Ind. Eng. Chem. Res. 2005, 44, 5193-5198
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Photon Absorption in Modified Taylor-Couette Flow: Theory and Experiment L. J. Forney* School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
J. A. Pierson and A. Giorges Electrooptics, Environment, & Materials Laboratory-Food Processing Technology Division, Georgia Tech Research Institute, Atlanta, Georgia 30332
The modified Taylor-Couette device operating at large rotation rates and with UV absorption through the transparent stator has the characteristics of a continuous stirred tank reactor or CSTR. In particular, the modifications include holes in the rotor that produce cavitation at large rotation rates. Experiments with the UV-induced oxidation of iodide I- to triiodate I3- agree well with the trends predicted by a CSTR. For the maximum rotor frequency covered, there were no effects of cavitation alone on the latter chemistry in the absence of UV. Moreover, greater than a two log reduction or 99.4% was observed for active E. coli in water. The inactivation levels of E. coli were reduced to ∼50% with the addition of a water-soluble dye due to photon absorption. The modified Taylor-Couette device in the present study should be particularly useful for applications that require both mass transfer in two-phase flow containing either bubbles or droplets and the simultaneous application of UV. The large shear provided by the cavitating flow at large rotation rates would reduce the bubble or drop size, thus significantly increasing the rate of mass transfer. 1. Introduction Common reactor configurations for bulk chemical production such as specialty organic chemicals are stirred tanks1 or static mixers.2 However, these reactor configurations are not ideal if the adsorption of photons is necessary to either promote photochemical reactions or disinfect liquids. In the present paper, the application of UV to a turbulent Taylor-Couette reactor operating at high rpm is considered. Such Taylor-Couette designs operating with either laminar or turbulent flow provide very large surface-to-volume ratios necessary to increase photon exposure with very small reactor volumes. In the present experiment, the reactor rotor has been modified to include holes that produce continuous hydrodynamic cavitation within the annular gap at large rotation rates.3 Hydrodynamic cavitation has been previously shown to hold potential for large-scale applications in cavitationally assisted chemical and physical transformations.4,5 Applications include cell disruption,6 gas/liquid two phase flows,7 and homogenization and emulsification.8 The rotating design used in the present study is manufactured by Hydro Dynamics Inc. (Rome, GA). The device supplied by Hydro Dynamics Inc. produces hydrodynamic cavitation in large-scale flows as compared to conventional designs such as venturi geometries or orifice plates where the latter have been recently discussed by Kumar et al.5 In the present study, two UV experiments are conducted. In the first, the photolytic production of iodine in the form of triidoide I3- from a solution of potassium * To whom correspondence should be addressed. Tel.: (404) 894-2825. Fax: (404) 385-2713. E-mail: larry.forney@ chbe.gatech.edu.
iodide KI is measured. In the second, the UV inactivation of E. coli is recorded. The procedure is similar to that used in an earlier study which considered a smooth rotor at low rotation rates and with laminar TaylorCouette flow.9,10 In the present experiments, the simultaneous application of UV and cavitation is considered at large rotation rates, that is, at large Reynolds and Taylor numbers, under conditions of continuous flow within the Taylor-Couette design. Such conditions are similar to those found in a continuous stirred tank reactor or CSTR.11 2. Theory 2.1. Taylor Number. Assuming water as the working fluid and a range of rotor frequencies 10 e f e 60 Hz, the Taylor number defined as
Ta )
xRd
Ud ν
(1)
varied over the range 2 × 103 < Ta < 12 × 103 for the device in Figure 1. Here, the rotor radius R ) 7.62 cm, ν ) 1 × 10-6 m2/s is the fluid kinematic viscosity, U is the rotor surface velocity, and the fluid gap width is d ) 0.32 cm. Thus, the device clearly operates in the regime of turbulent Taylor-Couette flow.12 For values of Ta > 103, the torque coefficient Cm is a weak function of the Taylor number where Cm ∝ τo ∝ Ta-0.2 and τo is the wall shear stress. Because the fluid boundary layer (laminar sublayer) thickness is δ ∝ τo-0.5 in fully developed turbulent flow, one concludes that the boundary layer δ is approximately a constant.12 Moreover, for large Ta (f g 10 Hz), the reactor approaches the characteristics of a CSTR.11
10.1021/ie0492698 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/23/2004
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Figure 2. Schematic of the rotor holes. Pv is the vapor pressure of the liquid. Um is the mean velocity within the fluid gap. Rv is the radius of the cavitation layer within the holes on the rotor. Pr and Ps are the static pressure at the rotor and stator surface, respectively.
Figure 1. Schematic of Taylor-Couette flow. R ) 7.62 cm is the rotor radius, d ) 0.318 cm is the fluid gap width, ω is the rotor angular velocity, and U is the rotor surface velocity.
2.2. Cavitation Number. The cavitation number is a dimensionless number defined as
Cv )
Ps - Pv 1/2FU2
(2)
where in most circumstances the vapor pressure of the liquid Pv , Ps, where Ps is the fluid static pressure and F is the fluid density.5 In the present experiments, the static pressure of the water was fixed at 20 psig which provides a range of cavitation numbers 0.61 < Cv < 20.4 for the experimental values of the rotation rate from 60 to 10 Hz. 2.3. Absorbed Gases. The penetration of UV radiation into the fluid from the stator wall is necessary to promote photochemical reactions. Accurate prediction of the photon penetration depth is possible if microbubbles formed from the cavitation process are absent in the fluid annular gap, in particular, near the stator wall. In the present experiment, water is subjected to maximum pressures of ∼35 psia at the stator wall and temperatures of ∼48 °C that are higher than standard conditions for the maximum rotation rate of 60 Hz and the minimum water flow rate of 0.5 L/min. For example, at 60 Hz, the static pressure decreases from a maximum pressure of ∼35 psia at the stator wall to the water vapor pressure of ∼1 psia at the cavitation layer shown in Figure 2. Saturated conditions for air are a solubility ratio (mass) of Sa ) ma/mw of 3.1 at a temperature of 48 °C and 35 psia compared to Sa ) 1.71 at 23 °C and 1 atm. Under these circumstances, Henry’s law states that gasfilled microbubbles present in a subsaturated liquid would dissolve. Another potential problem is heterogeneous nucleation at the stator wall. Microbubbles present at the solid-liquid interface are also assumed to be dissolved in the present subsaturated conditions.14 2.4. CSTR. Because the Taylor numbers Ta > 103 for the experiment are large, one assumes a continuous stirred tank reactor (CSTR). Thus, a material balance
for a reaction that is first order with respect to both the concentration of reactant and the photon intensity can be written in a simplified form
(Co - C)q )
∫KCI(r) dV
(3)
where q is the volume flow rate, K is the rate constant (cm2/mJ), Co is the inlet concentration, V is the reactor volume, I(r) is the radiation intensity I/Io ) exp[-E(R + d - r)], E is proportional to the fluid absorbance described below and in section 2.6, and r is the radius measured from the center of the rotor. Also, the concentration C is assumed to be constant along a radius within the reactor.15 The latter assumption is a simplification because the concentration C would vary near the surface boundary through which the radiation is passing. Integrating eq 3, one obtains
1 C ) Co 1 + KImτ
(4)
where τ ) V/q is the fluid residence time. The average radiation flux Im was approximated by the expression
Im )
Io (1 - e-Ed) Ed
(5)
where the latter expression was obtained by neglecting the effects of curvature in the narrow annular gap.16 In eq 5, E ) 2.3A, where A is the absorbance of the fluid and Io is the initial radiation intensity at the inside diameter of the stator as the photons enter the fluid. To account for the variation in C with radius, that is, the distance from the surface of the reactor or stator, eq 4 has been modified to
C 1 ) Co 1 + βImτ
(6)
where β ∝ K/δ and δ is the boundary layer thickness next to the stator.10,16 Some of the experimental results for the inactivation of E. coli were conducted at low flow rates of 0.5 L/min. Under these conditions, the maximum increase in fluid temperature was 25 °C at the maximum rotation rates of f ) 60 Hz due to cavitation. To include the possible
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 5195 Table 1. Photon Penetration Depth for KI (λ ) 254 nm) Co(KI) [M]
Co(KIO3) [M]
l [M]
E [m-1]
Ed
0.03 0.15 0.30
0.005 0.025 0.05
0.1 0.02 0.01
2300 11 500 23 000
7.3 36.5 73
thermal effects on the inactivation of E. coli, eq 3 can be modified to the form
(No - N)q )
∫{KNI(r) + N/D(T)} dV
(7)
where 1/D(T) is the rate constant due to thermal effects, N is the number density of the pathogens, and K is the rate constant for pathogen inactivation.15 Thus, the concentration of pathogens becomes
N 1 ) No [1 + βIm + 1/D(T)]τ
(8)
where β ∝ K/δ as described previously for eq 6. 2.5. Rate Constants. In the experiments for the oxidation of iodide I- to triiodide I3-, the rate constant K in eq 6 was assumed to be proportional to the quantum efficiency φ for the absorption of photons at 254 nm wavelength. In this case, K ∝ φ/R, where variations in φ were accounted for from the recent work of Rahn et al.17 and the conversion factor from photons to energy is R ) 4.72 × 105 J/mol photons. In the present experiment, a value of φ ) 0.75 mol triiodide/mol photons was used for an initial concentration of Co(KI) ) 0.3 M, φ ) 0.73 for Co(KI) ) 0.15 M, and φ ) 0.56 for Co(KI) ) 0.03 M. In the experiments for the inactivation of E. coli, the value of the constant K ) 0.89 cm2/mJ due to photon absorption was assumed from the work of Severin et al.15 Independent measurements of the rate constant 1/D(T) for inactivation due to thermal effects were also conducted in the present study for E. coli in a batch reactor consisting of a 10 mL test tube submerged in a heating bath. The surviving E. coli fraction N/No ) 8.3 × 10-2 was determined for a time period of 60 s at T ) 51 °C. Substituting into the expression for a batch reactor18
N/No ) 10-t/D
(9)
one finds that the time constant D ) 0.926 min or that the maximum expected reduction in viable pathogens is N/No ) 0.82 within the reactor fluid gap for the low flow rate of q ) 0.5 L/min. 2.6. Absorbance. The molar absorption coefficient ) 333 M-1 cm-1 for a mixture of 0.6 M KI and 0.1 M KIO3 was recently measured.19 These values provide an absorbance for the mixture of A ) 200 in a standard 1 cm path length depth of the UV photons. For 10% transmission where A ) Cl ) 1.0, the path length l is then determined from the expression 0.1 ) exp(-El), where E ) 2.3A. In Table 1 below are the initial concentrations of Co(KI), the path length (cm) for 10% transmission, E (m-1), and the product Ed that appears in the photon expression in eq 5. The photon penetration depth was shortened for two tests of E. coli inactivation. A commercial food coloring solution was added to water to provide a photon penetration depth of l ) 0.09 cm. In this case, exp(-El) ) 0.1 for 10% transmission or E ) 2555 m-1. 3. Experiment 3.1. Reactor Geometry. The reactor consisted of a rotor of radius R ) 7.62 cm with a gap width d ) 0.318
Figure 3. Triiodide absorbance versus rotor frequency.
cm as shown in Figures 1 and 2. The frequency of rotation for the rotor in the present study varied from 0 e f e 60 Hz. The rotor length in the axial direction was 2.54 cm with two rows of holes 0.95 cm in diameter and 2.5 cm in length separated by 1 cm around the circumference of the rotor. For these dimensions and rotor frequencies f > 10 Hz, the Taylor number covered the range of values from 2000 e Ta e 12 000 and is turbulent with a torque coefficient Cm ≈ 0.004.12 The volume of water contained within the annular gap exclusive of the holes was estimated to be 39.4 mL. For the two flow rates used in the present study of 1.5 and 0.5 L/min, the fluid residence time was 1.63 and 4.9 s, respectively. The stator in Figures 1 and 2 was quartz with a wall thickness of 1.9 cm. Four medium-pressure UV lamps with an individual photon wattage at 1 m of 42 µW/cm2 were placed outside the stator under a reflective aluminum shield. With an assumed 20% loss of photons, the UV intensity at the stator i.d. was estimated to be approximately Io ) 107 mW/cm2 entering the fluid gap. 3.2. Iodide-Iodate. Three iodide-iodate solutions listed in Table 1 were exposed to UV radiation from the four lamps described above. The flow rates were fixed at ∼1.5 L/min for these experiments. The triiodide concentrations were recorded for values of rotor frequency 0 e f e 60 Hz for each of the three solutions of KI listed in Table 1, and the results are shown in Figure 3. Levels of triiodide concentration were recorded with a spectrophotometer at a wavelength of λ ) 350 nm. A value of the molar extinction coefficient of ) 26 400 M-1 cm-1 for a 1 cm path length cell was used to determine the I3- concentrations described in the Results and Discussion section.19 3.3. E. coli. Solutions containing concentrations of ∼6 × 104 cfu/mL of the indicator organism E. coli were pumped through the reactor. Tests were conducted at two flow rates of water of 0.5 and 1.5 L/min. One test at 1.5 L/min contained a water-soluble dye such that the penetration depth of the photons was l ) 0.09 cm and the absorption coefficient of E ) 2555 m-1. Organism survival was measured for three conditions shown in Figure 4 over a range of frequencies from 0 e f e 60 Hz in increments of 10 Hz.
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Figure 4. E. coli inactivation versus rotor frequency. Figure 6. Normalized triiodide concentration versus normalized UV dosage. Table 2. Parameters for the Formation of Triiodide with a Frequency of Rotation of f g 10 Hz Co(KI) [M]
C(I3-) [M]
0.03 0.15 0.30
1.76 × 10-5 2.67 × 10-5 3.19 × 10-5
8/
-)/C
3C(I3
o(KI)
1.56 × 10-3 0.47 × 10-3 0.28 × 10-3
β
βImτ
0.75 × 10-4 0.96 × 10-4 1.0 × 10-4
1.76 × 10-3 4.51 × 10-4 2.34 × 10-4
Table 3. Parameters for the Formation of Triiodide with No Rotation of f ) 0 Hz Co(KI) [M] 0.03 0.15 0.30
Figure 5. E. coli inactivation versus fluid absorbance and flow rate.
The data of Figure 4 were replotted versus the dimensional parameter 1/Edq in Figure 5. The first three sets of data in Figure 5 cover the range of rotor frequencies 0 e f e 60 Hz with all four lamps of UV radiation. For the data with dye, the parameter Ed ) 9.45; otherwise, it was assumed that the dimensionless quantity was proportional to the absorbance Ed ) 1.0. Also included in Figure 5 are data with no UV (top curve) and data with UV but at zero frequency (bottom curve). It is apparent from Figure 5 that cavitation in the absence of UV does remove ∼90% of the E. coli. Including UV, the inactivation rate increases to greater than a two log reduction or 99.4%. However, the best condition for the data plotted in increments of 10 Hz over the range of 0 e f e 10 Hz is the application of UV with no cavitation or f ) 0, which corresponds to plug flow conditions with relatively large boundary layers. Thus, additional data but between the frequencies of 0 e f e 10 Hz were taken covering laminar TaylorCouette flow, and these data are presented in Figure 8 and discussed in section 4, Results and Discussion.
C(I3-) [M] 10-5
1.08 × 1.21 × 10-5 1.3 × 10-5
8/
-)/C
3C(I3
o(KI)
9.58 × 10-4 2.2 × 10-4 1.14 × 10-4
βImτ 8.78 × 10-4 2.26 × 10-4 1.15 × 10-4
at a flow rate of ∼1.5 L/min, providing a residence time for radiation exposure of τ ) 1.6 s. For each of the three KI concentrations, a range of discrete rotor frequencies 0 e f e 60 Hz was covered, and solution samples were taken at each of the seven rotation rates. A sample was also taken at f ) 60 Hz with no UV lamps to determine if cavitation was creating triiodide. The parameters for the rotating experiments are listed in Table 2. The proportionality factor for the photon energy flux β ∝ φ/δ is listed where φ is the quantum efficiency and δ is the turbulent boundary layer thickness. The latter value of δ is assumed constant in the present turbulent experiments. Also indicated in Table 2 is the mean photon energy flux Im across the annular fluid gap given by eq 5, including the extinction coefficient listed in Table 1. The normalized triiodide concentrations versus the photon energy flux are plotted in Figure 6 for the case Ta > 1000. The parameters for the stationary rotor experiments or f ) 0 Hz are listed in Table 3. Because the factor β ∝ 1/δ, the laminar boundary layer thickness δ was assumed to be twice its value for conditions of rotation or β is reduced to 50% of the values listed in Table 2. The form of the ordinate of Figure 6 was chosen from the stoichiometry of the net reaction for the UV-induced production of triiodide I3-. The net reaction from Rahn19 is
4. Results and Discussion 4.1. Iodide-Iodate. Three iodide-iodate solutions detailed in Table 1 were pumped through the UV reactor
8KI + KIO3 + 3H2O + hν f 3I3- + 6OH- + 9K+ (10)
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Figure 7. E. coli inactivation versus normalized UV dosage.
Figure 8. E. coli inactivation versus Taylor number.
Thus, for every mole of KI consumed by the photolytic reaction, there are 3/8 mol of triiodide I3- formed. Rearranging eq 6, one obtains the fractional moles of KI consumed in the form 1 - C(KI)/Co(KI) or
no rotation. Under these conditions, the reactor is operating at nearly ideal plug flow.
C(KI) βImτ 1) Co(KI) 1 + βImτ
(11)
or from eq 11 one obtains βImτ 8 C(I3 ) ) 3 Co(KI) 1 + βImτ
(12)
for a CSTR. The latter result is represented by the dashed line in Figure 6, which correlates the KI data. 4.2. E. coli. Experimental data for the UV induced inactivation of E. coli are plotted in Figure 7. The range of rotor frequencies for each set of data is 10 e f e 60 Hz. Also plotted in Figure 7 is eq 8 representing a CSTR. Here, the value of β ) 0.09 was chosen for a good fit to the theory, and thermal effects have been neglected. It should be noted from eq 8 for a CSTR that it would be difficult to achieve complete elimination of the E. coli because the functional form of the pathogen survival level is N/No ∝ 1/βImτ for large βImτ . 1.0. The latter result is in contrast to a plug flow reactor, where N/No ) exp(-βImτ). For example, if one has a relative small value of the parameter βImτ ) 2.0, the pathogen survival level is only N/No ) 50% for a CSTR, but for plug flow the survival level drops to N/No ) 13%. Additional inactivation data were taken for the low flow rate case q ) 0.5 L/min. The data were taken at the low frequencies of f ) 1.0 and 3.0 Hz. The latter two measurements correspond to values of Ta ) 225 and 675, respectively. Including the point with zero rotation or Ta ) 0, the three data points on the left of Figure 8 correspond to laminar plug flow conditions. The two data points on the right of Figure 8, in contrast, correspond to turbulent conditions at large Taylor numbers such that the reactor characteristics approach that of a CSTR. In the latter case, the residence time distribution RTD broadens, and some of the organisms pass directly through the reactor with reduced exposure to radiation. Consistent with earlier measurements with laminar Taylor-Couette flows,10 the optimum inactivation occurs at a Taylor number Ta ≈ 100 where the laminar boundary layer is thin relative to the case of
5. Conclusions The modified Taylor-Couette device operating at large rotation rates or f g 10 Hz and with UV absorption through the transparent stator has the characteristics of a continuous stirred tank reactor or a CSTR. In particular, the modifications consisted of holes in the rotor that induced cavitation near the fluid gap at large rotation rates. Experiments with the UV-induced oxidation of KI to triiodate I3- agree well with the trends predicted by a CSTR. For a rotor frequency of f ) 60 Hz, there were no effects of cavitation alone on the latter chemistry in the absence of UV. Inactivation rates of E. coli, however, were observed at f ) 60 Hz with only cavitation and no application of UV. In particular, a one log reduction resulted or 90% of E. coli was inactivated at f ) 60 Hz in water in the absence of UV. Earlier calculations in section 2.5 indicate that the fluid residence time within the annular gap was not great enough to account for these observations due to thermal effects alone. Either the fluid shear due to cavitation or the thermal effects within the sample tubing downstream from the reactor could account for the observed one log reduction. With UV applied over the range of rotor frequencies from 10 e f e 60 Hz, however, greater than a two log reduction was observed or 99.4% of active E. coli in water. Moreover, addition of a water-soluble dye reduced the photon penetration depth and thus the inactivation levels to ∼50% for all rotation rates or 10 e f e 60 Hz. The optimum inactivation rates, however, were achieved at a rotor frequency f ) 1 Hz corresponding to laminar plug flow with Taylor vortices but without cavitation. The rotating device in the present study should be particularly useful for applications that require both mass transfer in two-phase flow containing either bubbles or droplets and the simultaneous application of UV. The large shear provided by the cavitating flow at large rotation rates would reduce the bubble or drop size, thus significantly increasing the rate of mass transfer. Applications include the promotion of photolytic reactions or the inactivation of microorganisms. In the latter case, one useful example would include the
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simultaneous introduction of ozone with UV for the inactivation of pathogens.20 Acknowledgment We acknowledge support from the Georgia Tech Research Institute (J.A.P. and A.G.) and Georgia Research Alliance Grant GRA.IG04.400C (L.J.F.). Literature Cited (1) Paul, E. L. Design of Reaction Systems for Specialty Organic Chemicals. Chem. Eng. Sci. 1988, 43, 1773. (2) Brechtelsbauer, C.; Ricard, F. Reaction engineering evaluation and utilization of static mixer technology for the synthesis of pharmaceuticals. Org. Process Res. Dev. 2001, 5, 646. (3) Forney, L. J.; Ye, Z.; Kazem, B. Fast Competitive Reactions in Taylor-Couette Flow; Hydro Dynamics Inc.: Rome, GA (www.hydrodynamics.com). (4) Suslick, K. S.; Millan, M. M.; Reis, J. T. Chemistry induced by hydrodynamic cavitation. J. Am. Chem. Soc. 1997, 119, 9303. (5) Kumar, P. S.; Kumar, M. S.; Pandit, A. B. Experimental quantification of chemical effects of hydrodynamic cavitation. Chem. Eng. Sci. 2000, 55, 1633. (6) Save, S. S.; Pandit, A. B.; Joshi, J. B. Use of hydrodynamic cavitation for large scale cell disruption. Chem. Eng. Sci. 1997, 75, 41. (7) Moholkar, V. S.; Pandit, A. B. Bubble behavior in hydrodynamic cavitation: effect of turbulence. AIChE J. 1997, 43, 1641. (8) Pandit, A. B.; Joshi, J. B. Hydrolysis of fatty oils: effect of cavitation. Chem. Eng. Sci. 1993, 48, 3440. (9) Forney, L. J.; Pierson, J. A. Photolylic reactors: similitude in Taylor-Couette and channel flows. AIChE J. 2003, 49, 1285.
(10) Forney, L. J.; Goodridge, C. F.; Pierson, J. A. Ultraviolet disinfection: similitude in Taylor-Couette and channel flow. Environ. Sci. Technol. 2003, 37, 5015. (11) Forney, L. J.; Skelland, A. H. P.; Morris, J. F.; Holl, R. A. Taylor vortex column: large shear for liquid-liquid extraction. Sep. Sci. Technol. 2002, 37, 2967. (12) Schlichting, H. Boundary Layer Theory, 7th ed.; McGrawHill Book Co.: New York, 1979. (13) Derwent Water Systems Ltd. (Matlock, U.K.; www.engineeringtoolbox.com, 2004). (14) Leighton, T. G. The Acoustic Bubble; Academic Press: San Diego, CA, 1994. (15) Severin, B. F.; Suidan, M. T.; Rittmann, B. E.; Engelbrecht, R. S. Inactivation kinetics in a flow-through UV reactor. J. Water Pollut. Control Fed. 1984, 56, 164. (16) Forney, L. J.; Pierson, J. A.; Ye, Z. Juice Irradiation with Taylor-Couette Flow: UV Inactivation of E. coli. J. Food Prot. 2004, 67, No 11. (17) Rahn, R. O.; Mihaela, I. S.; Bolton, J. R.; Goren, E.; Shaw, P.; Lykke, K. R. Quantum Yield of the Iodide-Iodate Chemical Actinometer: Dependence on Wavelength and Concentration. Photochem. Photobiol. 2003, 78, 146. (18) U.S. FDA. Kinetics of microbial inactivation for alternative food processing technologies. Center for Food Safety and Applied Nutrition, 2000. (19) Rahn, R. O. Potassium iodide as a chemical actinometer for 254 nm radiation: use of iodate as an electron scavenger. Photochem. Photobiol. 1997, 66, 450. (20) Lenntech (Delft, The Netherlands;
[email protected], 2004).
Received for review August 11, 2004 Revised manuscript received September 23, 2004 Accepted September 29, 2004 IE0492698
