋯O and N-H⋯O inter-actions between all four carbonyl O atoms and H atoms from the cyclo-butane and dioxopiperidine rings, as well as between the N atom and an H atom from the cyclo-butane ring. In addition, weak π-ring interactions also occur between H atoms from the cyclobutane ring and the five-membered pyrrolidine ring. As a result, mol-ecules are linked into infinite chains diagonally along the [101] plane of the unit cell in an alternate inverted pattern.

Mathematical models of cobalt and iron ions catalyzed microwave bacterial deactivation.

Time differences for Enterococcus faecalis, Staphylococcus aureus, and Escherichia coli survival during microwave irradiation (power 130 W) in the presence of aqueous cobalt and iron ions were investigated. Measured dependencies had "bell" shape forms with maximum bacterial viability between 1 - 2 min becoming insignificant at 3 minutes. The deactivation time for E. faecalis, S. aureus and E.coli in the presence of metal ions were smaller compared to a water control (4 -5 min). Although various sensitivities to the metal ions were observed, S. aureus and E. coli and were the most sensitive for cobalt and iron, respectively. The rapid reduction of viable bacteria during microwave treatment in the presence of metal ions could be explained by increased metal ion penetration into bacteria. Additionally, microwave irradiation may have increased the kinetic energy of the metal ions resulting in lower survival rates. The proposed mathematical model for microwave heating took into account the "growth" and "death" factors of the bacteria, forming second degree polynomial functions. Good relationships were found between the proposed mathematical models and the experimental data for bacterial deactivation (coefficient of correlation 0.91 - 0.99).