Environ. Sci. Technol. 2002, 36, 3834-3843
Effect of Oxygen in a Thin-Film Rotating Disk Photocatalytic Reactor DIONYSIOS D. DIONYSIOU,* ARTURO A. BURBANO, AND MAKRAM T. SUIDAN* Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0071 ISABELLE BAUDIN AND J E A N - M I C H E L L A ˆI N EÄ CIRSEE, Centre International de Recherche Sur l’Eau et l’Environnement, ONDEO Services, 38 Rue du Pre´sident Wilson, 78230 Le Pecq, France
A novel experimental procedure was developed to measure oxygen mass transfer during the oxygenation of water in a thin film of a rotating disk photocatalytic reactor (RDPR). The increase in dissolved oxygen (DO) of initially deaerated water was monitored with time in the reactor vessel at different disk angular velocities after exposure of the reactor to the atmosphere. Oxygenation was predominantly achieved by oxygen mass transport through the thin liquid film carried by the disk and to a much lesser extent by direct oxygenation of the water in the reactor vessel via a surface renewal mechanism. A mathematical model was developed to simulate the phenomenon considering both cases of presence and absence of oxygen mass transport limitations. In the latter case, the model considered that the amount of liquid carried by the disk was saturated with oxygen when returning to the reactor vessel. On the basis of the model and the experimental data, it was proven that mass-transfer limitations existed until the water in the reactor vessel became saturated with oxygen. Results obtained from the model were validated by an alternative analysis using dimensionless groups characteristic to the system. The study revealed that the mass-transfer coefficient increased linearly with disk angular velocity and thus disk Reynolds number. The results showed that oxygen mass-transfer limitations decreased with increasing disk angular velocity, mainly due to an increase in the overall mass-transfer coefficient. In the presence of UV radiation, the influence of oxygen on the photocatalytic oxidation of 4-chlorobenzoic acid was investigated in the RDPR operated in batch and continuous mode. The photocatalytic reactions occurred in a thin film of liquid carried by the disk in the presence of UV radiation and STB01 composite spherical ceramic (SiO2/Al2O3) balls coated with anatase TiO2 catalyst. It was found that the initial degradation rate followed Langmuir kinetics with respect to oxygen concentration in the gas phase. When the oxygen concentration in the gas phase surpassed that in air, the degradation rates did not improve significantly, suggesting that operation with air instead of oxygen is most probably a more realistic practical choice. Measurements of DO during the presence and absence of UV radiation * Corresponding author phone: (513) 556-0724; fax: (513) 5562599; e-mail:
[email protected]. 3834
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suggested that the photocatalytic reactions were mainly oxygen concentration-limited rather than oxygen masstransfer-limited.
Introduction It is well-established in TiO2 photocatalysis that oxygen is a determining parameter for improving the degradation rates. Oxygen is an effective conduction band electron acceptor and suppresses electron and hole recombination. It is crucial that species which play the role of electron acceptors (i.e., molecular oxygen, hydrogen peroxide) are preadsorbed or preassociated with the surface of the catalyst to have a sufficiently fast rate of interfacial electron trapping (1). The latter is based on the fact that electron and hole recombination occurs in the nanosecond time range and is faster than diffusion from the bulk to the solid surface. On the other hand, it was proven experimentally that holes react much faster with organic species in the solution or solvent molecules than electrons do with oxygen (2). As a result, the rate of oxygen reduction by the conduction band electron is usually the rate-limiting step in a photocatalytic process. This was proven by Gerischer and Heller, who conduced a theoretical study on the role of oxygen during TiO2-assisted photocatalytic degradation of organic contaminants (3). On the basis of their results, they concluded that oxygen is necessary because it stabilizes the primary chemical species and is required for various reactions which are beneficial in the overall photocatalytic process. There is also evidence that oxygen does not compete with the organic contaminants for adsorption sites because it adsorbs at Ti3+ sites, whereas hydroxyl ions and organic contaminants adsorb at Ti4+-lattice oxygen sites (4). However, recent studies in gas-phase photocatalysis showed that UV light causes a significant increase in the rate of exchange between gas-phase molecular oxygen and water adsorbed on TiO2 (5) and that, in the absence of oxygen in the gas phase, lattice oxygen is extracted from the TiO2 surface by adsorbed organic molecules such as formic acid (6). In the latter case, it was observed that, as the surface oxygen was depleted, photocatalytic degradation was limited by oxygen diffusion from the bulk of the catalyst. It is not intended here to discuss in detail the fundamental chemical reactions of the generation of primary reactive species in TiO2 photocatalysis. Such discussions are given by others (3, 7-10). It is necessary, however, for the completeness of the presentation, to report some of the primary reactions which involve the participation of oxygen either in its molecular form or after its interaction with the surface of the catalyst and other chemical species. Besides recombining with the holes, the electrons (free or trapped) generated during the photoexcitation process interact with electron acceptors, such as oxygen, to form superoxide radicals
O2 + es- f O2-• or O2 + eT,s- f O2-•
(1)
or with adsorbed species to form hydroxyl ions, hydroperoxyl radicals, and so forth
e- + OHad f OH-
(2)
e- + O 2ad- + H+ f HO2-•
(3)
e- + HO 2ad f HO2-•
(4)
Other reactions which involve the formation and reaction of hydrogen peroxide are discussed elsewhere (11). As inferred 10.1021/es0113605 CCC: $22.00
2002 American Chemical Society Published on Web 07/26/2002
from reactions 1 and 3, oxygen adsorption is an important step in the photocatalytic process. Oxygen adsorbs on surface defect sites (i.e., crystal irregularities) and subsequently forms superoxide radical, O2•- as shown by eq 1 (3, 12). This superoxide radical can attack organic contaminants, protonate to form surface-bound hydroxyl radicals, or get involved in other surface reactions (1). It was reported that molecular oxygen adsorption does not occur at stoichiometric surface sites. In experiments using TiO2(110), it was shown that oxygen adsorbs at the surface Ti3+ sites by nondissociative adsorption, but above 400 K, all O2 molecules dissociate (13). The lower photocatalytic activity of rutile compared to that of anatase was attributed to the lower capacity of rutile surface to adsorb molecular oxygen, leading to higher rates of electron and hole recombination (1). Oxygen supply in the reaction solution is usually achieved by diffusion of fine air bubbles. In many experimental studies, oxygen is introduced in the reaction solution in its pure form. In the rotating disk photocatalytic reactor (RDPR), however, oxygenation of the reaction solution is achieved by oxygen transport from the gas phase to a thin film of liquid carried by the disk during its rotation as well as directly by diffusion into the reactor vessel (i.e., diffusion from the gas phase to the surface of the reaction solution). The latter is facilitated by mixing of the reaction solution during the rotation of the disk. On the basis of these unique design and operational characteristics (i.e., compared to any other photocatalytic reactor), it was evident that investigation of the effect of oxygen concentration on the rates of photocatalytic reactions was necessary. In addition, measurements for the rate at which the dissolved oxygen of the solution increases during the rotation of the disk as well as for the dissolved oxygen in the absence and presence of UV radiation could provide further information regarding the existence of oxygen masstransfer limitations in the RDPR.
Experimental Section RDPR. A detailed description of the RDPR was reported in a previous publication (14). Figure 1a shows a schematic of the RDPR operated in a continuous mode. In summary, the RDPR contains three major components: (a) a rotating disk support loaded with catalyst in the form of silica-alumina composite ceramic balls coated with TiO2 nanoparticles, (b) radiation sources emitting near UV radiation in the range of 300-400 nm with a peak at 365 nm, and (c) a semicircular reactor vessel (52 cm in diameter and 3.5 cm in gap thickness) containing the contaminated solution. The maximum volumetric capacity of the reactor vessel is 3.5 L. Half of the disk is located in the reactor vessel while its other half is exposed to air and UV radiation. UV radiation does not enter the reactor vessel. In this type of reactor, the photocatalytic reactions occur within a thin liquid film of contaminated solution carried by the disk during the course of the rotation. The reactions take place only at the upper semicircular part of the disk in the presence of TiO2, UV radiation, and oxygen from the atmosphere. It should be noted that the portion of submergence of the disk can be an important parameter for the optimization of the RDPR. In this study, however, it was kept constant to 50% to eliminate variations on the effective incident light intensity, time of exposure of the irradiated film, hydrodynamics of liquid flow, and effective surface area for oxygen transfer and reaction. The catalyst (ST-B01) immobilized on the rotating disk was in the form of composite ceramic balls with diameter of approximately 6 mm and specific gravity in the range 2.8-3.2. ST-B01 catalyst was supplied by Ishihara Techno Corp., Tokyo, Japan. ST-B01 catalytic balls were composed of an inner ceramic support (mainly, 60-80% SiO2, 15-35% Al2O3, and 5% max K2O + Na2O) and a thin film of TiO2 nanoparticles attached to the surface of the support. The TiO2 nanoparticles were of the
anatase crystal phase as determined using X-ray diffraction (XRD, Siemens Kristalloflex D500 diffractometer, with Cu KR radiation). The surface area of the TiO2 nanoparticles when detached from the support was approximately 50 m2/g, and it was determined with the Brunauer-Emmett-Teller method (Gemini 2360 V1.01, Micromeritics, Norcross, GA) using N2 adsorption. The size of the particles was approximately 30 nm. The thickness of the TiO2 layer coated onto the ceramic support of ST-B01 varied in the range 10-30 µm and was determined using scanning electron microscopy (SEM, Hitachi S-4000). More details on the physical and chemical characterization of the catalyst, hydraulic characteristics of the RDPR, and the procedures for catalyst immobilization and light intensity measurements are given elsewhere (14, 15). Photocatalytic Experiments in the RDPR. (A) Batch-Mode Operation. The effect of oxygen on the photocatalytic degradation of a model organic compound (4-chlorobenzoic acid, 4-CBA) in the RDPR operated in a batch mode was investigated under the following conditions: disk angular velocity, ω ) 6 rpm; average incident light intensity, I ) 896 µW/cm2; initial 4-CBA concentration, C0 ≈ 49 mg/L (∼310 µmol/L); ionic strength as potassium nitrate ) 10 mM KNO3; initial volume of reaction solution, V0 ) 3.5 L; pH ) 3.0; and room temperature, 20-24 °C. The reasons for the selection of 4-CBA as a model compound were presented in a previous study (14). 4-CBA is not volatile and does not interact with ozone or UV-A alone (12). The RDPR was closed at the top, and a mixture of oxygen and nitrogen (Wright Brothers, Inc.) was continuously passed through the headspace. The gas flow rate, Qgas, was 14.5 L/min (standard conditions). Prior to its addition to the reactor, the gas mixture was premixed and passed through an activated carbon column and a humidifier to remove any other contaminants and to avoid water evaporation in the reactor, respectively. Cooling of the reactor was achieved by the gas flow as well as by two cooling fans placed on top of the reactor cover. Before irradiation, the solution was left to equilibrate until the concentration of oxygen in the headspace reached the desired value (i.e., initially, the gas phase contained air) and until the reaction solution equilibrated in the dark (dark adsorption equilibrium). During irradiation, samples were taken every 10 min for 60 min. Samples were filtered and analyzed immediately for 4-CBA and total organic carbon (TOC) following procedures reported in an earlier work (14). (B) Continuous-Mode Operation. This experiment was performed with the reactor closed at the top and operated as shown in Figure 1a. The objective was to verify the results obtained using the RDPR in a batch-mode. This experiment was performed at pH ) 3.0 (influent and the solution inside the reaction vessel); disk angular velocity, ω ) 6 rpm; incident light intensity, I ) 896 µW/cm2; solution volume in the reaction vessel, VR ) 3.5 L; influent concentration of 4-CBA, Cin ) 49 mg/L (310 µmol/L); room temperature, 20-24 °C; and solution ionic strength of 10 mM KNO3. The RDPR was operated at a liquid flow rate Qliquid of 53 mL/min (residence time, τ ) 66 min). The gas flow rate Qgas was 14.5 L/min and the gas mixture (nitrogen and oxygen) was precleaned and humidified as described in the previous section. Cooling was also achieved as described previously. The irradiation phase of the experiment was 4 h (i.e., until steady state was achieved). Oxygen Uptake in the Dark. This experiment was performed to determine the rate of oxygen transfer from the gas to the aqueous phase of a deaerated solution as a function of the disk angular velocity. The RDPR was operated in a batch mode and closed at the top. A dissolved oxygen (DO) probe (Orion, 083010) was placed permanently inside the reaction vessel. The probe was connected to a digital meter (Orion, model 835) for continuous monitoring of the DO VOL. 36, NO. 17, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. (a) RDPR operated in a continuous-mode with the disk rotated clockwise, and (b) Setup of the RDPR for on-line measurements of the dissolve oxygen inside the reactor vessel. inside the reactor vessel. Figure 1b shows the setup for the fixation of the DO probe into the reactor vessel. The insertion procedure of the probe was performed in a very careful manner due to the sensitivity of the membrane of the probe as well as the narrow cross-sectional dimension (gap) of the reactor vessel. It is important to note that the DO meter was calibrated immediately prior to the insertion of the probe into the reactor vessel for accurate measurements. Prior to the beginning of the experiment, the RDPR was completely sealed. The reactor vessel was filled with 3.5 L of distilled water, and the disk was set to rotate at a specified angular velocity. After it was passed through an activated carbon column and a humidifier, pure nitrogen was introduced in the reactor vessel at a flow rate of 14.5 L/min. This caused the DO of the water to decrease gradually to values close to zero (∼0.06 mg/L). When this low level of DO was sustained for a sufficient time, the gas flow into the RDPR was paused with simultaneous removal of the top cover of the reactor. Immediately after that, the DO in the water was monitored 3836
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with time. The same procedure was repeated at different disk angular velocities in the range 2-40 rpm. Dissolved Oxygen in the Dark and During Photocatalytic Reactions. This experiment was performed to examine the significance of oxygen mass-transfer limitations during photocatalytic reactions. It was carried out in a continuousmode operation with the RDPR closed at the top and air as the gas phase. The liquid and gas flow rates were 53 mL/min and 14.5 L/min, respectively. The influent was a solution of 4-CBA at concentration of 50 mg/L (320 µmol/L), pH 3.0, and 10 mM KNO3. The temperature during the operation of the RDPR was in the range 22-25 °C. The DO was measured continuously as explained in the previous section. Initially, the experiment was performed in the dark. The disk was rotated at 2 rpm for 5 min, and the DO was recorded every minute. Then, the disk angular velocity was increased to 4 rpm and remained at this value for 5 min with DO recorded every minute. This procedure was continued with a gradual increase of disk angular velocity at 6, 10, 15, 20, 25, 30, 35,
FIGURE 3. Effect of oxygen concentration in the gas phase on the percent removal of 4-CBA and TOC in the RDPR (continuous-mode operation, closed at the top) at ω ) 6 rpm, pH ) 3.0, I ) 896 µW/cm2, VR ) 3.5 L, Cin,4-CBA ≈ 310 µmol/L, Qliquid ) 53 mL/min, and [KNO3] ) 10 mM.
FIGURE 2. Effect of oxygen concentration in the gas phase on (a) the initial (30 min) degradation rates of 4-CBA and (b) initial rates of TOC destruction in the RDPR (batch-mode operation, closed at the top) at ω ) 6 rpm, pH ) 3.0, I ) 896 µW/cm2, V0 ) 3.5 L, C0 ≈ 310 µmol/L, and [KNO3] ) 10 mM. and 40 rpm. This experiment was repeated in the same manner but under UV irradiation (I ) 896 µW/cm2) to allow for the photocatalytic reactions to occur.
Results Effect of Oxygen on the Photocatalytic Degradation Rates. (A) Batch-Mode Operation. Figure 2 presents results for the effect of oxygen concentration in the gas phase on the initial rates of 4-CBA degradation and TOC mineralization. The data show that the rates increase with oxygen concentration following a saturation-type dependency. It is interesting that, even at concentrations of oxygen close to zero, the reaction rate is small but not zero. For example, at oxygen concentration in the gas phase of 0.34%, the initial reaction rate is approximately 1.1 µmol/min. The reaction rate increases to 7.45 µmol/min in the presence of air and slowly rises to 10.74 µmol/min in the presence of oxygen. Although the data suggest a saturation-type dependency with a plateau reached above 60% oxygen, there is indication that the rates increase slightly as oxygen concentration in the gas phase increases. In a similar way, the TOC mineralization rates increased from 0.081 mg/min at 0.34% oxygen to 0.24 mg/min in the presence of air and finally reached the value of 0.47 mg/min in the presence of oxygen. Again, a plateau was reached above 60% oxygen with some indication that the rates continue to increase slightly as oxygen concentration increases.
FIGURE 4. Increase in dissolve oxygen concentration in the RDPR at different disk angular velocities. The RDPR was closed at the top, and it was operated in a batch-mode using distilled water (V0 ) 3.5 L) prepurged with nitrogen until the initial DO in water was close to zero. Fitting of the experimental data using the format of eqs M-9 and M-11 to determine the exponent coefficients Z. (B) Continuous-Mode Operation. The removal efficiencies at steady state for both 4-CBA and TOC are presented in Figure 3. The data show saturation-type dependencies but again there is indication that the rates increase slightly with oxygen concentration. At low oxygen concentrations (0.2521%), the increase in removal efficiencies is high when oxygen concentration is increased. However, as oxygen concentration surpasses 40%, this increase is much lower. Effect of Oxygen Uptake on the Increase of Dissolved Oxygen. Figure 4 (symbols) presents the results for the experiment examining the effect of disk angular velocity on the increase in DO of oxygen-free water after the top cover of the reactor was removed. When the disk was still in the reactor vessel, the DO did not increase noticeably after 18 min. However, even at 2 rpm, the DO started to increase significantly, reaching the value of 4.92 mg/L after 18 min of operation. As the disk angular velocity increased, it was shown that the rate of DO increase was higher. This resulted in reaching the saturation value for DO in a shorter time. At very high disk angular velocity, the DO reached values close to saturation in less than 2 min. Dissolved Oxygen in the Dark and During Photocatalytic Reactions. Comparison of the concentration of dissolved oxygen in the absence and in the presence of photocatalytic reactions is presented in Figure 5. During these two experiments, the disk angular velocity was increased as shown by the solid line. The values obtained for the DO were similar in both experiments with some small variations due to small VOL. 36, NO. 17, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Reaction Rates and Reaction Rate Constant in the Thin Liquid Film Carried by the Rotating Disk as a Function of Different Oxygen Concentration in Gas Phasea
FIGURE 5. Effect of disk angular velocity on the dissolved oxygen in the presence and absence of UV radiation. RDPR operated in a continuous mode and closed at the top at pH ) 3.0, I ) 896 µW/cm2, VR ) 3.5 L, Cin,4-CBA ≈ 310 µmol/L, Qliquid ) 53 mL/min, and [KNO3] ) 10 mM. temperature difference (2-3 °C) between the two experiments. The values for the DO increased slightly as the disk angular velocity increased. This small variation is believed to be mainly associated with the influence of mixing intensity and shear rate on the accuracy of the DO probe. Such small variations were also observed when oxygen saturation was reached at different disk angular velocities, as presented in Figure 4.
Discussion Effect of Oxygen on the Photocatalytic Degradation Rates. Most of the previous studies on the effect of oxygen on the photocatalytic degradation of organic contaminants in water reported a saturation-type dependency resembling the Langmuir equation. In earlier studies conducted in the 1980s, it was reported that oxygen adsorbed in a nondissociated form (note: see another report on cases of O2 dissociation at vacancy sites under certain conditions (16)). The pertinent photocatalytic reaction rates are usually described by the following equations (17-20):
r ) k h(I) f (C) g (CO2) g (CO2) )
KO2CO2 1 + KO2CO2
(5)
(6)
The adsorption coefficient obtained by various researchers ranged from 0.0182 to 1.1 kPa-1 (17, 19, 20). If the data of the x axis of Figure 2 are expressed in kPa, then the KO2 obtained in this work is 0.078 kPa-1, which is in the range of values reported in the literature. The Langmuir-type of dependency of the photocatalytic rates on oxygen concentration, in some cases called as Langmuir-Hinshelwood (L-H) mechanism as in the case of concentration, has been observed by other investigators. Chen and Ray investigated the photocatalytic degradation of 4-nitrophenol (NP) using TiO2 suspensions and reported that the observed reaction rates increase with oxygen partial pressure in the gas phase following noncompetitive Langmuir kinetics (i.e., saturation-type dependency) (21). They noted that the rates in the presence of air were approximately 70% of the maximum value, suggesting that, along with oxygen cost, air may be the best choice for oxygenating the suspension. In the same graph (i.e., Figure 7 of their study), they assumed that the rate in the absence of oxygen was zero. However, a projection of the line created by the next three points of their data gives a positive value for the observed reaction rate constant. The value of KO2 obtained in their study was 9.98 atm-1 (0.099 kPa-1) which is similar 3838
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O2b (% in gas phase)
rfilm (µmol/min/mLfilm)
rfilm (µmol/pass/mLfilm)
kr (µmol min-1 L-1)
0.34 9.44 21.00 41.05 52.85 71.21 86.98 99.28
0.0048 0.0251 0.0313 0.0371 0.0418 0.0432 0.0440 0.0452
0.0016 0.0084 0.0104 0.0124 0.0139 0.0144 0.0147 0.0151
5.946 31.801 39.945 47.638 53.881 55.856 56.887 58.518
a Rates are determined following a procedure presented in ref 38. Baseline conditions: C0 ) 320 µmol/L, pH ) 3.0, [KNO3] ) 10 mM, V0 ) 3.5 L, I ) 332.5 µeinstein/min. b
to the one obtained in this work. Low but positive reaction rates for the anaerobic photocatalytic degradation of 2,4dichlorophenol were also observed (22). These rates were low, even when Cu2+ adsorbed at the surface of TiO2 was used as an alternative electron acceptor. Langmuirian kinetics were also observed for the photocatalytic oxidation of ethylene, trichloroethylene, 4-chlorophenol, and as well as for the quantum yield and the rate constant of hydroxyl radical formation in TiO2 suspensions (18, 23-26). The data obtained for the reaction rates in the absence of oxygen in the gas phase (see Figures 2 and 3 and the correlations obtained therein) suggest that photocatalytic degradation reactions did occur, even in the absence of this electron acceptor. The rates of the reactions in the absence of oxygen, however, were very small. These data support the recent data obtained by Muggli and Falconer for the gasphase photocatalytic degradation of formic acid (6). As explained previously, these authors reported that, in the absence of oxygen in the gas phase, photocatalytic degradation reactions occurred by extraction of oxygen from the crystal lattice. Although such experiments to verify the involvement of lattice oxygen were not performed in our work, it is possible that lattice oxygen from the surface of the ST-B01 ceramic balls could participate in the photocatalytic degradation of 4-CBA. Table 1 shows comparative results for the reaction rate in the thin liquid film expressed as µmol/ min/mLfilm or µmol/pass/mLfilm. Column 4 of Table 1 presents the reaction rate constant in the thin liquid film calculated based on the L-H model. These data show that the reaction rate as well as the reaction rate constant of the photocatalytic reactions in the thin liquid film increase with oxygen concentration in the gas phase. Effect of Oxygen Uptake on the Increase of Dissolved Oxygen. The results presented in Figure 4 indicate that, as the disk angular velocity increases, the initial rate of increase in the dissolved oxygen of initially oxygen-free water increases, most probably due to two reasons. The first is associated with the increase of the amount of water carried by the disk as the disk angular velocity increases (14). As the amount of water carried by the disk increases, then a larger volume of aerated water returns to the reactor vessel causing the DO of the water in the reactor vessel to increase at a higher rate. The second reason may be associated with the increase in the mass-transfer coefficient with increasing disk angular velocity. Discussion of this effect will be given in the following discussion. Dissolved Oxygen in the Dark and During Photocatalytic Reactions. The data in Figure 5 show that similar values for the DO were observed in the presence and absence of UV radiation. Some small differences were observed, most probably due to a temperature difference by 2-3 °C, leading to some variation in the concentration of oxygen at saturation.
Increase in the oxygen concentration during the photocatalytic experiment via water photosplitting was not investigated in this study but is not excluded. Discussion on Mass-Transfer Limitations of Oxygen Transport in the Thin Liquid Film. A mathematical model has been developed to simulate the increase in DO of initially deaerated water in the reactor vessel of the RDPR as a function of disk angular velocity (ω) and time (t). The objectives of modeling this process are (i) to determine the presence or absence of mass-transfer limitations and (ii) to provide a practical method to determine the overall mass-transfer coefficient for this system. The reason behind our approach to determine experimentally the mass-transfer coefficient is the complex geometry of the rotating disk incorporating highly rough surface elements (i.e., partially embedded spherical catalytic balls) protruding from the disk surface. As explained in some of our previous publications (14, 38), the concept of the rotating disk was used in electrochemical applications, chemical vapor deposition, electro-deposition processes, wastewater treatment (i.e., rotating biological contactors), immobilized enzyme reactors, chemical synthesis, and solid dissolution into solvents. However, in most of these studies, previous modeling work focusing on determining mass-transfer coefficients or the hydrodynamics of flow employed disks with smooth surface or with significantly different design configuration. In many other cases, the associated process was completely different (i.e., two immiscible liquids and a solid catalyst). Consequently, in this study a new approach was necessary to determine experimentally the mass-transfer coefficient in the RDPR. The approach followed in this study is based on the analogy of this system with a rotating disk biological contactor (RBC). This is an established wastewater treatment unit process mainly used for the removal of carbonaceous biochemical oxygen demand (27). It is generally composed of a series of rotating disks mounted on a horizontal shaft partially submerged in the wastewater contained in a trough (28). A biomass film grows attached to the disks surface and is responsible for the biodegradation activity. Besides the structural similarities, this is the main resemblance with the RDPR, where the TiO2 catalyst film carries out a similar function. As in any other aerobic system, ensuring an adequate oxygen concentration in the water is a key parameter. Hence, oxygen must be transferred into the water at a rate high enough to avoid the problems derived from oxygen depletion (29). For this reason, multiple studies have been carried out in order to model oxygen transfer in RBCs (28-35). When oxygen consumption by the biofilm is taken out of the equation, the resulting expression can be used to describe oxygen transport in the RDPR. In this case, oxygen is transferred to the bulk solution contained in the reactor vessel both by (i) diffusion into the water film carried on the surface of the disk during its rotation and (ii) diffusion into the free surface of water in the reservoir which is continuously stirred by the disk rotation. In this model, the DO concentration in the tank is represented as CT. The reactor vessel (tank) contains a constant volume of water (VT), with an initial DO concentration of CT0. The disk exposes a certain volume of water to the air and oxygen transfer takes place, resulting in an increase in the concentration of DO in the RDPR. Part 1: Considering Mass-Transfer Limitations During the Oxygenation of the Thin Liquid Film. Mass-Transfer Equation. Because the system is directly exposed to air (i.e., 21% O2) and O2 is sparingly soluble in water (Henry’s law constant, kH ) 10-2.90 mol/atm), the gas-phase resistance can be assumed as negligible. Therefore, the liquid-phase resistance becomes the controlling mechanism of oxygen mass transfer. The oxygen partial pressure at the gas-liquid interface can be assumed to be that in the gas bulk and the
latter can be used to determine the DO of the water at the interface. Hence, the rate of oxygen mass transfer from the gas (atmosphere) to the liquid phase (thin liquid film carried by the disk) is
rO2 ) kLA(C∞ - C)
(M-1)
where rO2 is the oxygen flux from air to water (mg/s), kL is the mass-transfer coefficient (cm/s), A is the effective masstransfer area (cm2), and the term in parentheses (mg/cm3) is the difference between the maximum concentration of oxygen in water (i.e., saturation concentration, C∞, at certain conditions of P and T) and the concentration of oxygen in the thin film at a given time t (C). Elements of the Model. For a rotating disk contactor, the time of exposure of the water to the air is expressed as (35)
tE )
2π - θ 2πN
(M-2)
where tE is the time of exposure (seconds), θ is the angle of submergence, and N is the angular velocity (revolutions per second). The angle θ is the angle formed by the segments taken from the center of the disk to the two points in its circumference that are in contact with the water-free level. It is an index used to determine the portion of the disk that is submerged into the fluid. It can vary from a value of zero when the disk is not submerged (or is tangentially touching the water level) to 2π when it is completely immersed. For this case, half of the disk is submerged; therefore, θ ) π and ω ) 60N (rpm). As a result, eq M-2 is reduced to
tE ) 30/ω
(M-3)
As presented in one of our previous publications (14), the amount of liquid carried by the disk as a function of disk angular velocity is given by the following empirical equation:
Vd ) 134(ω)0.32
(M-4)
where Vd is the liquid carrying capacity of the disk (mL) and ω is the angular velocity (rpm). Therefore, the flow rate (Q) in the disk (oxygenation unit) can be expressed as
Q ) Vd/tE
(M-5)
Design Equations for the Model. (a) Mass balance of O2 in the disk is given by
dCD ) kLa(C∞ - CD) dtD
(M-6)
where CD is the DO concentration along the disk (mg/L), tD is the time during the rotation of water on the disk in the exposed part of the disk, kLa is the overall mass-transfer coefficient of oxygen at the air-water interface, and C∞ is the saturation concentration of oxygen in water. The value of a ()Ad/Vd) represents the effective interfacial area of oxygen transfer per unit volume, where Ad is the total interfacial area on the disk and Vd is the liquid carrying capacity of the disk. (b) Mass balance of O2 in the reactor vessel is given by
QCR - QCT + kwAw(C∞ - CT) )
dCT V dt T
(M-7)
where VT is the volume of water in the reactor vessel, CR is the DO concentration of the water that returns to the reactor vessel, CT is the DO of water in the reactor vessel at time t, kw is the mass-transfer coefficient of oxygen at the air-water VOL. 36, NO. 17, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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interface of the reactor vessel (i.e., direct oxygenation of the reactor vessel), and Aw is the interfacial area between air and water at the free water surface of the reactor vessel. The value of Aw is 133 cm2. For stirring conditions such as those taking place in the RDPR, which cause a constant renewal of water at the free surface, kw can be estimated using the surface-renewal theory (36) according to
kw ) xDs
(M-8)
where D is the diffusion coefficient of oxygen in water (2.5 × 10-5 cm2/s at 25 °C) and s is the fraction of renewal of the water surface (s-1). Metzger and Dobbins (37) provide values of s for different agitation regimes. On the basis of this information, a value higher than the reference for high agitation was chosen as a maximum value for s in order to account for the agitation effect generated by the disk rotation. The results obtained by running the model using different values of s under that limit did not change noticeably. This indicates that the change in the bulk oxygen concentration due to oxygen transfer through the free surface of the tank is not significant for the RDPR operated under the conditions shown in this study. In addition, because the value of Aw is around 2.5% of AT, it is reasonable that most of oxygen transfer is carried out in the disk surface. Thus, for this system, the product kwAw has a negligible impact on eq M-7. By solving eq M-6 for the boundary conditions (a) tD ) 0, CD ) CT and (b) tD ) tE, CD ) CR and replacing the resulting expression in eq M-7, the differential equation that describes the system is obtained
Z(C∞ - CT) )
dCT dt
(M-9) FIGURE 7. Effect of disk angular velocity (ω) on the disk flow rate (Q).
where Z is defined as
Z)
( )
1 [Q(1 - e-kLatE) + kwAw] VT
(M-10)
Solving eq M-9 by integrating CT (between CT0 and CT) and t (between t ) 0 and t ) t) leads to
CT ) C∞ - (C∞ - CT0)e-Zt
(M-11)
Finally, after replacing the expression for Z, eq M-11 takes the final form
CT ) C∞ - (C∞ - CT0) exp [-(1/VT)(Q(1 - e-kLatE) + kwAw)t ] (M-12) Equation M-12 represents the variation of the oxygen concentration in the reactor vessel (DO) as a function of time. Part 2: Assuming Absence of Mass-Transfer Limitations During the Oxygenation of the Thin Liquid Film. Absence of mass-transfer limitations denotes that the water carried by the disk is saturated with oxygen when returning to the reactor vessel. Assuming this condition (i.e., CR ) C∞) and solving eq M-7 for the boundary conditions (a) t ) 0, CT ) CT0 and (b) t ) t, CT ) CT, the following expression is obtained for the concentration of DO in the reactor vessel in the absence of mass transfer:
CT ) C∞ - (C∞ - CT0) e-((Q+kwAw)/VT)t
(M-13)
Part 3: Data Analysis. Figure 4 shows the experimental data and the fitting curves (solid lines) based on the form of eq M-12, which considers mass-transfer limitations. Some small deviation is observed at the smaller disk angular 3840
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FIGURE 6. Effect of disk angular velocity on the exponent coefficient Z.
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 36, NO. 17, 2002
velocities (underprediction at short times and overprediction at longer times). The coefficient Z described in eq M-10 is determined from Figure 4 and is plotted as a function of the disk angular velocity in Figure 6. The data indicate a linear increase of Z in this range of disk angular velocity (0-40 rpm). The results of the disk flow rate as a function of disk angular velocity are presented in Figure 7. This is a nonlinear dependency and the disk flow rate reaches a value of approximately 580 cm3/s at 40 rpm. On the basis of the Z values shown in Figure 6 and the definition of Z as shown in eqs M-10 and M-12, the overall mass-transfer coefficient for oxygen transfer in the liquid film was calculated. The results are presented in Figure 8. Figure 8 shows that the mass-transfer coefficient increases with the disk angular velocity following a linear relationship. The results also reveal that the overall mass-transfer coefficient increases with disk angular velocity following a power law correlation, indicating that, as the amount of liquid carried by the disk increases, oxygenation of the RDPR also increases because a higher fraction of water is oxygenated during the process. Figure 9 presents comparative results at different disk angular velocities for the increase in DO of the deaerated water in the RDPR as a function of time after the removal of the RDPR’s cover. In each of the graphs in Figure 9, the experimental data are compared with the results obtained assuming presence or absence of oxygen masstransfer limitations (eq M-13) during the oxygenation of a thin film of initially oxygen-free water in the RDPR. It is clearly seen that oxygen mass-transfer limitations do exist during the oxygenation of the thin film. The figures show that, at all of the investigated disk angular velocities (0-40 rpm), the thin film is not oxygen-saturated when returning to the reactor vessel. However, as the disk angular velocity increases,
FIGURE 8. Effect of disk angular velocity (ω) on (a) the overall mass-transfer coefficient (kLa) and (b) the mass-transfer coefficient kL. oxygenation of the thin liquid film improves significantly due to a considerable increase in the mass-transfer coefficient. Most of the aforementioned modeling work focused on determining mass-transfer coefficients in systems using disks with smooth surface or with significantly different design configuration (30-35). For those cases, several parts of the analysis are much more simple. The calculation of the value of a is straightforward and is constant for any value of ω. The film thickness (δ) can be estimated (33), and this allows for the use of Higbie’s penetration theory to estimate the values of kL (30, 33, 35) which turns out to be a function of ω0.5. Because a is constant, the overall coefficient (kLa) results to be also a function of ω0.5. According to this model, theoretical and experimental data are supposed to correlate well at high rotational velocities. This is usually the case when the depth of oxygen penetration in the film per disk revolution is much smaller than the film thickness (which is assumed constant over the disk surface). However, this model is not very accurate at medium and low values of ω. Bintanja (31) and Zeevalkink et al. (33) demonstrated that Higbie’s model does not hold for most of the values of ω, and they used more complex equations to estimate kL. The complexity of the problem is even higher when analyzing the RDPR. The irregular disk surface causes Vd to depend on ω, which makes a also a function of ω. Besides, the value of δ cannot be obtained by following the experimental procedures indicated for flat disks, and even more, the assumption of a uniform value of δ throughout the disk is most probably not valid. Therefore, the analysis of kL was carried out based on the observed trend of the experimental data (Z values). The correlation between this parameter and ω is strongly linear (R2 ) 0.99), indicating that the pattern
FIGURE 9. Influence of mass transfer on the dissolved oxygen increase in the RDPR: (a) ω ) 2 rpm, (b) ω ) 10 rpm, and (c) ω ) 40 rpm. of oxygen concentration build-up follows an exponential growth with a maximum determined by the oxygen solubility in water. Analyzing the definition of Z (eq M-10), VT is constant and kwAw is negligible. From the definitions of Q (eq M-5), tE (eq M-3), and Vd (eq M-4), Q is a function of ω1.32. Hence, for Z to be a linear function of ω, the parenthesis containing the exponential term must be a function of ω-0.32. Finally, from the expressions defining a and tE, it turns out that kL must be a linear function of ω. Generally, the mass-transfer coefficient (kL) is a function of the hydrodynamics of the system (31), which are described by the Reynolds number (Re ) d2ωF/µ), modified to consider circular motion. On the VOL. 36, NO. 17, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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the constants were K ) 6.76, m ) 0.89, and n ) 0.06. Then, eq M-14 for this particular system is
Sh ) 6.76Re0.89Fr0.06
FIGURE 10. Sherwood correlation for oxygen mass transfer in the RDPR. basis of the linear relationship of kL versus ω in the graph in Figure 8b and the linear correlation of Re versus ω, the relationship of kL versus Re is also expected to be linear. Regarding the slight model deviations observed at the smaller disk angular velocities (underprediction at short times and overprediction at longer times) shown in Figure 9, parts a and b, this effect is most probably due to two reasons. First, the model considers a constant value of s for each value of ω, which accounts for the turbulence on the free surface of the liquid. However, the initial motion of the disk could cause a higher agitation level, which decreases continuously until reaching the turbulence level represented by s after several minutes and remains constant afterward. This explains the higher oxygen concentrations observed at short times because the contribution from direct oxygenation of the film is small at those times. The graphs in Figure 9 also indicate that the time needed for reaching this constant value of s decrease with increasing value of ω. Second, the overprediction at longer times can be related to the assumption that all of the water film attached to the disk mixes up completely with the liquid bulk after each revolution of the disk. However, Zeevalkink et al. (33) reported that for flat disks only 50-75% of the film was mixed with the bulk water, and additional studies of Rittmann et al. (29) found results closer to the lower value. These studies showed that part of the liquid film stays attached to the disk surface. Although the incorporated disk elements (spheres and wire cage) in the RDPR may cause additional turbulence effects and improve film-bulk water intermixing, they may not achieve complete mixing of the thin liquid film with the bulk water in the reactor vessel. To validate the results obtained from the model, an alternative method of data analysis was used. Because the theoretical approach can be sometimes very complex, depending on the characteristics of the system (30), multiple studies on oxygen transfer based on analysis of dimensionless groups were reportedly used to interpret experimental data from similar systems (32, 34, 35). A comparative analysis of these models pointed to the following correlation (modified in this case for a half-submerged disk) as the one that provided the best fit (35):
Sh ) K Rem Frn
(M-15)
Equation M-15 is an alternative expression describing this system when mass-transfer limitations are considered. The data obtained in this work are very useful for understanding mass-transfer limitations in the RDPR. As was found in another study (38), the reaction rates for 4-CBA degradation did not significantly increase with an increase in disk angular velocity beyond 6-10 rpm. These data are further supported with the increase in the rate of the degradation reactions with an increase in light intensity in photocatalytic experiments performed at 6 rpm (38). Combination of these results suggests the absence of significant mass-transfer problems for the photocatalytic reactions at disk angular velocities higher than a critical value (i.e., 6 rpm). The data reported here for the increase in dissolve oxygen for deaerated water suggest that it takes some time until the solution in the reactor vessel becomes saturated with oxygen. However, when steady-state operation is achieved, this oxygen mass transport process does not limit the rates of photocatalytic reactions, most probably due to the small oxygen consumption during the reaction. As indicated from Figures 2, 3, and 5, the reactions are oxygen concentration-limited rather than oxygen mass-transportlimited. In addition, if we calculate the amount of oxygen (mg/min) that is required to mineralize 4-CBA based on the TOC mineralization rates and consider steady-state process (oxygen consumption equals oxygen mass transport), the concentration of oxygen in the RDPR determined based on eq M-1 will be lower than C∞ at the conditions of the experiment by only 0.1 mg/L. In another publication, we investigated the influence of mass transfer of organic solutes in the RDPR following quantitative analysis which included determination of the ratio of maximum possible reaction rate divided by the maximum possible mass-transfer rate, expressed using the dimensionless Damko¨hler number. In that study which was performed under similar conditions (i.e., light intensity, initial contaminant concentration, and air as the gas phase), it was shown that the reactions were not limited by mass transfer above a critical disk angular velocity (38). These results along with the data obtained in this work suggest that operating the RDPR at a sufficiently high disk angular velocity will eliminate the presence of significant mass-transfer limitations. However, it is important to point out that, in the case of considerably high incident light intensities and much higher reaction rates, oxygen or solute mass transport may be a limiting factor. Consequently, the effect of high incident light intensity on the degradation of organic contaminants coupled with oxygen mass transport from air to the thin liquid film warrants further investigation in the future.
Acknowledgments The authors thank the Center of International Research for Water and the Environment (Centre International de Recherche Sur l’Eau et l’Environnement, CIRSEE) of ONDEO Services for providing funding for the present study.
(M-14)
Nomenclature where Sh is the Sherwood Number, Re is the Reynolds Number, and Fr is the Froude Number. K, m, and n are constants unique for a given system. As shown in Figure 10, regression analysis on the data obtained from the model correlated well using this equation (R2 ) 0.99). This outcome indicates an agreement of the data from the model with the correlation presented by eq M-14. The obtained values for 3842
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Symbols Ad
effective interfacial mass-transfer area (cm2)
Aw
interfacial area between air-water at the free water surface of the reactor vessel (cm2)
CD
dissolved oxygen concentration along the disk (mg/L)
Ceff
concentration of the contaminant in the effluent (mg/L or µmol/L)
C0
initial solute concentration in the reactor vessel (mg/L or µmol/L)
CR
dissolved oxygen concentration of the water that returns to the reactor vessel (mg/L)
CT
oxygen concentration in the reactor vessel at time t (mg/L)
CT0
initial oxygen concentration in the reactor vessel (mg/L)
C∞
saturation concentration of oxygen in water at certain pressure and temperature (mg/L)
d
disk diameter (cm)
Fr
Froude Number ) (ω2d/g)
g
gravity acceleration (981 cm/s2)
I
light intensity (or more precisely radiant flux) (µW/cm2 or µeinstein/min)
K, m, n
constants of the dimensionless model
KO2
oxygen adsorption coefficient on ST-B01 composite ceramic balls (kPa-1)
kL
mass-transfer coefficient (cm/s)
k La
overall mass-transfer coefficient (cm3/s)
kw
mass-transfer coefficient at the air-water interface of the reactor vessel; according to the surface renewal theory (cm/s)
N
disk angular velocity (revolutions/s)
Q
flow rate of the liquid carried by the disk (cm3/ s)
Qgas
gas flow rate (L/min)
Qliquid
liquid flow rate (mL/min)
Re
Reynolds Number ) (d2ωF/µ)
r0
initial reaction rate (µmol min-1)
rO2
oxygen flux from air to water (mg/s)
s
fraction of renewal of the water surface (s-1)
Sh
Sherwood Number ) (kLd/D)
tD
time during the rotation of water on the disk in the exposed part of the disk (s)
tE
average time of exposure of the thin liquid film carried by the disk (s)
Vd
volume of liquid carried by the disk (mL)
V0
initial volume of liquid in the batch reactor or in the reaction vessel of the RDPR (L)
VR
volume of liquid in the reactor vessel during continuous-mode operation of the RDPR (L)
VT
volume of liquid in the reactor vessel during the oxygen transfer experiment (L)
Greek Symbols
F
water density (g/cm3)
µ
water viscosity (g/cm.s)
τ
residence time (min).
ω
disk angular velocity (rpm)
Literature Cited (1) Fox, M. A.; Dulay, M. T. Chem. Rev. 1993, 93, 341-357. (2) Midaka, M.; Kubata, H.; Gra¨tzel, M.; Serpone, N.; Pelizzeti, E. Neuv. J. Chim. 1985, 9, 67. (3) Gerischer, H.; Heller, A. J. Phys. Chem. B 1991, 95, 5261-5267. (4) Mills, A.; Davies, R. H.; Worsley, D. Chem. Soc. Rev. 1993, 22, 417-425. (5) Muggli, D. S.; Falconer, J. L. J. Catal. 1999, 181, 155-159. (6) Muggli, D. S.; Falconer, J. L. J. Catal. 2000, 191, 318-325. (7) Davydov, L.; Smirniotis, P. G. J. Catal. 2000, 191, 105-115. (8) Davydov, L.; Pratsinis, S. E.; Smirniotis, P. G. Environ. Sci. Technol. 2000, 34, 3435-3442. (9) Pelizzetti, E.; Minero, C. Electrochim. Acta 1993, 38, 47-55. (10) Turchi, C. S.; Ollis, D. F. J. Catal. 1990, 122, 178-192. (11) Dionysiou, D. D.; Suidan, M. T.; Bekou, E.; Baudin, I.; Laıˆne´, J.-M. Appl. Catal., B 2000, 26, 153-171. (12) Linsebigler, A. L.; Lu, G. Q.; Yates, J. T. Chem. Rev. 1995, 95, 735-758. (13) Kurtz, R. L.; Stockbauer, R.; Madey, T. E.; Roman, E.; de Segovia, J. L. Surf. Sci. 1989, 218, 178-200. (14) Dionysiou, D. D.; Balasubramanian, G.; Suidan, M. T.; Khodadoust, A. P.; Baudin, I.; Laıˆne´, J.-M. Water Res. 2000, 34, 29272940. (15) Dionysiou, D. D.; Balasubramanian, G.; Suidan, M. T.; Baudin, I.; Laıˆne´, J.-M. In Reaction Engineering for Pollution Prevention; Abraham, M. A., Hesheth, R. P., Eds.; Elsevier: Amsterdam, The Netherlands, 2000; Chapter 12, p 137. (16) Epling, W. S.; Peden, C. H. F.; Henderson, M. A.; Diebold, U. Surf. Sci. 1998, 412/413, 333-343. (17) Auguliaro, V.; Palmisano, L.; Sclafani, A.; Minero, C.; Pelizzetti, E. Toxicol. Environ. Chem. 1988, 16, 89. (18) Mills, A.; Wang, J. J. Photochem. Photobiol., A 1998, 118, 53-63. (19) Okamoto, K.; Yamamoto, Y.; Tanaka, H.; Itaya, A. Bull. Chem. Soc. Jpn. 1985, 58, 2023. (20) Ollis, D. F.; Pelizzetti, E.; Serpone, N. In Photocatalysis: Fundamentals and Applications; Serpone, N., Pelizzetti, E., Eds.; John Wiley and Sons: New York, 1989; pp 603-637. (21) Chen, D.; Ray, A. K. Water Res. 1998, 32, 3223-3234. (22) Zang, L.; Liu, C. Y.; Ren, X. M. J. Chem. Soc., Faraday Trans. 1995, 91, 917-923. (23) Yamazaki, S.; Tanaka, S.; Tsukamoto, H. J. Photochem. Photobiol., A 1999, 121, 55-61. (24) Chun, H.-D.; Park, J. K. Hazard. Waste Hazard. Mater. 1994, 11, 501-510. (25) Schwarz, P. F.; Turro, N. J.; Bossmann, S. H.; Braun, A. M.; Wahab Abdel, A.-M. A.; Du ¨ rr, H. J. Phys. Chem. B 1997, 101, 7127-7134. (26) Sun, L.; Bolton, J. R. J. Phys. Chem. 1996, 100, 4127-4134. (27) Metcalf & Eddy, Inc. Wastewater Engineering; McGraw Hill: New York, 1991. (28) Kim, M. J.; Ghim, Y. S.; Chang, H. N. Chem. Eng. Sci. 1985, 40, 2281-2286. (29) Rittmann, B. E.; Suozzo, R.; Romero, B. R. J. Water Pollut. Control Fed. 1983, 55, 270-277. (30) Yamane, T.; Yoshida, F. J. Chem. Eng. Jpn. Res. 1972, 5, 55-59. (31) Bintanja, H. H. J.; Van der Erve, J. J. V. M.; Boelhouwer, C. Water Res. 1975, 9, 1147-1153. (32) Ouano, E. A. R. Water Res. 1978, 12, 1005-1008. (33) Zeevalkink, J. A.; Kelderman, P.; Visser, D. C.; Boelhouwer, C. Water Res. 1979, 13, 913-919. (34) Boumansour, B. E.; Vasel, J. L. Water Res. 1998, 32, 1049-1058. (35) Ravetkar, D. D.; Kale, D. D. Chem. Eng. Sci. 1981, 36, 399-403. (36) Danckwerts, P. V. AIChE J. 1955, 4, 456-463. (37) Metzger, I.; Dobbins, W. E. Environ. Sci. Technol. 1967, 1, 5765. (38) Dionysiou, D. D.; Suidan, M. T.; Baudin, I.; Laıˆne´ J.-M. Appl. Catal., B 2002, 38, 1-16.
D
diffusivity of oxygen in water (cm2/s)
δ
film thickness (mm)
Received for review October 12, 2001. Revised manuscript received June 5, 2002. Accepted June 5, 2002.
θ
angle of submergence of the disk
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