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Journal of Water and Health Vol 07 No 4 pp 699–706 © IWA Publishing 2009 doi:10.2166/wh.2009.132
Mathematical models for Enterococcus faecalis recovery after microwave water disinfection
Earl Benjamin, Aron Reznik, Ellis Benjamin, Saroj K. Pramanik, Louise Sowers and Arthur L. Williams
Department of Chemistry and Physics, Arkansas State University, College of Sciences & Mathematics, PO Box 419, State University, AR 72467, USA Tel.: +1-609-364-9758 Fax: +1 870-972-3089 E-mail: earlbenjamin@astate.edu
Department of Mathematics, Morgan State University, The School of Computer, Mathematical and Natural Sciences, 1700 E Cold Spring Lane, Baltimore, MD 21251, USA
Department of Biology, Morgan State University, The School of Computer, Mathematical and Natural Sciences, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
Department of Chemistry, Richard Stockton College of New Jersey, Natural Sciences and Mathematics, PO Box 195, Pomona, NJ 08240, USA
ABSTRACT
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, 130 W) 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.
Keywords: bacteria; Enterococcus faecalis; exponential function; logistic function; mathematical model; microwave treatment
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