Indigo Carmine Degradation in Water Induced by a Pulsed Positive Corona Discharge in Air: Discharge and Postdischarge Effects

Abstract

In recent years, one of the fastest growing technological applications in the field of nonthermal plasmas is the degradation of organic contaminants of water. In this work, the degradation of indigo carmine (IC) in water induced by a pulsed positive corona discharge operating in ambient air is reported. Degradation levels in different volumes of IC in solution with distilled water treated with different plasma exposure times immediately after discharge (0 h), and in the postdischarge up to 24 h were examined. To explain the IC discoloration in the postdischarge phase, a chemical model was developed. The stability of the reactive species in solution nitrate (NO₃⁻), nitrite (NO₂⁻) and hydrogen peroxide (H₂O₂), as well as the properties of the solution (electrical conductivity, pH) were also measured. The results suggest that the hydroxyl radical (OH˙) as well as ozone (O₃) are the main oxidizing species during the discharge phase, being primarily formed in the gas phase through plasma-mediated reactions and then transferred to the liquid by diffusion, while the OH˙ production in the bulk liquid through the decomposition of peroxinitrous acid (O=NOOH) plays a major role in the IC degradation during the postdischarge. These results are associated with a noticeably increase in the energy-yield values observed at 24 h post-treatment.

1. Introduction

A plasma is a quasineutral gas of charged and neutral particles that exhibits collective behavior [1]. On a laboratory scale, the most usual mode of plasma generation is through electrical discharges in a gaseous medium [2]. These are usually divided into two broad categories: (i) thermal discharges, where the energies of the heavy particles are of the order of the electron energy (~1 eV = 11,600 K) [3]; and (ii) nonthermal discharges, where the electron energy is much higher (~1–5 eV) than the energy of the heavy particles (~300–3000 K) [3]. In the latter group, the electrical energy applied to the discharge is mainly delivered to the electrons, which in turn excite by collisions with the molecules of the gas where the discharge is established, thus generating large amounts of reactive oxygen and nitrogen species (RONS) and UV radiation in air or similar gas mixtures [4].

The applications of nonthermal discharges are wide, and in recent years, there has been a growing interest in nonthermal plasmas in (and in contact with) liquids due to their multiple technological applications, encompassing areas such as agriculture, medicine, nanomaterial deposition and environmental care, among others [5,6,7,8,9]. Within agriculture, one of the emerging applications is the curing of plants and seeds with liquids that have previously been exposed to plasma (referred to as ‘activated’ liquids), such as water treated with nonthermal discharges (plasma ‘activated’ water or PAW) [5]. In terms of environmental care, due to its ability to decompose organic in water, the use of nonthermal plasmas has focused on the degradation of dyes and pigments (e.g., indigo carmine) used in various industrial sectors, which are resistant and refractory to traditional treatment processes and generate serious damage to human health [10,11].

A widely used type of nonthermal discharge in contact with liquids is the pulsed corona discharge. The corona discharge is a nonuniform discharge that occurs in the vicinity of electrodes of small radius of curvature where the electric field is high enough, and therefore the ionization and luminosity of the discharge are located around these electrodes. Depending on the mechanism through which the ionization level of the discharge is sustained, that depends on the polarity of the electrode where the electric field is higher, the corona discharge is classified as (i) positive corona, when the high electric field is located in the vicinity of the anode and the breakdown mechanism is streamer-type; or (ii) negative corona, when the high electric field is located at the cathode and the breakdown mechanism is Townsend-type [4]. The region in the vicinity of the electrode where the electric field is sufficiently high and ionization processes take place is called the active volume of the corona. This is the most important part of the discharge, as this is where most of the reaction and excitation processes occur. However, the power of the quasi-steady-state corona discharges is typically very low and not suitable for many applications. On the other hand, if the voltage applied to the discharge exceeds a certain threshold, the corona discharge may eventually degenerate into the streamer–spark transition, and if external conditions allow it, into an arc. This transition may be a consequence of a thermal instability. One of the ways to avoid the spark transition—also strongly increasing the power of the discharge—is the application of voltage pulses of short duration (~100 ns) and fast rise time, i.e., the pulsed corona discharge [4].

The gas-phase chemistry of air discharges in contact with liquids produces large amounts of gaseous RONS (OH˙, H₂O₂, O₃, NO, NO₂) that enter the liquid volume by diffusion and induce the formation of secondary reactive species in the liquid, such as OH˙, H₂O₂, NO₂⁻, NO₃⁻, ONOO⁻; and O₂˙⁻/HO₂˙ radicals [12]. However, the most reactive gaseous species (e.g., OH˙ and O₃) are consumed rapidly in solution, so the depth of penetration into the liquid is a few hundred nm to tens of µm [13]. Furthermore, the plasma interacts with the liquid surface, generating reactive species directly at the gas–liquid interface [14]. This makes nonthermal plasmas an advanced oxidation technology [15]. Because the interaction between plasma and liquid is essentially concentrated in this boundary layer, a high-level of interaction requires high values of the gas–liquid interface area (e.g., injecting the liquid as an aerosol or thin layers [13,14,16]).

The OH˙ radical is of particular importance in plasma discharges in contact with liquids or in humid air. It has a high oxidizing power (E⁰ = 2.85 V), being the strongest oxidant in aqueous environments. It reacts with most organic compounds, and due to its high reactivity, its life time is very short (in the gas phase it lasts close to 200 µs; and much less in aqueous-phase, ~1 ns) and therefore, it can react with target molecules in its immediate neighborhood [17]. In the gas phase its generation is mainly through the dissociation of H₂O molecules via electron impact or via the quenching of the excited states of N₂ molecules, while in the liquid phase the photodissociation of water and charge-exchange reactions of incident positive ions on the liquid surface are the main pathways. In PAW, other important formation mechanism of OH˙ radical in the bulk liquid is through the degradation of peroxinitrous acid (O=NOOH)—formed by the reaction between H₂O₂ and NO₂⁻—in acidic conditions [13].

Pollutant degradation (such as pharmaceuticals, pesticides and organic dyes) in water induced by nonthermal plasma discharges in (and in contact with) liquids has been extensively studied, as summarized in a recent review articles [15,18]. The principal mechanism of pollutant degradation is associated with the most reactive species (OH˙, O₂˙⁻, O₃) formed in the gas phase during the discharge, which enter in the liquid bulk, react with the contaminant molecule, and fragment it. However, the results are highly dependent on the configuration of the discharge, as well as how the energy is deposited in the plasma.

In this work, the degradation of indigo carmine (IC) induced by a pulsed positive corona discharge operating in air is reported. Two volumes of IC solution in distilled water (50 and 100 mL) were treated with different plasma exposure times (10–30 min). Discharge and postdischarge effects on the IC degradation and the concentration of long-lived species in the aqueous phase (NO₃⁻, NO₂⁻ and H₂O₂), were investigated up to 24 h after treatment. In addition, a chemical model to explain the IC chromogenic-bond degradation in the postdischarge phase via the O=NOOH decomposition was developed. Moreover, for each of these volumes, the energy yield was estimated as the amount of dye degraded per kWh delivered to the discharge (g/kWh).

2. Materials and Methods

2.1. Pulsed Positive Corona Discharge

A (positive) pulsed corona discharge in open air in contact with liquid was used in the experiments. The discharge was powered with a capacitive pulsed source, capable of delivering voltage pulses with a time-width of ~100 ns, an amplitude of ~10 kV, and a pulse repetition frequency of ~42 Hz. The operation of the source is based on the charging of a capacitor bank (C = 224 nF) to a voltage level of 1500 V, which is in turn discharged by a thyristor onto a pulse transformer with ferrite core (Figure 1a).

The plasma reactor was set in a wire-to-plate electrode configuration with electrodes made in AISI 304 (Figure 1b). The anode consisted of an arrangement of 10 wires of 0.2 mm in diameter and 100 mm in length with a separation between them 10 mm. These wires were placed parallel and at a certain distance from the cathode, which consisted of a square reservoir with a side of 140 mm and a height of 10 mm, containing the distilled water or IC solution to be treated in the form of a thin layer. Two volumes of the liquid to be analyzed were used: 50 and 100 mL; and in both cases the same gas gap of 3 mm was maintained between the surface of the liquid and the wires that form the anode.

Discharge voltage (V) was obtained as the difference between the CH1 and CH2 voltage signals (Figure 1a). A high-voltage probe (Tektronix P6015A, 1000X, 3 pF, 100 MΩ) was used to measure CH1, while a coaxial shunt resistor (T&M SDN-414-025, 0.25 Ω, 1200 MHz) was used in CH2 to infer the discharge current (I). The signals of both channels were recorded with a 4-channel digital oscilloscope (Tektronix TDS 2004C, sampling rate 1 GS s⁻¹, bandwidth 70 MHz). Due to the difference in length between the measurement lines (the cable used in CH1 has a length of approximately 3 m, while the corresponding to CH2 has length of 1.5 m) a delay of approximately 10 ns in the voltage signal with respect to the current signal was measured.

Figure 2a shows typical voltage and current waveforms of the discharge for each applied voltage pulse. The voltage pulse reached a maximum value of ≈11 kV, while the current pulses reached a maximum near to 30 A, with a time width of ≈40 ns.

The instantaneous power and energy dissipated in the discharge are shown in Figure 2b. The instantaneous power (the product of V I) oscillated with the same frequency as the discharge current, reaching a maximum around 200 kW, while the average power per pulse was ≈21 kW. The energy per pulse, calculated as the time integral of the instantaneous power, reached a value of ≈21 mJ. Taking into account the pulse repetition frequency, the corresponding mean power resulted at about 0.9 W.

2.2. Treatments and Statistical Analysis

Volumes of 50 and 100 mL of distilled water (pH ≈ 5.2 and electrical conductivity ≈ 5 µS/cm) or IC solution subjected to different plasma exposure times were studied: 0 (control), 10, 20 and 30 min. Each of these experiments was performed in triplicate. Statistical analyses were performed with the R 4.1.1 software, R Core Team, R Foundation for Statistical Computing (Vienna, Austria) [19]. Data are shown as mean values ± SEM.

2.3. Physicochemical Determinations

2.3.1. IC Degradation

To study the IC degradation, 50 and 100 mL of a 20 mg/L dye solution (5,5′-Indigo sulfonic acid sodium salt, Cicarelli) were treated with plasma and the absorbance was measured at 285 and 610 nm [10,20] immediately at the end of the treatment and at 24 h after discharge. The treated samples were stored at room temperature in sterile flasks, tightly capped and in the dark for 24 h and the absorbance was remeasured at these wavelengths. The results are shown as percentage degradation of the IC with respect to the initial concentration: % = 100 (1 − A/A₀), where A is the absorbance of the treated sample and A₀ is the absorbance of the untreated sample.

2.3.2. pH and Electrical Conductivity

The levels of pH and electrical conductivity were determined using a HI 8314 pH meter (Hanna) with a range of 0 to 14 and a resolution of 0.01; and a CYBERSCAN COND 610 conductivity meter (Oakton Instruments, Vernon Hills, IL, USA) with a measurement range of 0 to 500 mS/cm with an accuracy of 1%. Both instruments were calibrated prior to the determinations using standard solutions (buffer pH 7, buffer pH 4 and KI 0.01 M solution with σ = 1413 µS/cm at 25 °C). The determinations were performed at the end of the plasma treatments.

2.3.3. Hydrogen Peroxide Measurement

A method using peroxidase was used [21]. The method is based on the reaction of H₂O₂ with a mixture of 4-aminophenazone and phenol to give as product a red quinoneimine (4-(p-benzoquinonamonoimino)-phenazone) that exhibits an absorption maximum at 505 nm.

2.3.4. Nitrate Measurement

The UV method was used [21]. Hydrochloric acid was added in a ratio water:HCl = 50:1 and the absorbance at 220 nm (A₂₂₀) and 275 nm (A₂₇₅) was measured. These values were used to obtain the corrected absorbance (A = A₂₂₀ − 2 A₂₇₅).

2.3.5. Nitrite Measurement

Nitrite concentration was measured using Griess reagents (I and II) [21]. This technique consists of detecting a color change of the solution to a pink when nitrite react sequentially with sulfanilic acid and α-naphthylamine. After adding the reagents, the sample is allowed to react for 20 min and the absorbance at 520 nm is measured.

At the same time, calibration curves and their respective quality controls were processed for the determination of the reactive species. Using these curves, the concentrations of the compounds in mg/L were calculated. The standards and quality controls were prepared with analytical quality drugs, with known concentrations and within the range of the measured concentrations.

Measurements of the reactive species in activated water were made at the end of the plasma treatment, at 5 h and 24 h after treatment, in order to correlate these concentrations with the results obtained in the IC degradation. The treated samples were stored at room temperature (25 ± 2 °C) in sterile flasks, tightly capped and in the dark.

2.4. Modeling of IC Degradation in the Postdischarge Phase

A chemical model to estimate the degradation rate of the IC chromogenic bond in the postdischarge phase via the O=NOOH decomposition was developed. To this end, the value of the third-order rate coefficient for the production of O=NOOH under the conditions considered was obtained [22].

3. Results and Discussion

3.1. pH and Electrical Conductivity in PAW

The levels of pH and electrical conductivity of PAW were measured immediately after treatment with plasma. The variation of these variables can be seen in Figure 3. The pH showed a significant decrease from ≈5.2 to 3.8 with increasing plasma exposure time and decreasing volume (Two-way ANOVA, p < 0.05). The pH variation depends on the type of discharge and gas used. The decrease in the pH of aqueous solutions treated with electrical discharges in air is mostly attributed to the formation of nitric and nitrous acids in solution [17].

The electrical conductivity increased significantly with treatment time for both volumes studied with an approximately linear dependence. For the 50 mL volume, the conductivity reached a significantly higher value, close to double, compared to 100 mL for all plasma exposure times. This is expected due to the higher level of gas–liquid interaction at the interface area in the thinner water layer. The increase in conductivity with plasma exposure time is associated with acidic effects and the formation of NO₂⁻ and NO₃⁻ ions in water [17].

3.2. Concentration of Reactive Species in PAW

In all cases, reactive species increased significantly with plasma exposure time and with decreasing volume of water (two-way ANOVA, p < 0.05) (Figure 4). The increase in the concentration of reactive species as the volume decreases was also documented by other authors [23,24], suggesting that the species responsible for the variation of pH, conductivity and formation of secondary species are formed at the gas–liquid interface and then transferred to the bulk liquid, and that the generation rate of the species does not depend on the treated volume. In plasma–liquid discharges, water evaporation enhances the generation of OH˙ and H₂O₂ in the gas phase, which in turn are transported to the plasma–liquid interface based on their solubility coefficients [12], thus promoting the formation of secondary species in the water phase.

3.2.1. Hydrogen Peroxide

H₂O₂ increased significantly with plasma exposure time (Figure 4), reaching a maximum of ≈7.2 mg/L in 50 mL and ≈3.3 mg/L in 100 mL. H₂O₂ formed in the gas phase by the discharge has a high Henry’s law solubility coefficient (≈9 × 10^–2 M^–3 Pa^–1), so almost all H₂O₂ (g) rapidly transfers to the liquid bulk [12]. Although H₂O₂ has a relatively high oxidation potential, its direct oxidation effect in water is low because it does not react significantly with most organic compounds. However, this species involves processes that affect water chemistry, including the formation of OH˙ radicals by reacting with nitrite through the formation of peroxynitrous acid [17]. Consequently, this advanced oxidation chemistry generates much more reactive species than H₂O₂; for this reason, nonthermal discharges produce very efficient processes for organic-compound degradation and water disinfection.

3.2.2. Nitrate and Nitrite

NO₃⁻ and NO₂⁻ concentrations increased significantly with plasma exposure time, reaching peak values of ≈15.6 mg/L for NO₃⁻ and ≈2.2 mg/L for NO₂⁻ (Figure 4) in 50 mL, obtaining a ratio of 1:7, similar to that established by other authors in solution [10]. Similar concentrations have been described by other authors using plasma equipment with a voltage of 15 kV and exposure time of 5 min [25].

Nitric oxide (NO) formed through dissociated oxygen and nitrogen in air discharges via the Zeldovich reactions reacts with oxygen or ozone to form nitrogen dioxide (NO₂), which upon dissolving in water leads to the formation of NO₂⁻ and NO₃⁻ ions through electron capture by NO₂ or through oxidation of NO [17]:

2 NO₂(aq) + H₂O → NO₂⁻ + NO₃⁻ + 2 H⁺,

(1)

NO(aq) + NO₂(aq) + H₂O → 2 NO₂⁻ + 2 H⁺.

(2)

In these reactions, it can be clearly seen that the formation of these ions in solution contributes to the drop in pH by the release of H⁺ ions into the water.

3.3. Time Evolution of the Concentration of Reactive Species in the Postdischarge

The stability of the reactive species in PAW up to 24 h after treatment is presented in Figure 5. The results corresponded to 50 mL sample volume treated for 30 min. The NO₃⁻ concentration remained stable for 24 h with a value of 15.7 mg/L immediately after treatment, and 15.5 mg/L after 24 h of storage. Similar results were reported by Vlad et al. [24], who showed that nitrate was also stable in solution for 20 days after treatment.

A significant decrease in hydrogen peroxide from 7.1 mg/L to 4 mg/L was observed after 24 h of storage time (Figure 5). Other authors [25,26] have documented decreases in hydrogen peroxide concentration after storage of plasma-treated solutions for 24 h. A significant drop in NO₂⁻ concentration from 2.3 mg/L to 0.5 mg/L at 24 h was also observed. Previous studies have also reported a significant decrease in nitrite and an increase in nitrate concentration after 48 h [25] or 7 days of storage [26]. The NO₂⁻ to NO₃⁻ disproportionation reaction is as follows [17]:

3 NO₂⁻ + 3 H⁺ → 2 NO + NO₃⁻ + H₃O⁺.

(3)

which is strongly pH-dependent and is not expected to be a significant pathway of nitrite loss under the conditions considered (proceeds faster at pH < 3.5). On the other hand, the peroxynitrous acid formation is an important pathway by which nitrite and hydrogen peroxide are consumed in the aqueous phase [17]:

NO₂⁻+ H₂O₂ + H⁺ → O=NOOH + H₂O,

(4)

Reaction (4) is of particular importance in plasmas in contact with water because of the large amount of H₂O₂ produced in discharges of this type. In acidic solutions, the predominant form of peroxynitrite is the protonated form (pKa = 6.8), which decays to OH˙ and NO₂˙ radicals via (5), and to NO₃⁻ via (6), with their corresponding branching values [13]:

O=NOOH → OH˙ + NO₂˙, b%,

(5)

O=NOOH → HNO₃ → NO₃⁻ + H⁺, (1 − b)%.

(6)

b values reported in the literature vary between 0.15 and 0.4 [13]. Although both radicals in reaction (5) can recombine to form nitric acid, the rate constant of that reaction (>3 × 10⁴ L mol⁻¹ s⁻¹) is several orders of magnitude lower than most of the rate constants of the destruction OH˙ reactions (10⁷ ÷ 10¹⁰ L mol⁻¹ s⁻¹), so the reactivity of peroxynitrous acid is determined primarily by the OH˙ radicals formed from (5) [17].

3.4. IC Degradation: Discharge and Postdischarge Effects

Indigo carmine degradation immediately after discharge (0 h) increased with both plasma exposure time and decreasing volume (Two-way ANOVA, p < 0.05), showing a significant difference between treatments. Maximum values for the degradation of the IC unsaturated bond (measured at 285 nm) at 0 h was obtained for a plasma exposure time of 30 min: 81.3% and 86% for sample volumes of 100 mL and 50 mL, respectively (Figure 6a), while corresponding values for the IC chromogenic bond (measured at 610 nm) at the same plasma exposure time were 93.4% and 99.1%, respectively (Figure 6b). These results can be primarily associated to the diffusion into the liquid of O₃ and OH˙ (main oxidizing species for the IC dye [27]) generated in the gas phase through plasma-mediated reactions. It should be noted that due to their short lifetime (<1 ns), plasma-generated OH˙ radicals are not expected to diffuse far beyond a thin boundary layer (of the order of 100 nm to 10 µm) near the gas–liquid interface [13]. As for O₃, it is worth mentioning that despite its hydrophobicity and low Henry’s law diffusion coefficient, the diffusion of O₃ in the liquid volume is favored, since upon entry it reacts with the IC molecule, being rapidly consumed in solution [10].

It is also observed that for low plasma exposure times (<20 min) the IC degradation of both the chromogenic and unsaturated bonds at 24 h post-treatment was higher than 0 h; with the IC degradation for 50 mL being higher than 100 mL (Figure 6). Such a marked difference in the IC degradation between measurements at 0 h and 24 h post-treatment suggests that the OH˙ production in the bulk liquid through the decomposition of the O=NOOH pathway (5) plays a major role in the IC degradation in the postdischarge [13]. Moreover, the difference in IC degradation between volumes could be related to a change in the level of the gas–liquid interaction. As quoted before, the concentration of nitrite and hydrogen peroxide—which increases the availability of OH˙ radicals—significantly increased their concentration at lower volume, leading to more oxidants in solution. However, for higher plasma exposure times, the IC degradation was almost independent of both the volume treated and the post-treatment time, thus indicating that the IC degradation limit was already reached.

3.4.1. Modeling of the IC Degradation in the Postdischarge Phase

In the postdischarge phase (i.e., without the generation of reactive species formed in the gas-phase by the plasma) it is reasonable to assume that the IC chromogenic bond degradation is due to the interaction of the dye molecule with the OH˙ radical, formed through the O=NOOH decomposition in the bulk liquid. The O=NOOH is formed via reaction (4) (i.e., NO₂⁻+ H₂O₂ + H⁺ → O=NOOH + H₂O); and quickly decomposes via (5) and (6) [13]. The formation rate of O=NOOH obtained from reaction (4) is as follows:

d[O=NOOH]/dt = k₄ [NO₂⁻] [H₂O₂] [H⁺],

(7)

where k₄ is the third-order rate coefficient of (4) and [NO₂⁻], [H₂O₂] and [H⁺] are the concentrations of NO₂⁻, H₂O₂ and H⁺, respectively. It is worth noting that estimating the formation rate of O=NOOH (and consequently the formation of OH˙ radicals in solution) necessarily implies knowing the k₄ value, which is pH-dependent. To estimate the k₄ value for the given conditions, the procedure developed by Lukes et al. was followed [22]. Due to the fact that during the postdischarge the pH data remained within a value of 3.87 ± 0.02, the corresponding concentration of H⁺ (=10^−pH) was almost constant. Under such conditions, the third-order reaction (7) can be simplified to a pseudo-second-order reaction as

d[H₂O₂]/dt = −k₄^SO [NO₂⁻] [H₂O₂],

(8)

where k₄^SO ≡ k₄ [H+] is the pseudo-second-order rate constant of reaction (4). Moreover, the rate of O=NOOH formation (7) can be expressed in terms of the rate of disappearance of reactants, as

d[O=NOOH]/dt = −d[NO₂⁻]/dt = −d[H₂O₂]/dt.

(9)

The integration of (8) and (9) between t = 0 and t gives:

ln ([NO₂⁻] [H₂O₂]₀) − ln ([H₂O₂] [NO₂⁻]₀) = k₄^SO ([NO₂⁻]₀ − [H₂O₂]₀) t,

(10)

where the zero subscript indicates species concentrations at t = 0 in the postdischarge. The experimental data for this analysis were used from post-treatment evolution of [NO₂⁻] and [H₂O₂] in a sample volume of 50 mL of PAW treated for 20 min (Figure 7a). The plot of (10) as a function of the time together with the corresponding linear fit is presented in Figure 7b.

It is observed in Figure 7b that the experimental data for H₂O₂ and NO₂⁻ satisfy the expression for the second-order reaction (10), the value of the second-order rate coefficient being determined from the slope k₄^SO ([NO₂⁻]₀ − [H₂O₂]₀). The third-order rate coefficient k₄ was then obtained as k₄ = k₄^SO/[H+] = (1075 ± 200) M⁻² s⁻¹. This value is in very good agreement with that reported by Lukes et al. (1100 M⁻² s⁻¹ for a pH of 3.3) [22], and Damschen et al. (1200 M⁻² s⁻¹ for a pH of 3.8) [28].

It is worth noting that as reactions other than the decomposition of O=NOOH arising from stable RONS in water (i.e., H₂O₂, NO₂⁻, and NO₃⁻) do not significantly oxidize indigo carmine, the measured concentrations of these species in PAW can be used to estimate the corresponding concentrations in IC solution. Measurements of NO₂⁻ and H₂O₂ in PAW and in IC solution were similar (data not shown). Moreover, as the O₃ would react with indigo carmine almost instantly [13], neglectable concentrations of O₃ in IC solution are expected in the postdischarge.

Once the k₄ value was determined for the given experimental conditions, it is possible to model the IC chromogenic bond degradation related to the O=NOOH decomposition based on the following bulk-liquid reactions:

d[IC]/dt = −k₁₁ [IC] [OH˙],

(11)

d[OH˙]/dt = b (0.13 + 0.87 [H⁺]) [O=NOOH] − k_11˙ [IC] [OH˙],

(12)

d[O=NOOH]/dt = k₄ [NO₂⁻] [H₂O₂] [H⁺] − (0.13 + 0.87 [H⁺]) [O=NOOH],

(13)

where (11) corresponds to the IC destruction by the OH˙ radicals, while (12) and (13) correspond to the processes of formation and destruction of OH˙ radicals and ONOO=H, respectively.

Since the timescale for the IC degradation under the given conditions (~1 h) is very large compared to the lifetimes of OH˙ and O=NOOH (the decomposition rate of O=NOOH is 0.13 + 0.87 [H+], s⁻¹ [29]) it is reasonable to assume that such species are in instantaneous equilibrium (i.e., the accumulation terms in (12) and (13) are taken as zero). Under such assumption, (11) can be rearranged as [13]:

d[IC]/dt = − b k₄ [NO₂⁻]₀ [H₂O₂]₀ [H⁺]₀ [IC]/[IC]₀,

(14)

with the branching value b being the parameter of the model. Figure 8 shows the IC degradation yielded by the model for b = 0.4, together with experimental data.

The good agreement between the experimental degradation data for the IC chromogenic bond and those obtained through the model (Figure 8) support the hypothesis that during the postdischarge phase, the most important mechanism of IC discoloration is by interaction with the OH˙ radical formed in the liquid bulk through the decomposition of O=NOOH [13].

3.4.2. Subproducts of the IC Degradation

The degradation of IC in water is a good indicator of the amount of oxygen-based reactive species produced, in particular ozone [30]. The molecule of IC in contact with the reactive species generated by the plasma fragments, leads to the formation of fragmented intermediates, such as isatin-5-sulfonic acid, which gives a yellowish or colorless appearance to the treated solution [30]. One way to corroborate the fragmentation of the IC molecule in isatin-5-sulfonic acid is by measuring the absorbance at 250 nm [10,31] immediately after discharge. Figure 9 shows the significant increase in absorbance at 250 nm for the 50 mL samples of IC treated 30 min.

3.5. Energy Yield G₅₀

The energy yield G₅₀ of the discharge was determined as the ratio between the amount of the converted IC and the energy required for 50% IC conversion: G₅₀ = 1.8 × 10⁶ C₀ V₀ M₀/(P t₅₀) [g/kWh], where C₀ is the molar concentration of the control IC, V₀ is the treated volume in liters, M₀ is the molecular weight of the IC in grams, P is the average power of the plasma reactor in watts, and t₅₀ is the time in seconds required for 50% conversion [16]. Although the G₅₀ value is usually calculated at 0 h, its calculation at 24 h becomes relevant if the treated liquid is not used immediately, having a storage time of at least 1 day. The G₅₀ values obtained at 0 h and 24 h post-treatment are shown in

Table 1. Energy yield G₅₀ for 50 mL and 100 mL of IC solution calculated at 285 nm and 610 nm at 0 h and 24 h post-treatment.

Post-Treatment Time	G50 [g/kWh]
	(at 285 nm)		(at 610 nm)
	50 mL	100 mL	50 mL	100 mL
0 h	5.2	5.2	6	6.2
24 h	15.5	8.5	17	9.6

.

Table 1 shows that regardless of the volume of the sample, the energy yield G₅₀ values calculated at 0 h are almost constant, with a value of around 5 and 6 g/kWh for the unsaturated and chromogenic bonds, respectively, indicating that the ratios t₅₀/V₀ are remarkably constant under the present conditions. These dependences are strengthened by the fact that in the discharge phase both O₃ and OH˙ are mainly formed in the gas phase through plasma-mediated reactions and then transferred to the liquid by diffusion; and that the generation rate of species does not depend on the sample volume. (Note that the rate of degradation through the O=NOOH pathway is dependent on the bulk concentrations of H₂O₂ and NO₂⁻ and thus changes with sample volume.) On the other hand, the energy yield G₅₀ values calculated at 24 h postdischarge decrease noticeably as the sample volume increases. This result is related to the higher concentration of NO₂⁻ and H₂O₂ in aqueous phase at the lower volume, which in turn increases the availability of OH˙ radicals in the liquid bulk through the pathway (5). It is also worth noting that large increases in the energy yield values are observed at 24 h post-treatment due to the beneficial effects induced by the O=NOOH decomposition. For instance, the energy yield G₅₀ for the degradation of the unsaturated bond calculated at 24 h and for the 50 mL volume is higher than that corresponding to 0 h by a factor of about 3. Obtained G₅₀ values are in between typical energy-yield values reported for the IC degradation by pulsed corona discharges in contact with water, ranging from 0.149 g/kWh to 294 g/kWh [16].

4. Conclusions

The degradation of indigo carmine (IC) in water induced by a pulsed positive corona discharge (pulse energy of 21 mJ at a repetition rate of 42 Hz) operating in ambient air was investigated. Degradation levels of two different volumes (50 and 100 mL) of IC in solution with distilled water treated with different plasma exposure times (10–30 min) immediately after discharge (0 h), and after 24 h were examined. The results show that:

• The OH˙ radical plays a primary role in the IC degradation. While both O₃ and OH˙ contribute to the IC degradation in the discharge phase, the OH˙ radical contributes in the postdischarge phase. While both O₃ and OH˙ are mainly generated in the gas phase and then transferred to the liquid in the discharge phase, the OH˙ radical is mainly produced through the O=NOOH decomposition in the postdischarge phase. Noticeably, increases in the energy yield values are observed at 24 h post-treatment due to the beneficial effects induced by the O=NOOH decomposition.
• Maximum values for the degradation of the IC unsaturated bond at 0 h were obtained for a plasma exposure time of 30 min: 81.3% and 86% for sample volumes of 100 mL and 50 mL, respectively; while corresponding values for the IC chromogenic bond at the same plasma exposure time were 93.4% and 99.1% for sample volumes of 100 mL and 50 mL, respectively.
• For low plasma exposure times (<20 min) the IC degradation of both the chromogenic and unsaturated bonds at 24 h post-treatment was higher than 0 h; being the IC degradation for 50 mL higher than 100 mL. However, for higher plasma exposure times the IC degradation was almost independent of both the volume treated and the post-treatment time.
• Concentrations of reactive species in the aqueous phase at 0 h increased with the plasma exposure time and decreased with increasing sample volume. The maximum values reached being 7.25 mg/L for H₂O₂, 15 mg/L for NO₃⁻ and 2 mg/L for NO₂⁻. While the concentrations of NO₂⁻ and H₂O₂ decreased with post-treatment time, the NO₃⁻ concentration remained stable.