Water is a precious but scarce resource that is essential for life. Only 3.5% of the Earth’s water is freshwater and fit for human consumption. Of this freshwater, only 1% is free-flowing in rivers, lakes, or streams (Fig. 1.1). Even so, there is sufficient drinking water on the planet to meet the needs of the population. However, accessibility and availability of safe drinking water (free from pathogens and priority chemical contamination) at the household level is not equal for all. Ensuring these basic needs is one of the greatest challenges currently facing humanity.

Over the years, global actions have been taken to satisfy basic water needs of the entire population (Fig. 1.2). On 28^th July 2010, the United Nations (UN) General Assembly recognised the human right to water and sanitation, declaring that clean drinking water and sanitation are essential to fulfil all human rights (United Nations (UN), 2010). In September 2015, the same assembly announced the Sustainable Development Goals (SDGs) in the 2030 Agenda action plan. There are 17 SDGs, and all work towards “ending poverty in all its forms”. They are the successors of the Millennium Development Goals (MDG) signed in 2000, but these new goals incorporate a specific 6^th SDG on water. SDG6 aims to “Ensure availability and sustainable management of water and sanitation for all” and includes eight global targets related to the management of natural water resources, wastewater, and the environment. The first target is to “Achieve access to safe and affordable drinking water” before 2030 since water accessibility is not guaranteed for a significant 29% of humanity. For example, 844 million people still lack access to safe drinking water, and approximately 1000 children die each day due to diseases related to unsafe drinking water or sanitation (United Nations (UN), 2018, 2015). Furthermore, the availability of water is becoming more unreliable and problematic due to the effects of the climate crisis (FAO, 2017; IPCC, 2018; UNU-INWEH/UNESCAP, 2013), the water demand of an ever-increasing population, the expansion of cities, and the developing economy (UNESCO/UN-Water, 2020; Wada et al., 2014).

The lack of safe drinking water affects communities in low-to-medium-income countries most. The lack of financial and technological resources impedes the implementation of drinking water treatment plants in these regions. To deal with this situation, Household Water Treatments (HWT) are required since they tend to be (McGuigan et al., 2012):

Most HWT are small-scale adapted water treatments that anyone can use. They can also include pre-treatments to remove solids that negatively influence disinfection treatment. At the household level, very simple forms of pre-treatment can be provided, including filtration through fabric or sand, flocculation-coagulation with natural substances, or sedimentation. However, these pre-treatments do not completely eliminate the pathogens (bacteria, viruses, and protozoa) responsible for waterborne diseases and other health risks (Gadgil, 1998; Pichel et al., 2019).

The most widely adopted HWT for pathogen removal are the following (their characteristics are summarised in Fig. 1.3):

SODIS has been found to be one of the most appropriate treatments for producing safe drinking water, because it is inexpensive and not dependent on consumables. The SODIS process is driven entirely by solar energy, and its effectiveness for the removal of pathogens from water has been widely proved.

The most widely accepted procedure for this simple technology is described in detail in the “SODIS manual: Guidance on solar water disinfection” published by Luzi et al. (2016). Briefly, water with a maximum level of 30 NTU should be exposed to the sunlight in clean 2-litre polyethylene terephthalate (PET) bottles for 6 h on sunny days, 48 h on cloudy days, while on days of continuous rainfall SODIS should not be used. PET bottles are selected due to their low-cost and wide availability. Concerns about chemical contaminants from plastic migration have been addressed by previous studies (Ubomba-Jaswa et al., 2010a; Wegelin et al., 2001). SODIS has been accepted by the World Health Organisation (WHO) and has been recommended for low-income countries and in the aftermath of natural disasters or humanitarian crises (World Health Organization (WHO), 2011, 2005).

Implementing SODIS treatment requires behaviour changes that sometimes generate obstacles to uptake. In this sense, any new SODIS-based innovations should be user-friendly, supported by local community elders, and ergonomically designed for a favourable reception. Many studies have reported successful SODIS implementation under diverse field conditions in locations such as Kenya, Cameroon, India, Cambodia, and Latin America (Center for Desease Control and Prevention (CDC), 2011; Conroy et al., 2001; Graf et al., 2010; Rose et al., 2006).

It is well-known that the higher the radiation intensity, the higher the cell damage. However, the photoinactivation mechanism, and, consequently, the inactivation rate, varies strongly with wavelength.

The SODIS process requires a UV-transparent container or reactor since the solar radiation must penetrate through the material. The selection of materials for manufacturing of SODIS containers must take into account not only optical properties but also mechanical properties, their long-term durability, and material availability. These properties are evaluated in this section and the optimal properties of a SODIS container are summarised in Fig. 1.5.

The earliest model for the inactivation of microorganisms by disinfectants derives from the Chick-Watson Law (Chick, 1908; Watson, 1908). This law states that the rate of microorganism destruction (dC/dt) is directly proportional to the number of organisms remaining at any time (C). This relation implies a uniform susceptibility of all species at a constant concentration of disinfectant — irradiance value in the case of the SODIS process — and is quantified by the kinetic constant (k). This model is based on a first-order kinetic in which the slope of the linear equation is the kinetic constant:

Many modifications of the Chick-Watson Law have been proposed to account for deviations from the simple first-order kinetics. For example, in 1972, Hom introduced an empirical generalisation to reproduce frequently observed curvilinear functions (Hom, 1972). In 1978, for cases where the radiation is not constant, Chamberlin and Mitchell redefined the kinetic constant expression as the product of the kinetic constant with downward irradiance (Chamberlin and Mitchell, 1978). Yet another example is the series-event model proposed by Severin in 1982 that is based on the fact that microorganisms have multiple targets, all of which must be inactivated before cell death, or that a single site within the microorganisms must be hit several times before inactivation (Severin et al., 1982).

All these models are based on empirical results. Empirical models are non-selective and straightforward, so they can be adapted to other pathogens relatively easily. However, for complex systems, these models do not accurately reproduce the actual results and do not respond well to situations outside the range of the operational conditions studied (interpolation is only recommended). In contrast, mechanistic models can account for such reactions and processes. Due to their accuracy and rigour, mechanistic models can handle any operational conditions (interpolation and extrapolation) and behaviours such as synergies. However, they are more specific and more complex. A rigorous description of all involved biochemical routes is far from reality. Therefore, mechanistic models capture the essential steps of the global process and are considered an optimal compromise between the fundamental description of the process and the simplicity of the model’s requirements for engineering purposes (Castro-Alférez et al., 2017b).

To develop kinetic models, contributions from all three types of damage (exogenous damage, direct endogenous damage, and indirect endogenous damage) should be contemplated. However, many kinetic models focus only on general endogenous damage since it is difficult to separate direct and indirect endogenous damage.

Other modifications derived from the Chick-Watson Law have been used to model thermal inactivation. In 1978, Mancini defined the kinetic constant by an exponential function depending on the temperature (Mancini, 1978). Later, this thermal inactivation model was adopted by Peng et al. (2008) for the modelling of the C. parvum protozoa inactivation as well as Kevin G. McGuigan et al. (1998) for the modelling of the E. coli bacteria die-off. In fact, this publication was the first kinetics considering the radiation-temperature synergistic effect. They reported a synergy parameter that multiplied the sum of the light and temperature kinetic constants. Values of this parameter larger than 1 indicate that synergy happens.

All the previous approaches are very close to the well-known Arrhenius equation which has been widely used for modelling the temperature dependence of reaction rates (complex reactions as well as elementary reactions) as follows:

This equation is seen as an empirical relation since the preexponential factor (k_o) and the activation energy (Ea) are temperature-independent constants experimentally determined for each reaction. Despite this consideration, Arrhenius explained that the activation energy concept indicates the minimum amount of energy acquired by substances to react. This term justifies the exponential nature of the relationship and can be calculated from statistical methods.

For reactions in which the relation between the kinetic rate and temperature are larger than exponential, the variant Modified Arrhenius equation (Eq. 1.8) can be used:

where the pre-exponential factor is proportional to T_n being T the temperature and n a constant. If n takes the value 1.0, this variant becomes in the original Arrhenius Equation.

The Arrhenius-like equation can be rewritten by introducing a threshold temperature (T₀) as follows:

As Peleg et al. (2012) demonstrated, the threshold temperature can be suppressed, which involves a different value of k₀ for the same value of k. However, the temperature threshold can be kept as a conceptual threshold to account for the temperature above which the thermal effect is observed.

The Arrhenius equation approach was used by Castro-Alférez et al. (2017a) to include the inactivation of E. coli bacteria in the dark as well as the UV-T synergistic effect, including this temperature dependence in the photoinactivation kinetic constant of their mechanistic model. However, this kinetic model does not consider the action spectral (the reactions are described like Eq. 1.1). The integration of both action spectral and synergistic effect can be possible if the reactions are described as Eq. 1.3 and the quantum yield is expressed as temperature-dependent.

A comprehensive kinetic model must consider all significant factors affecting the microorganism inactivation. Once all the significant photo-activated processes and thermal effects are identified and kinetically described following the approaches above-mentioned, the microorganisms’ inactivation balance can be solved. For that, the microorganism die-off depends on all the reactions related to endogenous damage (endogenous chromophores), synergistic effect, exogenous damage (external PPRI), and dark inactivation (usually thermal inactivation):

where:

However, some reactions rates can depend on other non-constant substances. Thus, the mass balance of these substances must also be taken into account.

If irradiance is homogenous inside the SODIS device, Eq. 1.10 can be easily solved because E(λ) is constant. If irradiance is not homogenous but the water is well-mixed, Eq. 1.10 can be solved using a unique value of E(λ) that represents the average incident radiation in the total volume. This value can be obtained by actinometry or numerical simulation. If the irradiance is not homogeneous and the system is not well-mixed, Eq. 1.10 must be simultaneously solved in each differential volume and this is only possible using numerical simulation.

The standard SODIS methodology presents some drawbacks that limit its widespread adoption:

This thesis aims to develop a comprehensive kinetic model that accurately estimates the required solar exposure time in large-volume containers that overcome the current challenges and limitations of the SODIS process. To achieve this goal, the spectral solar irradiance, the material of the container, the water composition and the temperature of the water have been considered as part of the following specific objectives:

The relation between the objectives, the chapters of results, and scientific publications is schematised in Fig. 1.8.

The photon flux density of sunlight at the solar noon (psnο(λ)) was calculated according to the following algorithm.

Firstly, the zenith angle at the solar noon should be determined. The maximum elevation angle (azimuth angle) (α) at solar noon is a function of latitude (φ) and the declination angle (δ) (Kalogirou, 2013):

where d is the day of the year (d = 1: 1 January; d = 365: 31 December).

Therefore, the zenith angle at solar noon (θ_sn) is given by:

Once the zenith angle is defined, the relative atmospheric depth crossed by solar rays (Air mass, AM_sn) is calculated using the equation by Kasten and Young (1989) (Eq. 2.4). AM is the depth of the atmospheric mantle crossed by the sun rays relative to its size when the Sun is at zenith (solar noon). Values of AM can vary from 0.0 (atmospheric depth crossed = 0) to 43.0 (maximum atmospheric depth crossed that is achieved at sunrise and sunset). Therefore, the atmospheric depth crossed at solar noon is 1.0. Note that Eq. 2.4 is only applied for zenith angles between -90° and 90° (the zenith angles at sunrise and sunset, respectively).

Later, the irradiance that reaches Earth’s surface at the solar noon (I_sn(λ)) is estimated applying the Lambert-Beer equation (Beer, 1852; Lambert, 1760) in which I_AM0(λ) is the solar spectrum in the external layer of the atmosphere (AM=0) (Eq. 2.5Eq. 2.6):

The solar spectra referred to AM 0.0 (I_AM0(λ)) and the atmospheric extinction coefficients (κ(λ)) can be obtained from the literature (Moreno-SanSegundo et al., 2021). I_sn(A) can be easily converted to the incident spectral flux density (p⁰(λ)) dividing it by λh⋅c⋅1Na,h being Planck’s constant, c the speed of light in vacuum and N_a the Avogadro’s number.

Finally, Eq. 2.6 allows calculation of p⁰_sn(λ):

where the solar spectrum that reaches the Earth’s atmosphere before crossing it (I_AM0(λ), AM = 0) and the atmospheric extinction coefficients κ(λ) were obtained from the literature (Moreno-SanSegundo et al., 2021), and δ is the sun declination angle that can be calculated as follows: δ=23.45°⋅sin(360365⋅(dy+284)) (Kalogirou, 2013). Note that d_y= 1 for 1 January and 365 for 31 December.

The day length (τ_DL) can be calculated with Eq. 2.7, which is only applicable for latitudes between 60°S and 60°N (Kalogirou, 2013):

Microsoft Excel® software was used to develop the Solar UV Calculator tool to predict the total radiation available and its spectral distribution within the SODIS containers as a function of the thickness and type of plastic. For this purpose, maximum solar radiation inside the device was calculated by applying Eq. 2.8 in the solar UV–Visible range from 290 nm to 800 nm:

where I_inside(λ) is the monochromatic radiation intensity (W • m^-2 • nm'¹) inside the device, I_sun(λ) the monochromatic solar radiation intensity (W • m^-2 • nm^-1) and T(λ) is the transmittance of the plastic material at each wavelength (dimensionless). The transmittance (T) is directly related to the absorbance (A) of the material (dimensionless) by the well-known Eq. 2.9:

whereas the absorbance is related to optical path length (L) in (m) by the Beer-Lambert law (Eq. 2.10):

where β(λ) is the monochromatic extinction coefficient (m^-1) for wavelength λ, which depends on the material.

Based on Eq. 2.8, Eq. 2.9, and Eq. 2.10, the radiation intensity inside the device can be expressed as:

where the optical path length for the light transmission is the wall thickness of the device (Th) in (m).

Radiation transport calculations in the TJC were carried out by numerical simulations using ANSYS® Fluent v.14.5 (ANSYS Inc.) software. First, the water container was geometrically defined using the ANSYS® Workbench tool which includes three parts: i) the air outside the container, ii) the container walls with the average PET absorption coefficient in the UV range (42.14 m^-1) and iii) the water domain that fills the interior of the container. A boundary condition was set in one of the lateral faces of the air domain to transmit the radiation received from the light source. All the domains were meshed with a total of 228,897 volumetric cells using ANSYS® meshing tool. The number of cells was confirmed to be sufficiently high to provide mesh independent simulation results of the global incident radiation and net radiation fluxes with a relative error below of 10_-6.

The numerical solution of the RTE was carried out using the DOM. 15 x 15 divisions were used for the directional discretisation. All the inter-domains surfaces were set as semi-transparent and zero-thickness. As the emission of radiation can be neglected at the low operation temperatures of the process, the temperature was fixed to 1 K in all domains to inactivate calculations of radiation emission. The water (bacterial suspension and water components) was considered a pseudohomogenous medium with a refractive index of 1.33 (refractive index of water). CAT and SOD enzymes and NADH were considered as the absorption components of the bacteria. The specific absorption coefficients (κ‘) were obtained from the literature, using an average value in the UVA range (300-400 nm): κ*_CAT as 2.6 • 10⁵ M_-1 • cm_-1 (Castro-Alférez et al., 2017b); κ*_SOD as 800 M^-1cm^-1 (Jackson et al., 2004); and κ*_NADH as 6220 M^-1 • cm^-1 (Nakamaru-Ogiso et al., 2010). Values of the absorption volumetric coefficients were estimated by assuming:

The resulting values were 3.05 • 10^-9 cm \ 4.68 • 10^-9 cm ^-1 and 3. 19 • 10^-12 cm_-1 for NADH, CAT and SOD, respectively. These values are sufficiently low that we can safely disregard any effect of the bacteria on the radiation field. However, absorption and scattering coefficients of water components (calculated in this work were included in the model resolution as extinction coefficients of the water. The Henyey-Greenstein phase function (Casado et al., 2017) was included in the model as a user-defined function (UDF), using an averaged value of g_λ for the whole UVA range. All these values can be considered constant with the time as well as the radiation intensities, being solved the radiation field in steady state. The main output parameters calculated from the simulations were the average incident radiation, its uniformity index, and the average radiation flux at the rear internal face of the container.

A second-order upwind discretisation scheme was used to solve the DOM equations. The simulations were carried out using the doubleprecision solver and with standard values of the under-relaxation factors due to good convergence and reasonable computational time. Scaled residuals of the numerical solution were monitored, considering that the equations converged when residuals (relative errors) achieved a value of 10^–6 for incident radiation and energy.

Three mechanistic kinetic models were developed for each type of microbial pathogen (viruses, protozoa, and bacteria). Elemental reaction steps were used to define the fundamental inactivation mechanisms.

Once the kinetic models are mechanistically defined, the kinetic parameters of each essential reaction were obtained. For this purpose, first and foremost, the kinetic parameters already available in the literature were fixed. For missing parameters, when possible, experimental data or data from the literature were used to estimate them independently. For the remaining parameters (there is no available data or procedures to estimate them independently), a regression was performed using the normalised root mean square (logarithmic) error (NRMS(L)E) between predictions and experimental data as the objective error function. The sequential quadratic programming (SQP) optimisation method from GNU Octave was used to minimise the error function. The system of differential equations was solved using explicit Euler. The steps followed to solve each kinetic model depended on the complexity of the global kinetic model.

The developed algorithm to calculate the actual daily dose (G_day) is based on the application of Eq. 3.1 for each wavelength (λ):

where:

The result of multiplying p°n(λ), T_DL and F1 corresponds to the maximum cumulated radiation in a day G_day(λ). In this sense, the product must match with the integration of the incident spectral photon flux density of sunlight p0(λ) over a 1-day time. Thus, the integration of p0(λ) was computed using the Solar Position Algorithm (SPA) from NREL (“National Renewable Energy Laboratory, Solar Position Algorithm| NREL.,” 2022) for a latitude of 45°N at λ = 307.5 nm (EMW for the direct damage of phiX174 virus), considering the 15th day of each month. These same data were then optimised with Eq. 3.1 to obtain the proportionality factor F1, minimising the NRMSE between the SPA data and those predicted by the fit function. F1 took a value of 0.43 with an NRMSE of 1%. The value of F1 thus obtained means that the average photon flux density of sunlight during the whole day length is 43 % of the photon flux density peak at the solar noon (pf_n(307.5 nm)). The excellent data fit suggests that this value of ^F1 (referred to fair-weather conditions at 45°N) is consistent during the year.

The next step consists in verifying if the value of F₁ depends on the latitude or if, in contrast, F1 = 0.43 obtained at φ = 45°N can be generalised. To do so, F1 was validated with predictions of the cumulated radiation for latitudes from 60°S to 60°N, with a step of 5°. The solid symbols reported in Fig. 3.1 represent the cumulated radiation referred to the 15th day of each month and calculated by integration using SPA data. The curves represent the predictions obtained with Eq. 3.1, by using ^F1 =0.43. All the predictions showed a very good agreement, with errors less than 13% for latitudes between 55°S-55°N, and 22% and 18% for 60°S and 60°N, respectively. This result means that a constant value ^F1 = 0.43 can be used over the whole year in the latitude belt between 60°S and 60°N.

The value of F2 is variable even for the same location and day of the year since it depends on the weather conditions. This parameter can be calculated experimentally or estimated with historical data. It is strongly recommended to measure the actual irradiance in the field and calculate ^F₂ by dividing the experimental value by the theoretical value. However, if actual measurements are not available, ^F2 can be estimated with historical data according to the procedure described by Moreno-SanSegundo et al. (2021). The values of ^F2 as a function of the latitude and longitude geocoordinates are graphically available in Fig. 3.2 and numerically in the Excel file (F2.xlsx) provided as SM in Article 5.

To evaluate ^F2 accurately, predictions for the cumulated incident radiation calculated from 8.00 h to 16.00 h at 52°N latitude multiplying by the ^F2 factor were compared to data from the literature (Frank and Kloöpffer, 1988). In the cited paper, Frank and Kloöpffer reported average radiation intensity (at 307.5 nm) referenced to the time interval of solar noon ± 4 h. To obtain the measured cumulated incident radiation, these values were multiplied by △t = 28,800 s (i.e., the time interval from 8.00 h to 16.00 h). F2 took a value of 0.58 (latitude 52°N, longitude 5°E). Fig. 3.3 shows a good agreement between the predicted and literature data when using the estimated value of F2 based on historical weather data, which reduces the NRMSE from 121% for F₂ = 1 to 25.5% for F2 = 0.58. Therefore, an approach based on historical data of the weather considerably improves the prediction with respect to the assumption of fair-weather conditions.

The developed algorithm can predict the actual daily dose depending on the latitude and day of the year. This algorithm has the following strengths:

However, the simplicity of the procedure also leads to a few limitations:

Mechanical properties and production costs for PS, PVC, PE, PP, PC, PET, and PMMA plastics were exhaustively reviewed with data from the literature.

Table 3.1 summarises the results obtained from the revision. In conclusion, PP, PC, PMMA, and PET were selected as suitable candidate materials for manufacturing SODIS devices: PP showed low durability but can be well economically replaced and its lifetime can be extended adding UV-stabiliser, PET and PC presented moderate durability and production costs, and PMMA is an expensive plastic but relatively unaffected by photodegradation.

Regarding the optical properties, the transmission spectra of the four materials were experimentally analysed and are shown in Fig. 3.4. PC, PP, and PMMA allow transmission of UVB, UVA and visible radiation. The solar radiation reaching the Earth's surface only includes wavelengths above 290 nm. For these wavelengths, the transmittance is higher in the case of PMMA and, therefore, this plastic is better for manufacturing SODIS devices than PP, followed by PC. PET blocks UVB radiation transmission and, as a result, the viruses and protozoa inactivation is difficult (Busse et al., 2019).

Due to the significant impact of weathering on SODIS devices, a deeper study was carried out through the accelerated ageing of plastics selected as suitable candidate materials and used in current SODIS processes: PMMA, PET, PP1 (PP with 1% by weight of UV-stabiliser), and PP2 (PP without UV-stabiliser).

The ageing of plastic materials due to weathering can affect both mechanical and optical properties, which leads to shorter lifetime and poorer disinfection rates, respectively. Table 3.2 summarises the main results obtained from the several techniques used to analyse mechanical properties and the estimated lifetime of SODIS devices manufactured with each plastic. In addition, Table 3.2 also summarises the degradation of optical properties with ageing (measured as a loss of UVA and UVB transmittance). The effect of the decrease of radiation transmission on the disinfection efficacy was experimentally demonstrated with experiments of E. coli bacteria inactivation. Fig. 3.5 depicts the evolution of the required solar exposure time to achieve 3 log reduction of E. coli bacteria with the ageing time for each plastic. Also, Table 3.2 contains the variation of required time to achieve 3 log reduction for each plastic.

PMMA and PP with a 1% of UV-stabiliser were identified as excellent materials for manufacturing SODIS devices. PMMA proved to be a very photostable material with stable mechanical properties and a lifetime of more than one year. Also, it was demonstrated to have the best optical properties and disinfection rates. Although it is a resistant and rigid material, PMMA is easily scratched and, therefore, it is recommended for static (non-potable) SODIS devices. PP with a 1% by weight of UV-stabiliser retained stable optical properties with high disinfection rates and good mechanical properties without signs of significant degradation after 9 months of solar exposure. Since it is a plastic with good tensile strength and good impact resistance, it is recommended for portable SODIS devices. PET and PP without stabiliser were also analysed. Their disinfection rates were the lowest since PET does not transmit UVB radiation, and the transmittance of PP decayed due to the significant ageing of the plastic. The lifetime of PET was estimated, at least, as 1 year of solar exposure while only 2 months was reached for PP without additives.

SODIS mainly relies on damage caused to pathogens by solar UV radiation. However, the pathogen’s sensitivity to photonic damage varies with the photon wavelength. Thus, the wavelengths transmitted into the interior of SODIS devices is a critical factor for disinfection performance. The Solar UV Calculator tool was developed to quantitatively estimate the available solar radiation and its spectral distribution inside a plastic SODIS container as a function of the plastic material and wall thickness (procedure described in Section 2.3.2. Solar UV Calculator tool). Two of its possible applications are: evaluating design parameters such as thickness and estimating experimental requirements such as solar exposure time.

The unlocked cells (input) allow to change:

The Solar UV Calculator returns:

The tool offers default radiation spectra for PMMA, PET, PC, and PP. Nevertheless, the developed Solar UV Calculator tool is freely available (SM of Article 1) to any potential user interested in the evaluation of SODIS processes with other materials and conditions, or even to the evaluation of other solar processes subjected to a strong spectral dependence on materials transmission.

Regarding the selection of new plastic materials, the highlights are:

Regarding the Solar UV calculator, this tool offers:

Bacterial inactivation experiments were carried out to check out the effect of the water composition on the SODIS process efficacy. Iron, solids, bicarbonates, soluble carbohydrates and humic acids were individually added to the water to assess the effect of common substances found in Sub-Saharan waters. Results were analysed based on the reduction of the viable bacteria count in comparison with unaltered water as a reference.

According to the results shown in Fig. 3.7.A, none of the substances enhanced the inactivation at the studied concentrations. A negligible effect was observed for the presence in water of bicarbonates and soluble carbohydrates. In contrast, the presence of iron, and especially of humic acids and solids showed a dramatic impact on the efficacy of the process. This effect can be attributed to the interference of the different substances in radiation transport which is confirmed by the transmission spectra in Fig. 3.7.B. In contrast, non-optically active substances (carbohydrates or bicarbonates) did not significantly affect the process.

To analyse the correlation between radiation transfer and disinfection efficacy from a quantitative approach, the absorption (k) and scattering (σ) coefficients and the g parameter of the Henyey-Greenstein scattering phase function of water with the different substances were determined experimentally (Table 3.3). In the case of solids, the attenuation is mainly due to radiation scattering, whereas for iron and humic acids the extinction is caused by photon absorption. As the radiation received by the bacteria decreases, more exposure time is required to achieve the same inactivation efficacy for the same level of irradiance. Therefore, in large-volume containers, the presence of solids, humic acids, and iron in water has a negative impact on the disinfection process because of their role as radiation attenuation factors. The effect of these optically active substances (iron, humic acid, and solids) was studied at different concentrations and UV irradiance values (11.3, 16.6, 21.6, and 28.2 W • m^-2) (experimental data shown in Article 2).

The distribution of radiation within the container volume for increasing concentrations of the optically active substances was studied by means of numerical simulations of the radiation field developed in Ansys Fluent software (Fig. 3.8.A and Fig. 3.8.B). In addition, the average incident radiation and the uniformity index were calculated (Table 3.4 and Table 3.5). Although in both cases a non-homogeneous distribution of radiation is observed (uniformity indexes lower than 1), significant differences appear depending on the absorption or scattering nature of the attenuation. Absorption by iron and humic acids (Fig. 3.8.A) led to a progressive decrease of incident radiation along with the container as the radiation pathway length increases, which means lower average incident radiation. In contrast, the scattering generated by the particles (Fig. 3.8.B) led to significantly more pronounced profiles with much higher values of incident radiation close to the front side, even above the irradiance, leading to a lower uniformity index. Experimental radiometric measurements at the rear of the container successfully validated the radiation modelling predictions.

Considering the photoactivated nature of the bacterial inactivation process, the disinfection kinetic constant experimentally observed (k) should be proportional to the average incident radiation in the water volume (G), being k₀ the proportional kinetic factor (constant and radiation independent). In low-volume containers, differences in radiation distribution could be neglected due to the short optical path. In contrast, in large-volume containers, we found that not only the kinetics of the process is affected by the average value of the incident radiation, but also by the homogeneity in the distribution of the radiation. The integration of the uniformity index (UI) allows to consider the significant differences existing in the radiation distribution for similar values of G when the extinction is mainly produced by absorption or by scattering (Eq. 3.2):

Experiments in reference water (no substances added) at different radiation intensities were used to obtain k₀ and experiments in water with optically active substances were used as validation. Fig. 3.9 shows the comparison of experimental and estimated first-order kinetic constant considering the model for low-volume containers (k = k₀ • G, where k₀ = 2.81 • 10^-3 m² • W^-1 • min^-1, R²=0.999) or large-volume containers (Eq. 3.2, where k₀ = 2.99 • 10^-3 m² • W^-1 • min^-1, R²=0.999).

The consideration of the uniformity index reduced the error (calculated as NRMSE): from 66% to 22% for solids and from 31% to 20% for humic acids. In contrast, Fig. 3.9.A and Fig. 3.9.B shows that the values of the kinetic constants of experiments in the presence of iron were always higher than those estimated by the model (59% and 69% of NRMSE, respectively). The same optical properties and radiation distribution led to significantly different results when the absorption was produced by humic acids or iron. Kohantorabi et al. (2019) found that a concentration as low as 1 mg · L^-1 of ferrous iron enhanced the disinfection rate since iron permeates into the cell and reacts with internal species to generate ROS that damage the bacteria (Kohantorabi et al., 2019; Rommozzi et al., 2020). These results observed in optically clear water and short optical path devices cannot be extrapolated to high-volume containers where the higher optical path length of the medium introduces radiation transport limitations. Consequently, whereas solids and humic acids has a negative effect on the efficacy of the solar disinfection process by their role as radiation attenuator, the effect of the presence of iron depends on a compromise between its detrimental role in the attenuation of radiation and its beneficial enhancement of the internal damage due to its permeation into the bacterial cell.

A novel procedure has been developed to calculate the available incident radiation in large-volume containers as a function of naturally occurring substances present in water using the average incident radiation and the uniformity index values previously calculated using numerical simulation. The highlighted findings are:

No kinetic description was required for the dark inactivation since the experimental data recorded in the potential environmental temperature range (up to 50°C) showed negligible inactivation results. This is in agreement with Romero et al. (2011) who found that direct photolysis was responsible for solar inactivation of MS2 in the temperature range 14-42°C in the absence of external sensitisers.

In clear waters, indirect exogenous damage does not happen because of the lack of external sensitisers. In virus, the indirect endogenous damage mechanism can be neglected due to their simple structure of the microorganism. Therefore, photoinactivation of viruses in clear water can be reasonably assumed to occur mainly through direct endogenous damage based on the absorption of UVB solar radiation by the genome. This mechanism can be expressed by a first-order kinetic model (Eq. 2.12) where the kinetic constant can be defined as Eq. 3.3 (see Eq. 1.4):

where MS2 virus extinction coefficients (ε_v(λ) = ε_RNA • [RNA]_v) were taken from the literature (Mattle et al., 2015), spectral data of the incident light from 280 nm to 400 nm (radiation absorption of MS2 virus is negligible above 400 nm) were experimentally measured, and the quantum yield was calculated using experimental results. To do so, experimental data of the inactivation at 30^°C (thermal effects can be neglected at 30°C) were fitted to a first-order kinetic model (Eq. 2.12) and the kinetic constant was obtained using Eq. 3.3. The calculated quantum yield was φ_v = 2.07 · 10^-3 viruses inactivated per absorbed photon (NRMSE = 11%).

Data from MS2 inactivation experiments under illuminated conditions (15, 20, 30, 40, and 50 W · m^-2) at different water temperatures (30, 40, 45, and 50°C) showed the clear effect of water temperature on photoinactivation rates at T > 40°C. This synergistic effect was included in the model by the temperature dependence of the kinetic constant according to the modified Arrhenius equation with a threshold (Eq. 1.8 + Eq. 1.9) using a value of 40°C (313 K) for the temperature threshold (T⁰). The quantum yield term in Eq. 3.3 was redefined to include its dependence on below line math error (n = 423, ∅y = 2.15 • 10'³ virus inactivated per absorbed photon and E_a/R = -1.30 · 10⁵ K) was carried out by simultaneous fitting of the experimental data for the entire range of irradiances and temperatures with an NRMSE of 9.2%. Fig. 3.10 depicts the comparison of the predicted and experimental Kinetic Constants showing excellent agreement.

As a result, the final expression for the kinetic constant is defined as follows:

The kinetic model was validated with a new set of experiments at different water temperatures, radiation intensities, and spectral distributions. To do so, different plastic samples were located between the reaction system and the radiation source, simulating that the process was performed in the PP and PPMA SODIS containers selected in Chapter II and the standard PET container (see Fig. 3.6 in Chapter II). Note that, from now on, PP1 (PP with 1% by weight of UV-stabiliser) will be named just as PP. Fig. 3.11 shows the comparison between the observed and predicted kinetic constants for PET, PP, and PMMA scenarios.

The agreement can be considered very good, with reasonable values of NRMSE of 28% and 18% for PP and PMMA, respectively. In the case of PET, the NRMSE is much higher (60%) due to the very low values of the inactivation rates (caused by low transmission in the UVB range). Thus, the UVB is the critical region where the virus absorption overlaps with the available solar incident radiation.

Model validation confirms the remarkable potential of the spectral-thermal synergistic model to predict MS2 photoinactivation with sunlight under different spectral and global irradiance values and temperatures around the world, specifically for the application of solar water disinfection processes with any type of container. In addition, the methodology and mathematical model presented can be easily extrapolated to other viruses with the obvious recalculation of specific kinetic parameters.

A novel comprehensive kinetic model for the MS2 virus inactivation has been developed as a function of the water temperature, irradiance, and spectral response of the virus. The highlighted findings are summarised as follows:

In any case, application of the model to field conditions could require recalibration of the kinetic parameters to account for specific substances present in the water that could either enhance the process by acting as sensitisers for PPRI generation or diminish the efficacy by their role as radiation attenuators (this study was only carried out for bacterial inactivation in Chapter III).

Experimental results of inactivation in the dark at different water temperatures confirmed a noticeable effect of temperature above 30°C. Thus, this effect was modelled using a first-order kinetic model where the thermal inactivation kinetic constant is defined with the Arrhenius equation with a threshold temperature at 30°C (k_To = 1.12 X 10_-4 h_-1 and E_ar/R = 4.37X 10⁵ K, NRMSLE of 8.59%). However, these phenomena do not necessarily follow an Arrhenius behaviour. For this reason, the obtained kinetic parameters were not the final values, they were just used as seeds for the fit of the entire collection of experiments. The viability of C. parvum decreases progressively for temperatures in the range from 30 to 50°C due to the melting point of the fatty acids and hydrocarbons present in the oocyst wall and the increase in the metabolic activity (Fayer and Nerad, 1996; Jenkins et al., 2010; King et al., 2005; Peng et al., 2008). Furthermore, temperatures above 37°C can induce the phenomenon of spontaneous excystation of C. parvum oocysts, making their survival impossible in the absence of a host (Gómez-Couso et al., 2009; Smith et al., 2005).

Solar inactivation of C. parvum is dominated by direct endogenous damage resulting from absorption of UVB radiation by the genome. Indirect endogenous damage is negligible since the action spectrum of C. parvum closely resembles that of the DNA absorption (Busse et al., 2019; Liu et al., 2015). Exogenous damage is also negligible since the presence of NOM, one of the most important external sensitisers, does not cause any effect on C. parvum viability, most likely due to its highly resistant thick oocyst wall (Liu et al., 2015). Due to the presence of a shoulder in the experimental disinfection curves performed under illuminated conditions at 30°C, a series-event kinetic model was used. Calculation of the Kinetic parametersn = 8, K_RAD = 4.05x10^-2 m² • W^-1 • h^-1, by fitting the experimental data, resulting in an NRMSLE of 2.44%. No recovery kinetic constant was required to fit the experimental results.

The coupling of the dark thermal inactivation model with the UV irradiance model to predict the inactivation of C. parvum failed at temperatures higher than 30°C (NRMSLE = 17.9%). The predictions clearly underestimate the experimental data, showing a higher error for higher temperatures, which supports the existence of a synergy between the thermal and photonic inactivation processes (Kevin G. McGuigan et al., 1998; Wegelin et al., 1994). The synergistic effect was included in the model through the temperature dependence of the kinetic constant of the series-event model according to the modified Arrhenius equation, using a value of 30°C for the temperature threshold again. All the kinetic parameters were recalculated using the provisional values in the previous submodels as seeds. The global fitting of the whole experimental data set for the complete range of irradiances and temperatures provides the values of the final kinetic parameters: kinetic parameters (n = 7 and k_RAD0=2.97 x 10^-2 m^-1 • h^-1, E_aRAD/R =6.90 x 10⁴ K, k_To = 4.19 x l0^-5 h^-1, and E_ar/R = 5.06 x 10⁵ K with an NRMSLE of 3.68% (Fig. 3.12). Now, whereas the predictions of the dark thermal inactivation and the photoinactivation at 30°C are very similar to those obtained previously, the prediction of the photoinactivation at higher temperatures improves significantly.

The inactivation kinetic constant can be calculated by multiplying the quantum yield by the volumetric rate of photon absorption as follows:

C. parvum extinction coefficients (ε_CP (λ)) and the spectral irradiance E(λ) from 280 to 400 nm for a global UV of 50 W • m^-2 can be found in the SM of Article 4. Following Eq. 3.5, the quantum yield for C. parvum inactivation was calculated as φcp = 3.94×10^-7 oocysts damaged per absorbed photon, indicating that C. parvum is more resistant to direct inactivation than viruses such as phiX174, MS2, and adenovirus (1.4×10^-2, 2.9×10^-3, and 2.5×10^-4 virus inactivated/absorbed photon, respectively) (Mattle et al., 2015).

The kinetic model was validated with a new set of experiments at different water temperatures, radiation intensities, and spectral distributions. To do so, the same procedure used to validate the kinetic model for viruses was applied: PET, PPMA, and PP plastic samples were located between the reaction system and the radiation source. Fig. 3.13 shows the comparison between the observed and the predicted inactivation profiles for the three scenarios.

Considering the fully predictive nature of the model inactivation curves (they are not fitting results), the agreement can be considered very good with values of NRMSLE of 5.54, 5.72, and 11.68% for PET, PP, and PMMA, respectively. The results can be easily interpreted based on the different UV transmission of the materials obtained with the Solar UV Calculator tool: 1%, 44%, and 57% in the global UVB range, and 59%, 60%, and 86% in the UVA range, for PET, PP, and PMMA, respectively.

For the PP and PMMA scenarios, the thermal effect and the irradiance effect can be observed for experiments at the same global UV irradiance and the same water temperature, respectively. In the case of PET, a plastic that essentially does not transmit UVB radiation, the thermal contribution is almost the only damage source. As a result, the same disinfection rates for different values of global UV irradiance (i.e., 30 and 50 W • m ^-2 at 44°C) are achieved. The absence of external sensitisers and the negligible inactivation with only UVA and visible radiation at 30°C confirm two things: the threshold on the thermal inactivation set to 30°C and the dominant mechanism of C. parvum photoinactivation by the direct damage caused by the UVB photons’ absorption by DNA. Thus, it also means that the thermal mechanism is the only pathway to inactivate C. parvum in standard SODIS PET containers. However, the temperature reached during solar water disinfection is easily raises above 30°C (Dejung et al., 2007; Gómez-Couso et al., 2010).

A novel comprehensive kinetic model for the C. parvum protozoon inactivation has been developed as a function of the water temperature, irradiance, and spectral response of the protozoon. The highlighted findings are summarised as follows:

Although protozoa show low susceptibility to external PPRI due to their resistant and thick wall, application of the model to field conditions may require recalibration of the kinetic parameters to take into account specific substances present in the water that could reduce the efficacy by their role as radiation attenuators or, conversely, even improve the inactivation by acting as sensitisers for PPRI generation (this study was only carried out for bacterial inactivation in Chapter III).

The kinetic analysis of the E. coli bacteria (model pathogen) inactivation enhanced with H₂O₂ was carried out by defining the significant reactions and estimating their kinetic parameters. Table 3.6 and Table 3.7 show the entire mechanism experienced by bacteria and H₂O₂, respectively.

Kinetics parameters obtained with the RM-1 (shown in Table 3.6 and Table 3.7) accurately reproduced the experimental data (NRMSLE=4.4% for bacteria and NRMSE= 12.9% for H₂O₂). The series-event model that reproduces the cell inactivation caused by radical’s attacks (R.9 and R.10), is capable of developing profiles with curvilinear shape, being more curved for more events. However, in this case, the shape is linear due to the high value of the recovery constant (k_R = 10.8 s^-1), which straightens the curve (dashed yellow lines in Fig. 3.15). Due to the linear shape of disinfection profiles, a pseudo-first-order kinetic constant of each experiment was obtained to compare with that obtained experimentally. Fig. 3.14 showcases the excellent agreement between the experimental and predicted data.

Kinetics parameters obtained with the RM-2 and RM-3 (showed in Table 3.6 and Table 3.7) successfully reproduced the effect of UV radiation and temperature on disinfection profiles (RM-2 NRMSLE=17.3% and RM-3 NRMSLE=14.0%). Despite the results in dark conditions, all the inactivation curves under UV illumination (Fig. 3.15 and Fig. 3.16) showed the characteristic curved shape of the series-event model.

In this case, the low value of the photonic recovery constant (1.75 • HPs'j is not capable of straightening the curve. The number of radicals’ attacks (m = 27) is 5.5 times higher than the number of damage levels by the direct photonic process, confirming the critical effect produced by photons in comparison with radicals. In contrast, the recovery constant for radical damage is much lower than the solar one, but it must also go through a higher number of levels to completely heal the bacteria, resulting again in higher potential damage produced by light, probably because bacteria are used to radical attacks due to cell respiration and not to photonic damage.

One of the advantages of studying the effect of H₂O₂ on bacteria disinfection is the opportunity to understand the underlying mechanisms and the role of internal substances (since H₂O₂ permeates into the cell), as well as to find reactions that do not play an important role, at least kinetically. Fig. 3.17 shows the integrated mechanistic proposal (the reactions and their kinetic parameters can be found in Table 3.6 and Table 3.7).

For example, the estimated values of the kinetic parameters agree with the mode-one killing cells by H₂O₂ (inactivation kinetic routes related to internal damage produced by radicals’ attacks, it reaches its maximum around 1-2 mM H₂O₂ external concentration (Imlay and Linn, 1986)), confirming that not only growing cells follow the two killing modes, but also stationary phase cells.

Another characteristic of the mode-one killing is a low value of the Fe²⁺ recycling rate. Although Fenton oxidation rate in cells is higher than usual (k₄= 4400 M^-1s^-1 at 37°C (Park et al., 2005), if the cell’s potential to reduce Fe³⁺ to Fe²⁺ is also high, then the concentration of Fe²⁺ would be constant, Therefore, the mode-one killing-would not exist (Uhl et al., 2015). The obtained value for k₅ (8.43 • 10^-2 s^-1) is low enough to guarantee the presence of Fe³⁺ under toxic levels of H₂O₂ and allows a decrease of Fe²⁺ concentration as the external H₂O₂ concentration rises.

Regarding the donor substance that performs the ferric to ferrous iron reduction, some authors suggest that O₂• or cysteine could be the reductant agent. During the oxidative process, the levels of O_2•- lightly increase (the model simulations show that the amount of HO_•- varies significantly with experimental conditions and over time, while O_2•- concentration experiences small variations), raising the kinetic rate. However, O₂•- is excluded since k₅ would take a value around 10^-5 s^-1 (rate constant 10⁵ M^-1s^-1 (Bielski et al., 1985) multiplied by the concentration IO^-10 M, and that would not suffice for the iron pool. So, another suggestion is cysteine. Free cysteine is present in low concentrations to generate the strong DNA damage observed. It was previously found that when H₂O₂ is present, cysteine homeostasis is disrupted, and free cysteine storage increases around eightfold (Park and Imlay, 2003). Therefore, cysteine could be the donor species, being in a concentration between 0.1-2 mM in the cell (Park and Imlay, 2003), which implies a more reasonable pathway, having a kinetic constant around 40-800 M^-1s^-1.

In spite of the SOD photoinactivation that also occurs (reducing the rate of H₂O₂ formation), the photoinactivation of CAT prevails (k₁₄>> k₁₃), reducing the H₂O₂ conversion and inadvertently increasing the H₂O₂ levels inside the cell.

Finally, the value of the activation energy is not very high (Ea_SYN= 7.47 • 10³ J • mol^-1) which involved a value of ki₈ only 1.33 times higher at 50°C than at 20°C. In contrast, the activation energy for the bacterial thermal inactivation resulted in being higher (Ea₁₁ = 1.38.10⁵ J.mol^-1) which implied a value of k₁₁ almost 200 times higher at 50 °C than at 20°C. Hence, the synergistic effect is not very significant for this specific bacterial strain and experimental conditions. Since this model should be optimised for each type of strain, we have decided to include the description of the synergy, allowing the possibility of considering this effect.

Another particular strength of this mechanistic kinetic model is the capability of elucidating the best operational conditions for the process. To do so, the required solar exposure time to achieve a 99.99% of E. coli removal (t99.99%) has been obtained from the model's predictions (Fig. 3.18). It can be seen that temperatures above 50°C have a strong effect on bacterial inactivation, whereas the thermal effect at 20-30°C is negligible. If the thermal effect is not present (scenarios at 20°C), the illumination with solar light is necessary to achieve inactivation times lower than 4 h (240 min). Even the addition of the highest H₂O₂ concentration (50 ppm) is not enough to require less than 6 h. Furthermore, if UV illumination and H₂O₂ addition are combined, the disinfection can be achieved in 50-120 min, and if the highest UV illumination or H₂O₂ dose (20.8 W • m^-2 and 50 ppm) is used, the required time (50-90 min) is comparable to the required times at 50°C. At 40°C, the thermal effect contributes in the same way as the radiation and H₂O₂ and its combination resulted in required time between 50-90 min.

A novel comprehensive kinetic model for the E. coli bacteria inactivation enhanced with H₂O₂ has been developed as a function of water temperature, irradiance, and H₂O₂ concentration.

The study of the enhancement caused by H₂O₂ addition helped to elucidate the internal cellular mechanisms and their kinetic parameters, for example:

Another particular strength of this mechanistic kinetic model is its capability to provide the best operational conditions for the process. The highlighted results are summarised as follows:

Finally, developing a mechanistic model for complex organisms such as bacteria complicates the account for all the variables involved in the SODIS process and increases computational costs and user efforts. For this reason, the influence of the radiation spectrum has not been included in this kinetic model. However, the complexity has helped to understand better the unknown bacteria pathways.

In this case, if the SODIS process is performed in PET containers, the model can be easily applied to field conditions applying the procedure developed in Chapter III to account for the effect of naturally occurring substances. For other materials, the recalibration of the kinetic parameters is recommended since sensitisers can be sensitive to UVB wavelengths which PET cuts.