effective water disinfection from fecal coliforms is a problem whose solution , leads to the improvement of environmental health conditions . presently , water disinfection of fecal coliforms commonly uses chemical and conventional radiant heating methods . . bacterial deactivation by conventional radiant heating is achieved through the thermal decay of biomolecules including proteins and dna . both of these methods maintain fundamental disadvantages including harmful side effects and extensive disinfecting time . to address this problem , the identification of rapid disinfection methods such as microwave heating was explored . microwave heating is the use of microwave radiation ( 2.45ghz ) to induce collisional deactivation resulting in thermal heating . this process maintains several advantages over conventional radiant heating for bacterial deactivation including rapid heating rates and reduced energy requirements . additionally , microwave heating has been found to heat more uniformly compared to conventional radiant heating thereby increasing energy efficiency . goldblith and wang   compared the deactivation of escherichia coli and bacillus subtilis spores using microwave irradiation versus conventional radiant heating . they suggested that the deactivation of these bacteria resulted from the dielectric heating and did not maintain any secondary effect from the microwave irradiation . .   found no difference between conventional radiant and microwave heating for the disinfection of b. subtilis spores in automated temperature monitoring systems . kazbekov and vyacheslavov   found a series of biochemical processes that were altered in e. coli and b. subtilis under microwave irradiation which included thymidine and thymine uptake , leakage of potassium and hydrogen ions , and uptake of dna . .   found no major differences in deactivation rates of e. coli in phosphate buffer between microwave and conventional radiant heating . .   also found no difference between conventional and microwave deactivation of clostridium sporogenes at 90c , 100c , and 110c . vela et al . , rosn   also found that the deactivation of several bacteria , including streptococcus faecalis ( later classified as enterococcus faecalis ) and saccharomyces cerevisiae , under microwave irradiation resulted from the dielectric heating . conversely , shin and pyun   compared the results of deactivation of lactobacillus plantarum by conventional heating at 50c versus continuous microwave heating and pulsed higher power microwave heating over a 30 minute period . they found greater reduction in bacterial survival for pulsed microwave heating relative to conventional and continuous microwave heating . these results suggested a secondary non - thermal mechanism assisted the deactivation of these bacteria during microwave irradiation . culkin and fung   and kozempel et al .   also suggest that a secondary non - thermal mechanism assisted in the deactivation of certain species of bacteria . heddleson and doores reported that non - thermal effects are likely to be due to the lack of precise measurements of the time - temperature history and its spatial variations . in our recent paper dependencies between bacterial viability of enterococcus faecalis , staphylococcus aureus , and escherichia coli versus microwave heating time and conventional radiant temperature , the proposed mathematical models for conventional and microwave heating took into account  growth  and  death  factors of bacteria whose , relationships formed second degree polynomial functions . these models were found to be consistent with experimental data maintaining correlation coefficients between 0.84  0.99 . watanabe et al . showed that ionic strength was able to influence the bacterial survival during microwave irradiation . they showed that 10-fold increase in e. coli deactivation rates in the presence of molar concentrations of nacl and kcl . several transitional metals , such as calcium , cobalt , copper , chromium , potassium , iron , magnesium , nickel , zinc , manganese , sodium , are essential for normal biochemical processes . in small concentrations they serve as micronutrients and are used for redox - processes , stabilize molecules through electrostatic interactions , are components of various enzymes , and regulate osmotic pressure . however , other transitional metals such as silver , aluminum , cadmium , gold , mercury , lead , have no biological role and are potentially toxic to bacteria . toxicity of transitional metal ions depends on their concentration , form , and other factors , including water temperature [ 25 , 26 , 27 ] . most scientific investigations with transitional metal ions were conducted with silver and copper ions in combination with other compounds [ 28 , 29 , 30 ] . al . reported that the addition of silver ions was effective against coliforms [ 31 , 32 ] . abad et al .   found that the existence of copper and silver ions in combination with low levels of chlorine leads to increased reduction of poliovirus . landeen et al . showed the efficiency of copper and silver ions in combination with low level of chlorine for deactivation of legionella pneumophilla . ragab - depre   found that addition of a hydrogen peroxide - ascorbic acid - cu(ii ) ( 60 min ) to secondary effluents resulted in 99% reduction of enterobacteriaceal , total and fecal coliforms and staphylococci . oganesov   proposed a mechanism for the deactivation of bacteria in water using silver ions . myers and nealson   studied the influence of manganese oxide on bacterial reduction and growth . calomiris et al .   studied the effects of different metal ions such as cu , pb , zn , al , sn , and cd on escherichia coli , staphylococcus aureus , and several other bacteria . they found that the existence of cu and zn sufficiently decreased the number of escherichia coli in water . staphylococcus aureus was sensitive to all of the metal ions mentioned above except the ion al . [ 41 , 42 ] described the resistance of staphylococcal strains to several metal ions and antibiotics . unfortunately , the process of bacterial deactivation using only transitional metal ions takes several hours . on the other hand , for example , butkus et al .   found that the addition of silver ions enhanced deactivation of coliphage ms-2 by uv disinfection . it is proposed that the presence of metal ions may increase the deactivation rate of bacteria during microwave treatment , thereby , reducing the time of treatment . in this work the effect of iron and cobalt ions in water on microwave deactivation of e. faecalis , s. aureus and e. coli was investigated . stock cultures of e. faecalis , s. aureus and e. coli ( ward natural scientific , rochester , ny ) were created by growing them in tsb ( tryptic soy broth ) overnight in a labline imperial iii incubator ( model # 305 ) at a temperature of 37c . an aliquot of 10l of stock culture was then placed into 250 ml sample vials containing 100 ml of distilled deionized water purified by a barnsted e - pure system ( model # d4641 ) . the sample vials were then heated in a panasonic inverter microwave ( model # nn - s543bf ) at power 130w for 1 , 2 , 3 , 4 , and 5 minutes . fifty microliters of the test solutions were plated in exponential spiral fashion on to 10 tsa ( tryptic soy agar ) plates for each sample group using a spiral biotech autoplate 4000 ( model # ap 4000 ) . the plates were then incubated overnight in a labline imperial iii incubator ( model # 305 ) . finally , the colony forming units were counted using a spiral biotech q - count ( model # 510 ) auto - plate reader set for a 50l exponential spiral pate setting . the cfus ( colony forming units ) were then calculated and graphed using grapad prism . stock cultures of e. faecalis , s. aureus and e. coli ( ward natural scientific , rochester , ny ) were created by growing them in tsb ( tryptic soy broth ) overnight in a labline imperial iii incubator ( model # 305 ) at temperature of 37c . an aliquot of 10l of stock culture was then placed into 250 ml sample vials containing 100 ml a 1.0  10 m of iron or cobalt ion solution . the sample vials were then microwave heated in a panasonic inverter microwave ( model # nn - s543bf ) at power 130 w for 1 , 2 , 3 , 4 , and 5 minutes . the cfus of a 50l aliquot of the test solutions were calculated using the same method previously described for distilled water samples . stock cultures of e. faecalis , s. aureus and e. coli ( ward natural scientific , rochester , ny ) were created by growing them in tsb ( tryptic soy broth ) overnight in a labline imperial iii incubator ( model # 305 ) at a temperature of 37c . an aliquot of 10l of stock culture was then placed into 250 ml sample vials containing 100 ml of distilled deionized water purified by a barnsted e - pure system ( model # d4641 ) . the sample vials were then heated in a panasonic inverter microwave ( model # nn - s543bf ) at power 130w for 1 , 2 , 3 , 4 , and 5 minutes . fifty microliters of the test solutions were plated in exponential spiral fashion on to 10 tsa ( tryptic soy agar ) plates for each sample group using a spiral biotech autoplate 4000 ( model # ap 4000 ) . the plates were then incubated overnight in a labline imperial iii incubator ( model # 305 ) . finally , the colony forming units were counted using a spiral biotech q - count ( model # 510 ) auto - plate reader set for a 50l exponential spiral pate setting . the cfus ( colony forming units ) were then calculated and graphed using grapad prism . stock cultures of e. faecalis , s. aureus and e. coli ( ward natural scientific , rochester , ny ) were created by growing them in tsb ( tryptic soy broth ) overnight in a labline imperial iii incubator ( model # 305 ) at temperature of 37c . an aliquot of 10l of stock culture was then placed into 250 ml sample vials containing 100 ml a 1.0  10 m of iron or cobalt ion solution . the sample vials were then microwave heated in a panasonic inverter microwave ( model # nn - s543bf ) at power 130 w for 1 , 2 , 3 , 4 , and 5 minutes . the cfus of a 50l aliquot of the test solutions were calculated using the same method previously described for distilled water samples . experimental results for microwave irradiation of e. faecalis , s. aureus , and e. coli in the presence of cobalt ions in water are summarized into table 1 and figs . 1 and 3 ( square points ) . the results showed the existence of two distinct processes : increasing of number of viable bacteria with microwave time of during the first stage of heating , and passing through maximum value of bacterial viability then decreases in relationship to microwave time . the  growth factor  was found in the first minute of microwave heating showing a 2.4% increase in bacterial viability . above the optimal microwave time the  death factor  occurred between the first and third minutes showing 102.4% decrease in bacterial viability . the greatest drop in bacterial viability reduction ( 96.6% ) was found between the second and third minutes of microwave heating . table 1 shows the bacterial viabilities of e. faecalis , s. aureus , and e. coli ( n=10 ) when microwaved for 4 minutes in the presence of cobalt ions compared to control samples ( distilled water ) . the results showed notably lower bacterial viability in the presence of cobalt versus that of the control samples . e. coli also had a  growth factor  in the first minute of microwave irradiation ( 25.0% increase bacterial viability ) . the largest drop in e. coli viability ( 116% ) was found between the second and third minutes of microwave irradiation . in contrast with other bacteria , s. aureus showed no major change in bacterial viability in the first minute of the microwave heating . after this initial minute , s. aureus viability then slowly decreased in the second minute with a 34.9% reduction . we can explain this fact by assuming that the  death factor  is influenced by the presence of cobalt ions which had a powerful effect on s. aureus compared to other test organism . for comparison , in table 1 and figs . 1 and 3 we also show data from our previous paper   for microwave treatment for e. faecalis , s. aureus and e. coli in distilled water ( triangular points ) . this data illustrates that the disinfection s in the presence of cobalt ions ( 3 min ) is less than that of the distilled water control ( 4  5 min ) . therefore , the presence of cobalt ions into water increased the efficiency of the microwave deactivation of bacteria . experimental results for microwave irradiation of e. faecalis , s. aureus , and e. coli in the presence of iron ions into water are summarized into table 2 and figs . 4 and 6 ( square points ) . the results also showed the existence of both  growth  and  death  factors . in this circumstance , the  death  factor for e. faecalis is weaker , and s. aureus and e. coli are stronger in comparison with the influence of cobalt ions . for e. faecalis the  growth factor was found in the first minute of microwave heating showing a 4.7% increase in bacterial viability . the  death factor  for e. faecalis occurred between the first and fourth minutes leads to 104.7% of bacterial viability reduction . the greatest decline in bacterial viability reduction was found between the second and third minutes of microwave irradiation ( 63.7% ) . however , the influence of iron ions on e. faecalis was weaker when compared with the influence cobalt ions , and at the third minute results ( 38.2% ) . table 2 shows the bacterial viabilities of e. faecalis , s. aureus , and e. coli ( n = 10 ) when micro - waved for 4 minutes in the presence of iron ions compared to control samples ( distilled water ) . the results showed that the presence of iron reduced the disinfection time for all test bacteria . the most significant decrease was e coli whose disinfection time reduced from four minutes to one minute . the number of viable s. aureus was constant during the first two minutes of microwave treatment with a rapid decrease ( 94% ) during the third minute . e. coli viability showed a sharp decline during microwave heating in the presence of iron ions . during the first minute of microwave treatment bacterial viability for e. coli contrary to other data , e. coli disinfection denotes the strong influence of iron ions on micro - organisms . for comparison , table 2 and figs . 4 and 6 , data for microwave treatment of e. faecalis , s. aureus and e. coli in distilled water ( triangular points ) was included from our previous paper . this data showed that disinfection time in the presence of iron ions ( 13 min ) is less than in distilled water ( 4  5 min ) . so , the presence of iron ions in water increased the efficiency of the microwave deactivation of bacteria . experimental results for microwave irradiation of e. faecalis , s. aureus , and e. coli in the presence of cobalt ions in water are summarized into table 1 and figs . 1 and 3 ( square points ) . the results showed the existence of two distinct processes : increasing of number of viable bacteria with microwave time of during the first stage of heating , and passing through maximum value of bacterial viability then decreases in relationship to microwave time . the  growth factor  was found in the first minute of microwave heating showing a 2.4% increase in bacterial viability . above the optimal microwave time the  death factor  occurred between the first and third minutes showing 102.4% decrease in bacterial viability . the greatest drop in bacterial viability reduction ( 96.6% ) was found between the second and third minutes of microwave heating . table 1 shows the bacterial viabilities of e. faecalis , s. aureus , and e. coli ( n=10 ) when microwaved for 4 minutes in the presence of cobalt ions compared to control samples ( distilled water ) . the results showed notably lower bacterial viability in the presence of cobalt versus that of the control samples . e. coli also had a  growth factor  in the first minute of microwave irradiation ( 25.0% increase bacterial viability ) . the largest drop in e. coli viability ( 116% ) was found between the second and third minutes of microwave irradiation . in contrast with other bacteria , s. aureus showed no major change in bacterial viability in the first minute of the microwave heating . after this initial minute , s. aureus viability then slowly decreased in the second minute with a 34.9% reduction . we can explain this fact by assuming that the  death factor  is influenced by the presence of cobalt ions which had a powerful effect on s. aureus compared to other test organism . for comparison , in table 1 and figs . 1 and 3 we also show data from our previous paper   for microwave treatment for e. faecalis , s. aureus and e. coli in distilled water ( triangular points ) . this data illustrates that the disinfection s in the presence of cobalt ions ( 3 min ) is less than that of the distilled water control ( 4  5 min ) . therefore , the presence of cobalt ions into water increased the efficiency of the microwave deactivation of bacteria . experimental results for microwave irradiation of e. faecalis , s. aureus , and e. coli in the presence of iron ions into water are summarized into table 2 and figs . 4 and 6 ( square points ) . the results also showed the existence of both  growth  and  death  factors . in this circumstance , the  death  factor for e. faecalis is weaker , and s. aureus and e. coli are stronger in comparison with the influence of cobalt ions . for e. faecalis the  growth factor  was found in the first minute of microwave heating showing a 4.7% increase in bacterial viability . the  death factor  for e. faecalis occurred between the first and fourth minutes leads to 104.7% of bacterial viability reduction . the greatest decline in bacterial viability reduction however , the influence of iron ions on e. faecalis was weaker when compared with the influence cobalt ions , and at the third minute results ( 38.2% ) . table 2 shows the bacterial viabilities of e. faecalis , s. aureus , and e. coli ( n = 10 ) when micro - waved for 4 minutes in the presence of iron ions compared to control samples ( distilled water ) . the results showed that the presence of iron reduced the disinfection time for all test bacteria . the most significant decrease was e coli whose disinfection time reduced from four minutes to one minute . the number of viable s. aureus was constant during the first two minutes of microwave treatment with a rapid decrease ( 94% ) during the third minute . e. coli viability showed a sharp decline during microwave heating in the presence of iron ions . during the first minute of microwave treatment bacterial viability for e. coli contrary to other data , e. coli disinfection denotes the strong influence of iron ions on micro - organisms . for comparison , table 2 and figs . 4 and 6 , data for microwave treatment of e. faecalis , s. aureus and e. coli in distilled water ( triangular points ) was included from our previous paper . this data showed that disinfection time in the presence of iron ions ( 13 min ) is less than in distilled water ( 4  5 min ) . so , the presence of iron ions in water increased the efficiency of the microwave deactivation of bacteria . results show that differences between bacterial survival and microwave time have similar  bell  shape forms for both with and excluding metal ions in most circumstances . lower survival rates were found for e. faecalis , s. aureus and e. coli in the presence of metal ions under microwave heating when compared to their distilled water controls . the results suggest that metal ion s ability to enhance bacterial deactivation primarily occurs above temperatures needed for optimal growth . microwave disinfection times for all three bacteria were also lowered in the presence of metal ions such as cobalt and iron . this shift found a reduction of bacterial viability becoming insignificantly small at the third minute of microwave heating . experimental controls of distilled water found bacterial viability requiring 4  5 min of microwave irradiation for significant reduction . the rapid reduction of viable bacteria during microwave irradiation in the presence of aqueous metal ions indicates an increase of kinetic energy of the solution . metal ions with higher kinetic energy have a greater possibility to enter into the bacteria . as the kinetic energy of the metal ion increases , there is an increase in ion penetration . following metal ion penetration , they begin to damage the cell membranes of bacteria , disrupt cellular functions , and destroy the structure of dna . for preparation of mathematical model for bacterial deactivation in the presence of metal ions , growth of bacteria by improving conditions of their reproduction on initial stage of microwave heating , and following reduction of survival bacteria by increasing of  death  factor with increasing the time of microwave irradiation . in our previous work we found that rate of change ( dn / dt ) of bacterial survival with water temperature ( t ) is described by formula : 
 ( 1)dndt=where ,  and  - growth and decay of viable bacteria with changing water temperature on 1c related with  birth factor  and  death factor  , respectively . and  depend on temperature , and in the first approximation , we can use linear functions : 
 ( 2)=a0t+b0  and  =a1t+b1where , a0,b0,a1,b1 -coefficients that depend on forms of bacteria . assuming , the water contains metal ions with concentration m we have to change the formula ( 1 ) and include the term that gives influence of metal ions on bacteria death . after this transformation formula ( 1 ) will be : 
 ( 3)dndt=12where , 1=a1t+b1 - decay of bacteria number that relates with changing water temperature on 1c , 2(m ) decay of bacteria number that relates with changing metal ions concentration . if metal ions concentration is permanent , we can decide that 2(m ) is constant . then after taking integral from ( 3 ) we will receive : 
 ( 4)n(t)=a1t2+b1t+c1where a1,b1,c1 - coefficients that depend on bacteria forms , type and concentration of metal ions . also , we can use relationship between microwave time t and temperature t of water , and find dependence between number n of viable bacteria and microwave time t : 
 ( 5)n(t)=a2t2+b2t+c2where a2,b2,c2 - coefficients that depend on bacteria forms , type , and concentration of metal ions . therefore , we can expect that relationship between number n of viable bacteria and microwave time t will be given by second order polynomial function ( 5 ) . in accordance with this theory , 1 and 6 show the results of this approximation ( solid curves ) . for comparison with previous results , we also provided theoretical curves for water without metal ions ( dotted curves ) . the values of the coefficients a2,b2,c2 that gave the best correlation with experimental results were calculated by using the least squares method and placed into table 3 . table 3 shows the coefficients for the theoretical mathematical models for e. faecalis , s.aureus , and e. coli . the mathematical models show between a 0.99 and a 0.91 correlation coefficient when compared to experimental data . comparison of mathematical model with experimental results shows good correlation ( coefficient of correlation 0.91  0.99 ) for most results that confirm the assumptions accepted in this model . an exception is the influence of iron ions on microwave bacteria deactivation . for this influence , existence of mathematical model for microwave heating of water with metal ions allows for the determination of viable bacterial levels at predetermined times .