Effects of Light Intensity and Titanium Dioxide Concentration on

Oct 15, 1996 - Photocatalytic sterilization of Escherichia coli (bacterium) or Saccharomyces serevisiae (yeast) was conducted with a rectangular ...
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Ind. Eng. Chem. Res. 1996, 35, 3920-3926

Effects of Light Intensity and Titanium Dioxide Concentration on Photocatalytic Sterilization Rates of Microbial Cells Yasuhiko Horie, Diago Abreu David, Masahito Taya, and Setsuji Tone* Department of Chemical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan

Photocatalytic sterilization of Escherichia coli (bacterium) or Saccharomyces serevisiae (yeast) was conducted with a rectangular bubble-column photoreactor (40 mm in width, 40 mm in breadth, and 250 mm in height) containing slurried TiO2 semiconductor particles. The profiles of cell deactivation with sterilization time could be expressed in fair agreement with experimental data, based on a series-event model and a second-order kinetics with respect to the concentrations of microbial cells and oxidative radicals generated by photoexcitation of TiO2 particles. Sterilization rate constants for the microbes were determined under various conditions of TiO2 concentrations (0-5 × 10-1 kg/m3) and average light intensities (0-223 W/m2) in the photoreactor. Linear relationships were obtained between the rate constants and average light intensity at TiO2 concentration of 1 × 10-2 kg/m3. When incident light intensity was kept constant (27 W/m2 for E. coli or 238 W/m2 for S. cerevisiae), the correlations between the rate constants and TiO2 concentration were interpreted considering a fraction of TiO2 particles adhered to the cells in slurry. Introduction In recent years, the photocatalytic sterilization with TiO2 has attracted attention as an alternative to the procedures such as heat treatment, ultraviolet ray irradiation, and chemical disinfectant dosage. Semiconductor TiO2 acquires a reducing or oxidizing potential when photoexcited by light rays with wavelength below 410 nm, and thus it catalyzes various chemical reactions including the decomposition of organic compounds and deactivation of organisms. Matsunaga et al. (1985) and Onoda et al. (1988) reported the photosterilization of Escherichia coli and Saccharomyces cerevisiae, and Streptococcus mutans in TiO2-suspended solutions under light irradiation, respectively. Cai et al. (1992) also demonstrated that cultured animal cells (HeLa cells) led to death in the presence of photoexcited TiO2 particles. However, there have been only a few studies on kinetics for the process of photocatalytic sterilization of viable cells in the TiO2 system. In our previous study (Tone et al., 1993), it was reported that Bacillus stearothermophilus spores were sterilized in TiO2 slurry under illumination using a high-pressure mercury lamp. Furthermore, the photocatalytic sterilization process of the spores was kinetically analyzed on the basis of a single-hit multitarget model, and the determined sterilization rate constant was correlated to average light intensity in the slurry, taking into account scattering and reflecting of light caused by TiO2 particles. In the present work, the photocatalytic sterilization of vegetative cells of bacterium (E. coli) or yeast (S. cerevisiae) was conducted in TiO2 slurry using a highpressure mercury lamp under a variety of light intensities and TiO2 concentrations. The photocatalytic sterilization processes were analyzed on the basis of a series-event model and a second-order kinetics with respect to the concentrations of oxidative radicals generated by photoexcited TiO2 particles and microbial cells. The effects of average light intensity and TiO2 * Author to whom correspondence is addressed. E-mail: [email protected].

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concentration in the slurry on sterilization rate constants were discussed in consideration of adsorption of TiO2 particles to cells. Experimental Section Materials. Escherichia coli IAM12119 and Saccharomyces cerevisiae IAM4274, which were obtained from the Institute of Molecular and Cellular Bioscience, The University of Tokyo, Tokyo, Japan, were used as test cells for sterilization. E. coli was cultivated for 5 h at 310 K in an L-type tube with 1.0 × 10-5 m3 of nutrient broth (pH 7.0) including 3 kg of Bacto Beef Extract (Difco Lab., Detroit, MI) and 5 kg of Bacto Peptone (Difco Lab., Detroit, MI) per m3 of water. S. cerevisiae was also cultivated for 14 h at 298 K in an L-type tube with 1.0 × 10-5 m3 of a Yeast Malt Extract (YME; pH 6.2) medium containing 10 kg of glucose, 5 kg of peptone, 3 kg of yeast extract, and 3 kg of malt extract per m3 of water. Both cells were centrifuged for 10 min at 277 K and 12 000g, washed twice using 9 kg/m3 of NaCl aqueous solution, and suspended in the NaCl solution at the concentration of Nt)0 ) 1 × 1011-1 × 1013 cells/m3. By means of microscopic measurement, the mean sizes of E. coli (as a rodlike shaped cell) and S. cerevisiae (as a spherical shaped cell) were estimated as a diameter of 0.91 µm by length of 2.0 µm and a diameter of 5.6 µm, respectively, and then the mean volumes of E. coli and S. cerevisiae, Vc, were calculated to be 1.3 × 10-18 and 92 × 10-18 m3/cell, respectively. TiO2 particles (P25, mainly anatase type, Japan Aerosil Co., Tokyo, Japan) were used as a photocatalytic semiconductor. The particles have the physical properties of a surface area of 1 × 105 m2/kg, a density of FT ) 3.8 × 103 kg/m3, and a mean particle size of dT ) 21 × 10-9 m. In sterilization experiments, TiO2 particles were added to the prepared cell suspension at the concentration of CT,O ) 0-5 × 10-1 kg/m3. Sterilization Test. As described in our previous study (Tone et al., 1993), the sterilization experiments were conducted with a rectangular bubble-column photoreactor (40 mm in width, 40 mm in breadth, and 250 mm in height). The reactor was constructed using © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3921

Plexiglas except an irradiation face made of quartz glass. The reactor was externally illuminated using a 500-W high-pressure mercury lamp (EHB-WIF500, Eikosha Co., Osaka, Japan) with 100 mm of effective illumination length through a Pyrex glass filter (5 mm thick) and a liquid filter (mixture of 0.356 kmol/m3 CoSO4‚7H2O and 1.98 kmol/m3 KNO3). The effective light wavelengths through the filters were 365 and 405 nm. A test solution (VL ) 3.0 × 10-4 m3) was introduced into the reactor column. The filtered air through a humidifier was sparged from the bottom of the reactor column at a gas velocity of 5.0 mm/s. The solution height was 192 mm, and the light irradiation area of the test solution, A, was 7.7 × 10-3 m2. The sterilization tests were carried out at 303 K and at the concentration of dissolved oxygen of 7.7 × 10-3 kg/m3. To obtain reliable data on sterilization rates, the respective incident light intensities for E. coli and S. cerevisiae were preliminarily determined as follows. The incident light intensity for E. coli was varied in the range of 0-60 W/m2 by changing the distance between the light source and reactor column from 150 to 250 mm. The incident light intensity for S. cerevisiae was in the range of 0-238 W/m2, and the distance between the light source and the reactor column was changed from 50 to 200 mm. Analysis. The incident light intensity was measured by a chemical actinometer (Hatchard and Parker, 1956). The light intensity at a given position in the reactor column, I, was measured by means of inserting a quartz glass tube with diameter of 4 mm and length of 300 mm containing the chemical actinometer (liquid height of 192 mm) in the TiO2 suspension according to the method described previously (Tone et al., 1993). The average light intensity in the reactor column, hIobs, at a given TiO2 concentration, was evaluated from the distribution profiles of light intensity using the equation

hIobs )

∫0

0.04

∫0

I d(x - x0)/

0.04

d(x - x0)

(1)

where x ) horizontal distance (in meters) between a lamp and a given position in the reactor column and x0 ) horizontal distance between a lamp and the irradiation face of the reactor column. To evaluate the cell viability of E. coli or S. cerevisiae, aliquots of the test solution (100 mm3) were withdrawn from the reactor column and diluted using a 9 kg/m3 NaCl aqueous solution when necessary. The diluted test solution was spread on nutrient broth agar plates for E. coli and YME agar plates for S. cerevisiae. After cultivating E. coli and S. cerevisiae for 24 h at 310 K and for 48 h at 298 K, respectively, the number of viable cells was evaluated by counting the developed colonies on the agar plates.

In the present work, to analyze the processes of the photocatalytic sterilization of microbial cells with TiO2 particles, the following assumptions are made: 1. The cell deactivation obeys a second-order reaction between cells and oxidative radicals, and the death of a cell is caused by n times reactions on the basis of a series-event model according to Severin et al. (1984). 2. The concentration of oxidative radicals is constant under quasi-steady state as described by Tone et al. (1993). On the basis of a second-order kinetics and a seriesevent model, the photocatalytic sterilization process can be expressed as the following series reaction: OX

OX

OX

OX

M0 98 M1‚‚‚Mi-1 98 Mi 98 Mi+1‚‚‚Mn-1 98 Mn f death (2) where Mi is the population of cells which are at each event level i (i ) 0-n) and OX denotes oxidative radicals. The material balance of Mi yields the following equations according to Severin et al. (1984):

dNi/dt ) -kCOXNi (i ) 0)

(3)

dNi/dt ) kCOXNi-1 - kCOXNi (i ) 1 to n)

(4)

where Ni ) cell concentration of Mi, k ) sterilization rate constant of viable cells, and COX ) concentration of oxidative radicals generated by TiO2 particles. The following equation is obtained by integrating eqs 3 and 4 with respect to i ) 0 to n - 1.

Nt)0(k′t)i exp(-k′t) Ni ) i!

(5)

Since the cells which are at reached level n - 1 or less are surviving, the concentration of viable cells after light irradiation of t hours, Nt, is expressed as the following equation: n-1

Nt )

Ni ∑ i)0

(6)

Thus, the cell viability at a given time, Nt/Nt)0, is expressed as follows.

Nt

n-1

) Nt)0

Ni

∑ i)0 N

n-1(k′t)i

) exp(-k′t)

t)0

∑ i)0

i!

(7)

The apparent sterilization rate constant, k′, is expressed as follows:

k′ ) kCOX

(8)

Kinetic Expression of Photocatalytic Sterilization Based on Series-Event Model

Results and Discussion

Riegel and Bolton (1995) and Brezova et al. (1994) described that oxidative radicals such as hydroxyl radicals (•OH) and perhydroxyl radicals (HO2•) are generated from dissolved oxygen or water by the catalysis of photoexcited TiO2 particles. Cai et al. (1992) reported that, in photocatalytic sterilization, cells are deactivated by these radicals. Severin et al. (1984) expressed chemical disinfection rates of microbial cells with oxidants like chloramine and chlorine on the basis of second-order kinetics with respect to the cell and oxidant concentrations and a series-event model.

Effects of Light Intensity and TiO2 Concentration on Cell Deactivation. Figures 1 and 2 show the changes in cell viabilities of E. coli and S. cerevisiae, respectively, during light irradiation at CT,O ) 1 × 10-2 kg/m3 under various conditions of average light intensities. The sterilization rates of E. coli and S. cerevisiae increased with increasing hIobs in the ranges of 0-57 and 0-223 W/m2, respectively. These results indicate that, when TiO2 concentration is constant, the sterilization rates of the cells depend on the average light intensity in the photoreactor. As seen from Figure 1, the changes

3922 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996

Figure 1. Changes in cell viabilities of E. coli during light irradiation at various light intensities.

Figure 2. Changes in cell viabilities of S. cerevisiae during light irradiation at various light intensities.

Figure 4. Changes in cell viabilities of S. cerevisiae during light irradiation at various TiO2 concentrations.

light intensity was kept at a constant value of 27 W/m2 for E. coli or 238 W/m2 for S. cerevisiae, and depending on CT,O values employed, the values of hIobs for E. coli and S. cerevisiae were in the ranges of 12-27 and 109238 W/m2, respectively. The sterilization rates of E. coli and S. cerevisiae increased with increasing value of CT,O from 0 to 1 × 10-1 kg/m3. However, when CT,O was larger than 1 × 10-1 kg/m3, the sterilization rates of E. coli and S. cerevisiae decreased with an increase in CT,O. It is considered that these results are attributed to the decrease in the average light intensity owing to light scattering and reflection by TiO2 particles in the photoreactor, indicating the existence of an optimal TiO2 concentration with respect to sterilization efficiency. Estimation of Kinetic Parameters. Severin et al. (1984) analyzed the chemical disinfection rates with oxidants such as chloramines and free chlorine based on both the single-hit multitarget model and the seriesevent model and described that, in the case of the sterilization rate analysis for the cells with a repairing ability, the series-event model yields reasonable results compared with the single-hit multitarget model. In the present work, the sterilization data of E. coli were first analyzed with the single-hit multitarget model, in which cell viability is expressed as the following equation reported by Severin et al. (1984):

Nt/Nt)0 ) 1 - {1 - exp(-k′t)}L

Figure 3. Changes in cell viabilities of E. coli during light irradiation at various TiO2 concentrations.

in cell viabilities of E. coli were relatively small for the early period of light irradiation. This finding may support that the deactivation of E. coli cells occurs via the series reaction with the multiple steps as expressed by eq 2. As shown in Figure 2, on the other hand, the changes in cell viabilities of S. cerevisiae exhibited the linear profiles, suggesting that S. cerevisiae cells are deactivated via a single reaction step. Figures 3 and 4 show the changes in cell viabilities of E. coli and S. cerevisiae, respectively, during light irradiation at various TiO2 concentrations ranging from 0 to 5 × 10-1 kg/m3. In these experiments, the incident

(9)

where L ) target number of a viable cell. According to the procedure described by Severin et al. (1984), eq 9 was matched to sterilization data shown in Figures 1 and 3 with the correlation coefficient of 0.985 (data not shown). As a result, an L value of 531 for E. coli was obtained. As pointed out by Severin et al. (1984), the value of L ) 531 for E. coli was too large to be reasonable. The vegetative cells of E. coli are considered to possess a repairing ability against chemical deactivation, which may contribute to the large value of L in the single-hit multitarget model. Next, the sterilization rates of E. coli were analyzed on the basis of the series-event model. Severin et al. (1984) reported that, when the chemical disinfection rates of microbial cells with chloramines and free chlorine were analyzed on the basis of this model, the lethal number of reactions, n, were constant independent of oxidant concentration. The values of n were 5 for E. coli with chloramines, 6 for Candida parapsilosis with chloramines, and 4 for C. parapsilosis with free

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3923

Figure 7. Relationship between k′/Ihobs and CT,O values for S. cerevisiae. Figure 5. Relationships between k′ and hIobs values.

Figure 6. Relationships between k′/Ihobs and CT,O values for E. coli.

chlorine. According to their method, the value of n for E. coli was determined by matching eq 7 to experimental data shown in Figures 1 and 3 using the nonlinear leastsquares method. As a result, the value of n was 8 for E. coli. The apparent sterilization rate constants, k′, were then evaluated using the value of n under various conditions of TiO2 concentrations and average light intensities. The solid lines indicated in Figures 1 and 3 were calculated by eq 7 using determined values of k′ and n for E. coli. In this case, the correlation coefficient was 0.989. Subsequently, the sterilization data of S. cerevisiae shown in Figures 2 and 4 were analyzed based on the single-hit multitarget model using eq 9. As a result, the value of L ) 1 was obtained for S. cerevisiae. When the value of L is unity, eq 9 in the single-hit multitarget model becomes identical to eq 7 at n ) 1 in the seriesevent model, yielding a second-order kinetics on cell viability expressed by the following equation:

Nt/Nt)0 ) exp(-k′t)

(10)

The solid lines indicated in Figures 2 and 4 show the results calculated by eq 10 using determined values of k′ for S. cerevisiae. In this case, the correlation coefficient was 0.987. Figure 5 shows plots of the values of k′ for E. coli and S. cerevisiae against the value of hIobs at CT,O ) 1 × 10-2 kg/m3. Proportional relationships between k′ and hIobs for E. coli and S. cerevisiae were observed, and k′ for E. coli was larger than that for S. cerevisiae. Figures 6 and 7 show the effect of TiO2 concentration on sterilization rates of E. coli and S. cerevisiae, respectively. To

eliminate the effect of CT,O on hIobs, in these figures, the values of k′/Ihobs are plotted against CT,O. As seen from Figure 6, relationships between k′/Ihobs and CT,O for E. coli depended on Nt)0. At Nt)0 ) 1 × 1011 and 3 × 1012 cells/m3, k′/Ihobs gradually approached a saturated value with increasing CT,O, while at Nt)0 ) 1 × 1013 cells/m3, a linear relationship was apparently recognized. On the other hand, as seen from Figure 7, k′/Ihobs for S. cerevisiae at Nt)0 ) 1 × 1011 cells/m3 was enhanced with a steep slope in the range of CT,O ) 0-5 × 10-2 kg/m3, while beyond CT,O of 5 × 10-2 kg/m3, the k′/Ihobs value showed a gradual increase. These nonlinear relationships at Nt)0 ) 1 × 1011 and 3 × 1012 cells/m3 for E. coli in Figure 6 and for S. cerevisiae in Figure 7, respectively, seem to arise from the adsorption of TiO2 particles to the cells, as pointed out by Saito et al. (1992). Correlation of Apparent Sterilization Rate Constants to Light Intensity and TiO2 Concentration. As described in our previous study (Tone et al., 1993), the apparent sterilization rate constant of B. stearothermophilus spores was correlated to the average light intensity by expressing the concentration of oxidative radicals at quasi-steady state as a first-order function of the average light intensity. In a similar manner, in the present work, the concentration of oxidative radicals at quasi-steady state was expressed as follows:

COX ) φOXAIhobs/kOXVL

(11)

Assuming that the oxidative radical generation occurs on the surface of TiO2 particles (Tone et al., 1991), the quantum yield is proportional to the specific surface area of TiO2 particles. When the volumes of cells and particles are negligibly smaller than that of bulk liquid, the quantum yield of TiO2 particles is expressed as the following equation:

φOX ) kφaT,O ) 6kφCT,O/dTFT

(12)

where aT,O ) specific surface area of TiO2 particles on a liquid volume basis. COX is then expressed as the following equation:

COX )

(

)( )

6kφCT,O AIhobs dTFT kOXVL

(13)

The following equation is obtained from eqs 8 and 13:

( )( )

6kφ A k′ )k C hIobs dTFT kOXVL T,O

(14)

According to eq 14, k′/Ihobs is proportional to CT,O. As shown in Figures 6 and 7, however, for the data of E.

3924 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996

Thus, COX,A and COX,F are written as follows, respectively:

COX,A )

COX,F )

(

(

)( )

6kφ,AqA AIhobs dTFTVL kOXVc

)( ) {

(21)

6kφ,FCT,F AIhobs ) dTFT kOXVF 6kφ,F(CT,O - Nt)0qA) AIhobs (22) dTFT kOXVF

}( )

Using the adsorption equilibrium constant, K, given by the equation

K)

Figure 8. Conceptual drawing of the sterilization of cells with TiO2 particles adsorbed to a cell and suspended ones.

coli at Nt)0 ) 1 × 1011 and 3 × 1012 cells/m3 and those of S. cerevisiae at Nt)0 ) 1 × 1011 cells/m3, the profiles of k′/Ihobs against CT,O could not be described by eq 14. Saito et al. (1992) reported that the adsorption of TiO2 particles to cells plays an important role in the deactivation of cells. To explain the relationships between k′/ hIobs and CT,O, in the present work, the following assumptions are made considering the adsorption of TiO2 particles to cells: 1. As shown in Figure 8, TiO2 particles adsorbed to cells and those suspended in the bulk exist in slurry. The cell deactivation is caused by oxidative radicals generated by TiO2 particles in both states. 2. Adsorption equilibrium between TiO2 particles and a cell is held according to the following equation:

s + TiO2(F) {\ } s-TiO2(A) k

(15)

-1

where s, TiO2(F), and TiO2(A) denote an adsorption site on a cell surface, TiO2 suspended in liquid, and TiO2 adsorbed to a cell, respectively. When the photocatalytic sterilization rate considering the adsorption of TiO2 particles to a cell is expressed as the sum of sterilization contributed by adsorbed TiO2 particles and that by suspended ones, k′ is rewritten by the following equation:

k′ ) kACOX,A + kFCOX,F

(16)

where COX,A and COX,F ) concentrations of oxidative radicals generated by adsorbed TiO2 particles and by suspended ones, respectively. Based on eq 11, COX,A and COX,F are expressed as the following equations, respectively:

COX,A ) φOX,AAIhobs/kOXVc

(17)

COX,F ) φOX,FAIhobs/kOXVF

(18)

where Vc and VF ) volumes of a cell and bulk liquid, respectively. When the volumes of cells and TiO2 particles are negligibly smaller than the volume of bulk liquid, the quantum yields of adsorbed and suspended TiO2 particles are expressed as the following equations, respectively:

φOX,A ) kφ,AaT,A ) 6kφ,A(qA/VL)/dTFT

(19)

φOX,F ) kφ,FaT,F ) 6kφ,FCT,F/dTFT

(20)

(23)

the amount of TiO2 particles adsorbed to a cell is expressed as follows:

qA )

1/K + CT,O + Nt)0qm × 2Nt)0 4Nt)0qmCT,O 1- 1(1/K + CT,O + Nt)0qm)2

[ {

}] 1/2

(24)

where qm ) maximal amount of TiO2 particles adsorbed to a cell. Thus, the following equation is derived from eqs 1622 and 24:

hIobs

( )( [ { [ ( [ {

)

R 1/K + CT,O + Nt)0qm

k′ )

k+1

qA k+1 ) k-1 (qm - qA)(CT,O - Nt)0qA)

Vc

2Nt)0

1- 1-

×

}]

4Nt)0qmCT,O

1/2

+

(1/K + CT,O + Nt)0qm)2 1/K + CT,O + Nt)0qm β CT,O × 2 1- 1-

)

4Nt)0qmCT,O (1/K + CT,O + Nt)0qm)2

} ]] 1/2

(25)

where R ) 6AkAkφ,A/dTFTkOXVL and β ) 6AkFkφ,F/ dTFTkOXVF. When the effect of suspended TiO2 particles is very small, the second term of eq 25 can be neglected. Moreover, when CT,O . 1/K + Nt)0qm and CT,O , 1/K + Nt)0qm, eq 25 can be approximated by the following equations, respectively:

()

R k′ ) q hIobs Vc m

( )(

(26)

)

qm k′ R ) C hIobs Vc 1/K + Nt)0qm T,O

(27)

On the other hand, when the effect of adsorbed TiO2 particles is negligible, eq 25 can be approximated by the following equation:

k′/Ihobs ) βCT,O

(28)

According to the procedure shown in Figure 9, the parameters in eq 25 were determined. The value of Rqm was first calculated by substituting the values of k′/Ihobs

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3925

10-2 kg/m3. The calculated results were in fair agreement with the data. The solid lines shown in Figures 6 and 7 were also calculated by eq 25 using the values listed in Table 1. It was found that the lines showed the close agreement with the data. As shown in Figure 7, k′/Ihobs for S. cerevisiae was calculated against CT,O at Nt)0 ) 1 × 1014 cells/m3, although experimental data could not be obtained under the conditions employed in this study, owing to the extremely high concentration of the cells. The calculated result also exhibited an apparently linear relationship between k′/Ihobs and CT,O as observed for E. coli in Figure 6. It was thus possible that apparent rate constants were correlated to the average light intensity and TiO2 concentration by taking into account the adsorption of TiO2 particles to the cells. Conclusions

Figure 9. Calculation procedure for parameters of R, β, K, and qm in eq 25. Table 1. Evaluated Values of Parameters of Equation 25 R [m5/(J‚kg)] β [m5/(J‚kg)] K [m3/kg] qm [kg/cell] Vc [m3/cell]a a

E. coli

S. cerevisiae

6.2 × 10-8 8.8 × 10-5 85 8.2 × 10-14 1.3 × 10-18

6.2 × 10-8 8.8 × 10-5 85 2.8 × 10-14 92 × 10-18

Experimentally determined value.

for E. coli at CT,O ) 5 × 10-1 kg/m3 and Nt)0 ) 1 × 1011 cells/m3 in Figure 6 into eq 26 using the experimentally determined value of Vc ) 1.3 × 10-18 m3/cell for E. coli. Then the values of R, K, and qm for E. coli were determined by matching eq 27 to the data at Nt)0 ) 1 × 1011 and 3 × 1012 cells/m3 in Figure 6 using the linear least-squares method. Furthermore, by matching eq 27 to the data at Nt)0 ) 1 × 1011 cells/m3 in Figure 7 using the linear least-squares method, the value of qm for S. cerevisiae was determined using the experimentally determined value of Vc ) 92 × 10-18 m3/cell for S. cerevisiae. The value of β was determined by matching eq 28 to the data in Figure 7 using the linear leastsquares method. The determined values are summarized in Table 1. The value of qm for E. coli was larger than that for S. cerevisiae, and the experimentally determined value of Vc for E. coli was smaller than that for S. cerevisiae. According to eqs 21 and 24, therefore, COX,A for E. coli can be estimated as a large value compared with that for S. cerevisiae, which is most likely responsible for the relatively large value of k′ for E. coli as shown in Figure 5. The solid lines shown in Figure 5 were calculated by eq 25 using the values listed in Table 1 and CT,O ) 1 ×

The photocatalytic sterilization of E. coli or S. cerevisiae with TiO2 particles was carried out using a highpressure mercury lamp under various conditions, and the following could be concluded. 1. The sterilization rates of the microbial cells increased with an increase in the average light intensity from hIobs ) 0 to 57 W/m2 for E. coli and from hIobs ) 0 to 223 W/m2 for S. cerevisiae. The sterilization rates increased with an increase in TiO2 concentration from CT,O ) 0 to 1 × 10-1 kg/m3, while beyond CT,O ) 1 × 10-1 kg/m3, the rates decreased with increasing CT,O. 2. The photocatalytic sterilization processes of the microbes could be expressed on the basis of a seriesevent model, considering a second-order kinetics with respect to the concentration of oxidative radicals generated by photoexcitation of TiO2 particles and microbial cells. 3. The determined values of k′ for E. coli and S. cerevisiae were proportional to hIobs at CT,O ) 1 × 10-2 kg/m3. Nonlinear relationships were observed between k′/Ihobs and CT,O under the conditions of Nt)0 ) 1 × 1011 and 3 × 1012 cells/m3 for E. coli and Nt)0 ) 1 × 1011 cells/m3 for S. cerevisiae. 4. The apparent sterilization rate constants could be correlated to the incident light intensity and TiO2 concentration by considering a fraction of TiO2 particles adsorbed to the cells of E. coli and S. cerevisiae in slurry. Acknowledgment This work was funded in part by a supplementary budget of 1995 from the Ministry of Education, Science, Sports and Culture, Japan, for the construction of “GasHydrate Analyzing System (GHAS)” at Department of Chemical Engineering, Osaka University. Nomenclature A ) cross section of reactor column for light absorption, m2 aT ) specific area of TiO2 particles on a liquid volume basis, m2/m3 COX ) concentration of oxidants, mol/m3 CT ) concentration of TiO2 particles, kg/m3 dT ) diameter of a TiO2 particle, m I ) light intensity at a given position in the reactor column, W/m2 I0 ) incident light intensity, W/m2 hIobs ) average light intensity in the reactor column, W/m2 K ) adsorption equilibrium constant, m3/kg k ) sterilization rate constant of viable cells, m3/(mol‚s)

3926 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 k′ ) apparent sterilization rate constant of a viable cell, s-1 k+1 ) adsorption rate constant, m3/(kg‚s) k-1 ) desorption rate constant, s-1 kOX ) apparent decomposition rate constant of oxidative radicals, s-1 kφ ) coefficient in eq 12, mol‚m/J L ) target number of a viable cell in the single-hit multitarget model, dimensionless Ni ) concentration of viable cells at reached event level i in the series-event model, cells/m3 Nt ) concentration of viable cells at a given time, cells/m3 Nt)0 ) initial concentration of viable cells, cells/m3 n ) lethal number of reactions in the series-event model, dimensionless qA ) amount of TiO2 particles adsorbed to a cell, kg/cell qm ) maximum amount of TiO2 particles adsorbed to a cell, kg/cell t ) irradiation time, s Vc ) volume of a cell, m3/cell VF ) volume of bulk liquid, m3 VL ) volume of test solution, m3 x ) horizontal distance between a lamp and a given position in the reactor column, m x0 ) horizontal distance between a lamp and the irradiation face of the reactor column, m φOX ) quantum yield of TiO2 particles, mol/J FT ) density of a TiO2 particle, kg/m3 Subscripts A ) adsorption F ) suspension O ) overall amount

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Received for review January 26, 1996 Revised manuscript received July 22, 1996 Accepted August 2, 1996X X Abstract published in Advance ACS Abstracts, October 15, 1996.