E. coli Inactivation Kinetics Modeling in a Taylor-Couette UV Disinfection Reactor

Posgrado en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Campus Chamilpa, 62209 Cuernavaca, Morelos, Mexico Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Campus Chamilpa, Cuernavaca, Morelos 62209, Mexico Instituto de Biotecnología, UNAM, Av. Universidad 1001, Campus Morelos, 62209, Mexico


Introduction
In recent years, UV light exposure has been recognized as one of the best available options for water treatment [1,2]. However, the design of a reliable UV disinfection system should take into account several factors [3,4], such as germicidal effect, sensor, water quality, UV reflection, and divergence. The microbial inactivation prediction is a useful tool because it provides guidance to assess the efficiency of UV disinfection systems. The survival behavior of microorganisms subjected to UV disinfection may obey different kinetic models [4][5][6][7][8][9]. However, for a long time, it was documented that, under certain experimental conditions, the survival behavior of the microorganisms subjected to UV disinfection may obey a simple exponential curve [10]. Indeed, in the absence of shoulder effects or in the case that they can be ignored, the UV inactivation of microorganisms can be fitted to a first-order decay rate [4,8,11]: where N is the initial microbial concentration, N t is the microbial concentration after contact time t, UV dose is the fluence (mW s cm -2 ), and k is the inactivation rate constant (cm 2 mW -1 s -1 ). However, if some deviation from the exponential law is noticed, UV inactivation of microorganisms must be interpreted by a more complex inactivation kinetics model [6,[12][13][14]. Although equation (1) looks simple, the prediction/modeling of a practical microorganism inactivation behavior based in such equation is a challenging task. Indeed, the parameter UV dose may be defined as where UV flux is the radiant power (W), t is the exposure time (s), and radiating surface is in cm 2 . Although some protocols for determining the UV dose were developed for low-pressure mercury vapor lamps (LP UV) [3,[15][16][17], it is difficult to select a UV dose value that can inactivate a given microorganism under different experimental conditions. Indeed, the presence of a set of attenuation/expansion factors affects exposure time and UV flux ; therefore, the UV dose is affected [18]. If one of the main attenuation/expansion factors is systematically changed while the rest are kept constant, its contribution to the UV inactivation process can be evaluated by the inactivation rate constant (k). Indeed, this parameter can be evaluated from experimental data and its interpretation is strongly related to the sensitivity of microorganisms to the UV dose . The best set of experimental conditions during UV disinfection can be identified taking into account the numerical value of k. Surely, a high k value is always associated to one or more good combinations of the components of equation (2). This criterion can be illustrated by a couple of examples: Firstly, the inactivation profiles of four different microbial species were obtained at the same wavelength as a function of the UV-LED exposure time. It was found that E. coli was the more sensitive species because its k was the highest obtained value [19]. Secondly, it was found that k (evaluated from fluence inactivation response of B. subtilis spores) is not altered by the flow rate (10.8 to 7.8 mL min -1 ). However, the k value increased when the disinfection experiment was repeated in a static test [20].
In the absence of shoulder effects, the kinetics of microbial inactivation is a function of UV dose and it might be described by equation (1). However, due to the set of attenuation/expansion factors, such equation fails to describe the experimental inactivation of microorganisms during UV irradiation. Such phenomenon has been noticed for a long time. As an example, it can be mentioned that a commercial UV water purifier was used to inactivate E. coli (obeying an apparent first-order decay rate) at different flow rates [21]. The highest percent kill was achieved at the lowest flow rate (0.03 mL min -1 ). However, if the fluid pattern is modified to force all water closer to the UV lamp, the percent kill at the fastest flow rate (1.92 mL min -1 ) was raised. Since then, it was understood that the flow field and reactor geometry are linked to the UV disinfection systems [20,22]. Depending on the reactor design, batch/flow-through reactors may develop flow conditions, at low or high flow rates, leading to water volumes of lower UV radiation. Additionally, the spatial distribution of microorganism concentration is also linked to the fluid pattern. A proper simulation/prediction of the UV dose implies the combination/integration of several models that describe the fluence rate, flow pattern, and kinetics of microbial inactivation. During the past decades, several models have been developed to predict UV disinfection systems, and such models evolved from a fairly limited approach to models that globally include complex UV systems. In the first case, a model was used to predict the radiation intensity field [23] and another model was focused on the inactivation behavior of microorganisms [24] in UV reactors; similarly, using computational fluid dynamics (CFD), a radiation model was developed to improve the fluence rate distribution in an annular UV reactor [25]. In the second case, two or more models were combined to simulate a more complex UV microbial inactivation. Under this approach, experimental radiation profile data were used to derive a radiation distribution model. This model was then combined with the CFD software to predict the fluence rate distribution within the reactor [26]. In fact, when the prediction of UV microbial inactivation includes the hydrodynamics of the UV reactor, CFD is a powerful tool for describing the fluid pattern. The simulation of UV disinfection in an open channel configuration [27] was performed using a combination of four mathematical models (hydrodynamic pattern, intensity field, dose distribution, and inactivation kinetics) fed with several experimental data sets (collimated beam, Doppler laser velocimetry, UV transmittance, and UV output power). The design of the UV reactor (including the water inlet/outlet) and the position and distribution of the UV lamps located inside the reactor modify the fluid pattern and can be described by CFD [28,29]. Therefore, the UV dose within a reactor depends largely on the accuracy to numerically describe the turbulent structures developed based on the geometry of the UV reactor [30][31][32][33]. With the growing technique of LP UV disinfection for water treatment, the interest of modeling and after predicting the inactivation behavior of microorganism is justified.
The aim of this work is to improve and predict the kinetics of microbial inactivation by the LP UV disinfection technique. The survival behavior of the microorganisms subjected to UV disinfection in a Taylor-Couette reactor is systematically studied according to the fluid pattern. The set of experimental results obtained are used to develop a simple model (using a minimum number of parameters) that combines the kinetics of microbial inactivation (equation (1)) with the numerical description of the fluid pattern to predict the experimental inactivation kinetics of E. coli in a Taylor-Couette UV disinfection reactor. However, the microbial inactivation kinetics model and the numerical description of the fluid pattern model are carried out separately, which provides a simple model to predict UV disinfection. This approach offers greater flexibility for discussions of results and interpretations. The simulated UV response kinetics in E. coli based on its concentration and the hydrodynamic pattern when a Taylor-Couette vortex was absent and then formed, are included in this work. In both cases ( Taylor   2 International Journal of Photoenergy vortex is present/absent), the simulation of UV disinfection showed good agreement with the experimental results.

Specifications of the UV Disinfection Reactor.
A schematic configuration of the Taylor-Couette UV disinfection reactor is depicted in Figure 1. Both cylinders were made of Pyrex glass with the same length (17 cm

Fluid Dynamics
Modelling. The numerical description of the fluid pattern inside the Taylor-Couette UV disinfection reactor was performed by a commercial CFD package (Fluent, Ansys version 15) based on a finite volume method.
The fluid flow can be described considering the conservation of mass, momentum, and energy. However, considering some practical restrictions, the fluid pattern can be described simply by simultaneously solving mass and momentum conservation equations, as described in more detail elsewhere [34]. The stagnant fluid contained between two coaxial cylinders generates a set of counterrotating vortices in the annular gap when the inner cylinder rotates. The effects of this turbulence can be further described by turbulence models that can be solved alongside the set of mass and momentum conservation equations. Nowadays, CFD packages include a set of turbulent models to better describe a turbulent fluid flow.
The selection of the best turbulence model depends on the nature of the hydrodynamic problem to be solved, the level of accuracy required, and user expertise [30]. In this work, the normalization-group model (RNG) was selected to describe the development of the fluid pattern as a function of the rotating speed of the internal cylinder. The accuracy of the numerical solution depends on the cell number (thin or rough grid) of the computational domain (the reactor annular gap). Several simulations were performed to find out the grid dependency of the results. A set of four different cell numbers (2:5 × 10 5 , 5 × 10 5 , 1:0 × 10 6 , and 1:5 × 10 6 ) were investigated. Finally, the computational domain is discretized in 505,164 hexahedral cells (the convergence index of the grid was 0.205%) in whose center the equations are solved. Once the boundary conditions for a particular cell center are established, the solution is applied to the cell boundaries by interpolation. The information obtained is used to advance stepwise to the neighboring cell until the entire domain is covered. The boundary conditions were defined as inlet conditions according to the inner cylinder rotating velocity (0, 300, 600, 1200, and 2000 rpm) and the physical properties of the fluid (density: 998.2 kg m -3 ; cinematic viscosity: 1:01 × 10 −6 m 2 s -1 ; dynamic viscosity: 0.001 kg m -1 s -1 ; and temperature: 25°C).

Modeling of Survival
Curves. In our approach, microorganisms were considered as soluble species reacting; therefore, they are transported in the UV reactor throughout a spatial distribution described by the fluid velocity profile (Eulerian approach) [35,36]. The parameters that were not directly evaluated in this work are UV intensity, UV fluence rate, UV fluence received by particles, and reflective and diffuse fraction of the Pyrex glass walls. All of them were taken as unknown constant values. However, their important contribution to the UV microbial inactivation kinetics was experimentally evaluated by the inactivation rate constant. Except in the first 100 minutes, the microbial inactivation kinetics follows an apparent first-order kinetic equation and 3 International Journal of Photoenergy can be adjusted to equation (1). In this model, N is a constant but does not represent the initial microbial concentration (such constant has no physical meaning in the studied experimentation). However, the rest of the parameters in equation (1) kept the same meaning described before. All the experiments were repeated three times and then averaged. For a given bacteria concentration, four microbial inactivation curves (log ðN t /NÞ vs. exposure time) were obtained in the Taylor-Couette UV disinfection reactor, as a function of the Taylor number (Ta). From each microbial inactivation curve, a pair of N and k values were obtained. For a given bacteria concentration, k values can be correlated to the Ta number (the hydrodynamic pattern describing the Taylor-Couette vortex) expressed as a polynomial equation. Inside of the experimental conditions studied, a k value can be obtained for an unknown Ta number by the polynomial equation. Therefore, a microbial inactivation simulation curve can be obtained when time starts to increase in equation (1). Similar correlations were used to develop simple chemical models for predicting wastewater treatment [37][38][39].

Results and Discussion
3.1. Numerical Description of Taylor-Couette Vortex. The fluid contained in the annular gap of two coaxial cylinders presents instability when the inner cylinder rotates. Instability produces a series of counterrotating vortices throughout the annular gap. The vortices move the flow of the fluid into and out of the best-lit region of the reactor, creating a highly effective radial mixing within the Taylor-Couette vortex. Between vortices, the hydraulic boundaries form a mass transfer barrier that minimizes the exchange of fluid elements between them [40] and improves the kinetics of microbial inactivation, which is one of the objectives of this work.
The residence time of the bacteria near the UV lamp is, therefore, a function of both, the vortex size and its angular velocity (mainly, axial linear velocities, y-direction and radial linear velocities, and x-direction). Without axial flow, the fluid pattern is a function of the Ta number defined as follows [40][41][42]: where r i is the inner cylinder radius (cm), d is the gap width between two concentric cylinders (cm), ω i is the angular velocity of the inner cylinder (s -1 ), and ν is the kinematic viscosity (cm 2 s -1 ). When the Ta number exceeds a critical value, Ta C (this numerical value depends on d/r i ), the counterrotating toroidal vortices along the cylinder axis develop, describing five modes of flow along the annular gap [41,42]: (1) Laminar flow Ta < Ta C (2) Laminar vortex (individually periodic) flow Ta C < Ta < 800 The maximum average linear velocity was evaluated as 3:4 × 10 −3 m s -1 (Figure 3). As the angular velocity gradually increases, the resulting toroidal vortices increase in both size and linear velocity. As Ta increases, a smaller number of counterrotating toroidal vortices formed along the length of the reactor, in the annular gap. For the angular velocity of 95.5 rpm (Ta = 1309), 18 vortices were well formed with 1.29e -3 1.16e-3 1.03e -3 9.00e -4 7.72e -4 6.43e -4 5.15e -4 3.86e -4 2.57e -4  (Ta = 27,437), the rotating toroidal vortex number further decreased to 13 and 10, respectively, while their maximum average linear velocities increased to 3:1 × 10 −1 m s -1 and 5:7 × 10 −1 m s -1 , respectively. In addition, for the highest angular velocity studied, at the ends of the reactor length, the vortex size increased dramatically in the annular gap, while at the center of the reactor length, the toroidal shape of the vortex begins to gradually be lost in the annular gap ( Figure 5). This last phenomenon can negatively impact the kinetics of microbial inactivation. Figure 6 shows the axial velocities, evaluated in the middle of a toroidal vortex height, as a function of the annular gap distance (x-direction, from 0 to 0.01 m) at different angular velocities. The location of the observation point, 9.78e -2 8.80e -2 7.82e -2 6.84e -2 5.86e -2 4.89e -2 3.91e -2 2.93e -2 1.95e -2 9.72e -3 -5.93e -5 -9.84e -3

International Journal of Photoenergy
OP (from which the axial velocities were numerically evaluated), was set at the top of the reactor at 0.14 m (y-direction, Figure 1) at 300 rpm. For the last three angular velocities (600, 1200, and 2000 rpm), the OP was located at 0.11 m. This variation was necessary to match the middle height of the toroidal vortices. The symmetries of the numerical axial velocities obtained indicate a well-formed toroidal vortex shape. For 300 rpm, Figure 7 shows the radial velocities of the 16 counterrotating toroidal vortices formed along the length of the reactor in the annular gap.
Some intercalated red jet flow structures emerge at high radial velocities (1:13 × 10 -1 m s -1 ) from the inner wall (swivel) and go to the outer wall (fixed). Such a fluid pattern is found between the cells and forms a mass transfer barrier between adjacent vortices; such phenomena were observed before [43].

Inactivation of E. coli by Taylor-Couette UV Disinfection
Reactor Treatment. The effect of angular velocity on the formation of counterrotating toroidal vortices and their impact on the kinetics of UV microbial inactivation were experimentally evaluated. It was found that, during UV irradiation, the survival behavior of microorganisms has the same removal of bacterial efficiency in the following cases: (a) when the fluid contained in the reactor annular space is immobilized and (b) when a low angular velocity (<200 rpm) is applied. From the kinetic point of view of microbial inactivation, when the Ta number exceeds a critical value of Ta C (in this case is 2743 or 200 rpm), the hydrodynamic pattern has a notable impact on the kinetics of UV microbial inactivation, in the Taylor-Couette UV disinfection reactor used in this work. At higher Ta C values, the removal of bacterial efficacy is improved.
The UV microbial inactivation kinetics was experimentally evaluated for three different concentrations of bacteria. For the first bacterial concentration of 35,000 PFU mL -1 , four microbial inactivation curves were obtained in the Taylor-Couette UV disinfection reactor based on the following angular velocities: 0, 300, 600, and 2000 rpm (  Figure 9. Taking as reference the constant value of the inactivation rate obtained at 0 rpm, the angular velocity increases improve the kinetics of microbial inactivation. The k value gradually improves by 11%, 66%, and 82% when the angular velocity increases by 300, 600, and 2000 rpm, respectively. Starting from 0 rpm and following the same angular velocity sequence, the removal of bacterial efficiency (Y% = ðN − N t /NÞ × 100) in 900 s was 63%, 67%, 79%, and 83%, as shown in Figure 9.
For this bacterial concentration, the inactivation rate constant was correlated with ω (angular velocity, measured in rpm), including the stationary fluid, by the following polynomial equation: 1.13e -1 1.03e -1 9.27e -2 8.28e -2 7.28e-2 6.29e -2 5.30e -2 4.30e -2 3.31e -2 2.32e -2 1.32e -2 3.28e -3 For any arbitrary angular velocity, within the experimental conditions studied, a k value can be obtained using equation (4). Therefore, a simulation curve of microbial inactivation can be obtained using equation (1). Figure 10 shows (dashed lines) the first 900 s of simulation of the survival behavior of microorganisms subjected to a UV irradiation process in the Taylor-Couette reactor at different angular velocities (0, 600, and 2000 rpm). The corresponding experimental data are shown in the same figure.
For the second bacterial concentration equal to 400,000 PFU mL -1 , five microbial inactivation curves were obtained in the Taylor-Couette UV disinfection reactor as a function of the angular velocity ( Figure 11). The following set of k values of each microbial inactivation curve was Also, in this case, the microbial inactivation kinetics is a function of angular velocity.
Taking as a reference the constant value of the inactivation rate obtained at 0 rpm, the constant of inactivation rate gradually improves by 14%, 35%, 70%, and 73% when the angular velocity increases by 300, 600, 1200, and 2000 rpm, respectively. Starting from 0 rpm and following the same angular velocity sequence, the removal of bacterial efficiency in 1200 s was 66%, 73%, 78%, 80%, and 83% ( Figure 11). For this concentration of bacteria, the inactivation rate constant was correlated with ω (including the stationary fluid) by the following polynomial equation: k = 9:418 × 10 −11 ω ð Þ 2 + 3:557 × 10 −7 ω ð Þ + 0:4057, Following the same procedure as before, within the experimental conditions studied, for any angular velocity a k value can be obtained from equation (5). Therefore, a simulation curve of microbial inactivation can be obtained using equation (1). Figure 12 shows the first 1200 s of simulation of the survival behavior of microorganisms subjected to a UV irradiation process in the Taylor-Couette reactor at different angular velocities (0, 600, and 2000 rpm).
For the third bacterial concentration of 30,000,000 PFU mL -1 , five curves of microbial inactivation were obtained in the Taylor-Couette UV disinfection reactor as a respectively. In the same order, the bacteria efficiency removal was 67%, 79%, and 83%. . It was found that, for both angular velocities of 600 and 1200 rpm, the microbial inactivation curves were very similar and only one of them is represented in Figure 13.
In addition, for 2000 rpm, the microbial inactivation kinetics does not follow an apparent first-order kinetic equation and was not included in Figure 13). The bacteria exposure time near the UV lamp is a function of the flow pattern (angular velocity) and a random bacteria association to form a clump (getting more important at higher bacteria concentration). Although the cause of the observed deviation is not clear, it is accepted that at short exposure time or subsequent exposure of microorganisms, damage by UV rays to higher fluences can alter the kinetic breakdown of the microorganism [8,20]. Therefore, it is likely that at higher angular velocities and a higher bacteria concentration, the bacteria exposure time near the UV lamp was not enough to cause an irreparable damage in the bacteria DNA/RNA. A partial DNA/RNA damage could be repaired. This may be attributed to the observed deviation from the apparent first-order UV disinfection kinetics. Taking as a reference the constant value of the inactivation rate obtained at 0 rpm, the inactivation rate constant improves rapidly from 66% to 89% when the angular velocity increases by 300 and 600 rpm, respectively. From 0 rpm and following the sequence of 300 and 600 rpm, the removal of bacterial efficiency in 2700 s was 90%, 98%, and 100% ( Figure 13). For this concentration of bacteria, the inactivation rate constant was correlated with ω (including the stationary fluid) by the following polynomial equation: k = −9:572 × 10 −10 ω 2 + 1:179 × 10 −6 ω ð Þ + 4:054 × 10 −4 R 2 = 1:0000: ð6Þ Figure 14 shows the first 4500 s of simulation of the survival behavior of microorganisms subjected to a UV irradiation process in the Taylor-Couette reactor at different angular velocities (0, 300, and 600 rpm). The bacterial efficiency removal, subjected to the experimental conditions studied here, was expected to be better at higher concentrations (>~10 6 PFU mL -1 ) than at lower concentrations (~10 4 PFU mL -1 ). In fact, the number of microorganisms    Figure 13: Experimental data are represented by symbols. Lines represent a tendency. For 30,000,000 PFU mL -1 , at 0 rpm, k = −4:05 × 10 −4 s -1 and the bacteria efficiency removal was 90% (○). The k value improves gradually by 66% and 89% when the angular velocity increases by 300 rpm (•) and 600 rpm (◊), respectively. In the same order, the bacteria efficiency removal was 98% and 100%. 8 International Journal of Photoenergy (or a group of them, considered as soluble reacting species) present in the solution is finite. Therefore, the probability that a single microorganism is irreparably damaged by UV irradiation decreases constantly as the treatment progresses. As time passes, there are fewer microorganisms available. Additionally, the bacterial efficiency removal improves as a function of the angular velocity. Table 1 summarizes the effect of the most important parameters (angular velocity and bacteria concentration) on the inactivation rate constant (k).
High k values are always associated to the best experimental conditions. Although under the approach presented in this work, it is not possible to evaluate/predict directly important parameters (such as UV intensity, UV fluence rate, UV fluence received by particles, reflective and diffuse fraction of Pyrex glass walls, and the hydrodynamic pattern) that can accelerate/delay the kinetics of UV microbial inactivation, all these parameters are collected in the inactivation rate constant.
This procedure is less complicated than other approaches [25][26][27]. In addition, the simulation of the survival behavior of the microorganisms subjected to a UV irradiation process in the Taylor-Couette reactor coincided well with the experimental results.

Conclusions
It was observed that E. coli is not resistant to UV irradiation in discontinuous experiments performed in the reactor in the absence/presence of a Taylor-Couette vortex. Although the formation of counterrotating toroidal vortices within the annular space formed well at~14 rpm, they have no notable impact on the kinetics of microbial inactivation. The improvement in the bacterial efficiency removal starts from 200 rpm. The removal of bacterial efficiency is improved depending on both of the following parameters: the angular velocity applied and bacteria concentration. The constant value of the inactivation rate increases between 70% and 90% when angular velocity (600 rpm~1200 rpm) is applied to the Taylor-Couette reactor. Beyond 2000 rpm, such improvement begins to decrease. The experimental results (hydrodynamic and kinetic pattern of microbial inactivation) can be correlated with a simple mathematical model to predict the simulation of the survival behavior of E. coli subjected to a UV irradiation process in the Taylor-Couette reactor in a wide range of concentrations of bacteria (10 4~1 0 6 PFU mL -1 ) and different angular velocities. This approach would be attractive to biological water treatment designers, since it requires few experiments and minimal physical parameters to define a representative experimental domain of a target water biological treatment.

Data Availability
The data used to support the findings of this study are included within the article.