HCOO − aq degradation in droplets by OH aq in an atmospheric pressure glow discharge

Plasmas in contact with liquids can degrade organic molecules in a solution, as reactive oxygen and nitrogen species produced in the plasma solvate into the liquid. Immersing small droplets (tens of microns in diameter) in the plasma can more rapidly activate the liquid compared to treating a large volume of liquid with a smaller surface-to-volume ratio. The interactions between a radio frequency glow discharge sustained in He/H 2 O and a water droplet containing formate (HCOO − aq ) immersed in and flowing through the plasma were modeled using a zero-dimensional global plasma chemistry model to investigate these activation processes. HCOO − aq interacts with OH aq , which is produced from the solvation of OH from the gas phase. The resulting HCOO − aq concentrations were benchmarked with previously reported experimental measurements. The diameter of the droplet, initial HCOO − aq concentration, and gas flow rate affect only the HCOO − aq concentration and OH aq density, leaving the OH density in the gas phase unaffected. Power deposition and gas mixture (e.g. percentage of H 2 O) change both the gas and liquid phase chemistry. A general trend was observed: during the first portion of droplet exposure to the plasma, OH aq primarily consumes HCOO − aq . However, O 2 − aq , a byproduct of HCOO − aq consumption, consumes OH aq once O 2 − aq reaches a critically large density. Using HCOO − aq as a surrogate for OH aq -sensitive contaminants, combinations of residence time, droplet diameter, water vapor density, and power will determine the optimum remediation strategy.

Plasmas in contact with liquids can degrade organic molecules in a solution, as reactive oxygen and nitrogen species produced in the plasma solvate into the liquid. Immersing small droplets (tens of microns in diameter) in the plasma can more rapidly activate the liquid compared to treating a large volume of liquid with a smaller surface-to-volume ratio. The interactions between a radio frequency glow discharge sustained in He/H 2 O and a water droplet containing formate (HCOO − aq ) immersed in and flowing through the plasma were modeled using a zero-dimensional global plasma chemistry model to investigate these activation processes. HCOO − aq interacts with OH aq , which is produced from the solvation of OH from the gas phase. The resulting HCOO − aq concentrations were benchmarked with previously reported experimental measurements. The diameter of the droplet, initial HCOO − aq concentration, and gas flow rate affect only the HCOO − aq concentration and OH aq density, leaving the OH density in the gas phase unaffected. Power deposition and gas mixture (e.g. percentage of H 2 O) change both the gas and liquid phase chemistry. A general trend was observed: during the first portion of droplet exposure to the plasma, OH aq primarily consumes HCOO − aq . However, O 2 − aq , a byproduct of HCOO − aq consumption, consumes OH aq once O 2 − aq reaches a critically large density. Using HCOO − aq as a surrogate for OH aq -sensitive contaminants, combinations of residence time, droplet diameter, water vapor density, and power will determine the optimum remediation strategy.
Keywords: atmospheric pressure plasma, droplet activation, modeling, formate degradation (Some figures may appear in color only in the online journal) * Author to whom any correspondence should be addressed.
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Introduction
Atmospheric pressure plasmas in contact with liquids are used in a wide variety of applications, including water treatment, plasma electrolysis, and plasma medicine [1][2][3]. These applications rely on plasma-produced reactive oxygen and nitrogen species (RONS) solvating into the liquid and chemically activating the liquid.
In most reactor configurations, transport limits the activation of the liquid through both solvation of the RONS in the gas into the liquid and transport of the RONS in the liquid. RONS produced in the plasma need to transport to the surface of the liquid to solvate. If the liquid is immersed in the plasma in the form of droplets, the distance between where the RONS are produced and the liquid can be shortened, and this transport limit can be mitigated. Once the RONS reach the surface of the liquid, these species need to transport from the surface into the bulk of the liquid. One way to mitigate this limit is to have a high surface-to-volume ratio (SVR) of the liquid, which decreases the time it takes for the RONS to transport from the surface into the bulk liquid. Using small water droplets (aerosols) in the plasma reduces both of the limits imposed by transport [4].
Experiments have shown how SVR influences the concentrations of RONS in a liquid. Hassan et al compared the solvation of H 2 O 2 (high Henry's law constant) and O 3 (low Henry's law constant) into bulk liquid and electrosprayed droplets [5]. They showed that increasing the surface area between the gas and liquid increased the concentration of H 2 O 2aq and O 3aq . (The aq subscript denotes a solvated or aqueous species.) However, their results showed that the H 2 O 2aq concentration was only four orders of magnitude larger than the O 3aq concentration, despite the difference in the Henry's law constants being seven orders of magnitude. This difference was attributed to the depletion of H 2 O 2 in the gas phase before the liquid reached Henry's law saturation. Liu  aq ) in water increase as the SVR increases [6]. Liu et al further showed that cancer cell-containing media treated with plasmaactivated water with a higher SVR were more effective at producing cell death due to the higher concentrations of RONS in the solution.
Plasma has been proposed as an advanced oxidation process to remove organic pollutants from water [1]. Singh et al used plasma sustained in Ar to treat landfill leachate samples containing per-and polyfluoroalkyl substances (PFAS) [7]. The perfluoroalkyl acids (PFAAs) and precursors were transported to the liquid surface by bubbling Ar through the liquid, forming a foam at the surface. Singh et al showed that over 90% of perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) and over 99.9% of long-chain PFAAs were degraded within 10 min of treatment by plasma. Jose and Philip used air plasma to degrade four toxic volatile organic compounds commonly found in pharmaceutical wastewater [8]. The water was sprayed into the plasma reactor and recirculated. For a hydraulic retention time of 33.3 min, over 90% of the four volatile organic compounds were removed.
Using samples of pharmaceutical wastewater, instead of prepared solutions, over 90% of the volatile organic compounds were removed by plasma treatment. Jaiswal and Aguirre compared the effectiveness of He and Ar atmospheric pressure plasma jets (APPJs) on degrading methylene blue dye [9]. They observed that the Ar APPJ was more effective at degrading methylene blue compared to the He jet, an outcome they attributed to increased fluxes of oxygen radicals onto the solution produced by the Ar APPJ. Casado et al used an Ar plasma jet to degrade benzene present on top of a water layer [10]. They showed that phenol, catechol, and nitrobenzene were the main products formed from plasma interaction with benzene. These molecules are formed by benzene reactions with OH aq and NO 2aq , likely formed by interactions between the ambient air and Ar excited states.
Sremački et al injected aerosol droplets (about 22 µm) into an Ar plasma jet to observe changes to the RONS and ultraviolet (UV) radiation from the plasma [11]. Aerosols in the plasma decreased the UV radiation by absorbing the radiation in the gas phase, and gas phase reactive oxygen species (ROS) were also decreased. Products of the reactions between OH aq and cysteine, used as a model biological molecule and dissolved in the aerosol, were detected. Cysteine conversion was highest when the bulk liquid was exposed to the plasma, presumably due to the increase in UV photons. Plasmas have also been shown to inactivate bacteria and viruses in a solution. Xia et al used a packed-bed dielectric barrier discharge to inactivate viruses in aerosols in the plasma [12]. At least a 2.3 log reduction in the infectious virus concentration was observed in this reactor.
With the goal of investigating the transport of plasmaproduced ROS to droplets in a plasma, we have computationally investigated the degradation of formate (HCOO − aq ), a model organic compound, by OH aq , a short-lived reactive species produced by gas phase reactions and solvation into the droplet. The effect of in-droplet reactions such as UV/vacuum UV (VUV) photolysis are also discussed. HCOO − aq is dissolved in a water droplet (tens of microns in diameter) immersed in an atmospheric pressure He/H 2 O radio frequency (RF) glow discharge. Previous experimental work in this reactor is described in Nayak et al and Oinuma et al [13][14][15][16]. Nayak et al measured the electron temperature and density in plasmas formed in this reactor sustained in He and Ar, as well as He metastable densities [13,14]. In Oinuma et al, droplets with 2 mM HCOO − aq , produced by hydrolysis of formic acid HCOOH aq , flowed through the He/H 2 O plasma [15]. The droplets were exposed to OH formed in the gas phase that then solvates into the droplet. The HCOO − aq concentration after exposure to the plasma was measured, and the change in HCOO − aq concentration gave an estimate of OH transport into the droplet. Results of a one-dimensional (1D) reaction-diffusion model showed that the interaction between OH aq and HCOO − aq happened primarily at the surface of the droplet. Nayak et al investigated the effects of other reactive species on the HCOO − aq concentration in the same reactor and found that, besides OH aq , another reactive species that may consume HCOO − aq is O aq [16].
Using a global plasma chemistry model, the interactions between the plasma-produced ROS and a droplet were modeled for a reactor based on the experimental work by Nayak et al and Oinuma et al [13][14][15][16]. The global plasma chemistry model incorporates a local diffusion length from the plasma to the droplet and a reactive layer at the surface of the droplet. The base case (1 atm, He/H 2 O = 99.8/0.2, 14.3 W) has a water droplet 41 µm in diameter with an initial HCOO − aq concentration of 2 mM and has a transit time of 10 ms through the plasma with an additional 10 ms flow time before collection. The consequences of plasma-produced OH on HCOO − aq degradation is discussed, as is the influence of the photolysis of H 2 O. In the liquid phase, the concentration of HCOO − aq decreases due to reactions with OH aq that consume the OH aq . As the HCOO − aq is decreased, the primary consumption of OH aq changes to reactions with the products of HCOO − aq degradation. The consequences of gas mixture, droplet diameter, initial HCOO − aq concentration, flow rate (residence time), and power are discussed.
In section 2, the model and conditions used in this study are described, as well as a brief description of the experiments the modeling is based on. The plasma properties and gas and liquid phase species densities are discussed in section 3. These properties are discussed in section 4 while varying the droplet diameter, initial HCOO − aq concentration, flow rate, power, gas mixture, and water percentage in the inlet gas mixture. Concluding remarks are shown in section 5.

Description of the model and experiments
This investigation was performed with the global plasma chemistry model GlobalKin to simulate conditions based on the experiments performed by Oinuma et al and Nayak et al [15,16]. The plasma reactor used by Nayak et al and Oinuma et al is an atmospheric pressure radio frequency glow discharge formed between two parallel plate electrodes separated by 2 mm and which are 9.5 mm long. A schematic of the reactor is shown in figure 1(a). Water droplets are released from a dispenser and pass through the plasma entrained in the gas flow, spending around 10 ms in the plasma depending on the flow rate of the gas. After flowing through the plasma, the droplets are frozen on an ultra-thin glass cover slip placed on an aluminum insert at the bottom of the reactor, which was kept at a temperature below freezing to preserve the exposed liquid for later chemical analysis. For the base case, a 2 mM solution of formic acid, HCOOH aq , was used. The formic acid hydrolyzes to produce formate (HCOO − aq ) and hydronium (H 3 O + aq ). HCOO − aq reacts with OH aq in the droplet, largely resulting from the solvation of OH produced in the plasma. Measuring the change in the HCOO − aq concentration gives a measure of the OH transport to or formation of OH aq in the droplet. Further details on the experiments, including details of the measurements performed and the reactor, can be found in Nayak et al and Oinuma et al [13][14][15][16].
GlobalKin has been described previously in Lietz and Kushner [17] and so will only be briefly discussed here. As  [18]. (b) Schematic of the primary processes in the HCOO − aq reaction mechanism. Reprinted from [18], with the permission of AIP Publishing. a global model, GlobalKin is zero-dimensional (0D), with the gas and liquid phases treated as separate, well-mixed volumes. Each gas phase species has a matching liquid phase species, interacting by solvation of the gas phase species into the droplet or desolvation of the aqueous species into the gas phase. Each species density is determined by their individual rate equation, including sources and losses due to reactions and diffusion to surfaces. Charged particles diffuse to surfaces based on their ambipolar diffusion coefficient. The diffusion coefficient of negative ions is scaled by a Boltzmann factor to account for the negative ions having to climb the potential barrier intended to confine electrons. The electron energy conservation equation determines the electron temperature in the gas phase based on the specified power. In this global model, power is specified and there is no explicit dependence on, for example, RF frequency. Electron-impact rate coefficients are calculated by solving Boltzmann's equation for the electron energy distribution in the steady state.  Transport of species from the gas phase into the liquid occurs as a result of the liquid being treated as a surface in contact with the plasma. The loss of gas phase species to the liquid is then a function of the specified surface area of the liquid. For neutral species, Henry's law equilibrium determines the transport between the liquid and the gas. A diffusion flux of neutral species from the gas phase to the liquid is calculated. If the liquid is not saturated with the aqueous analogue of the gas phase species, a flux of gas phase species is allowed to diffuse into the liquid where the gas phase species is converted into its solvated analogue. If the liquid is super-saturated, there is a desolvation flux of liquid phase species into the gas that are then converted back into gas phase species. Charged species directly solvate into the liquid. Evaporation of the liquid into the gas phase occurs by specifying a vapor pressure of the liquid at the surface of the droplet. Diffusion of the liquid vapor then occurs from the droplet into the bulk until the gas phase reaches the saturated vapor pressure.
GlobalKin allows for two diffusion lengths to account for transport processes to surfaces: one to solid surfaces in contact with the plasma, and one to liquid in contact with the plasma. The diffusion length to surfaces in contact with the plasma is dominated by the parallel electrodes bounding the plasma, having a gap of 2 mm. Transport to these surfaces produces a diffusion length of 0.637 mm. Transport from the bulk plasma to the droplet is through a gas boundary layer surrounding the droplet, producing a diffusion length to the droplet of 100 µm.
The residence time of the droplet in the plasma, about 10 ms in the base case, is too short for solvating species to diffuse throughout the volume of the droplet. To account for the finite plasma exposure time, a reactive layer of finite thickness is specified at the droplet surface. Doing so divides the liquid volume into a surface layer in which plasma-initiated reactions occur and a nonreactive core. This formulation accounts for short-lived species in the droplet, in particular OH aq , not being uniformly distributed throughout the droplet. These short-lived species are instead found near the droplet surface. As shown by Oinuma et al, the density of HCOO − aq is degraded at the droplet surface while being only nominally changed in the center of the droplet [15]. Specifying the reactive layer thickness in GlobalKin therefore limits the amount of HCOO − aq that the OH aq can interact with during the finite transit time of the droplet through the reactor. The species densities produced by GlobalKin are only for this reactive layer. In the experiments, the total average density of species in the droplet is measured. The total average density n t in the droplet in the model is then calculated from where x i is the initial mole fraction of the species, 3.347 × 10 22 cm −3 is the density of liquid water, V c is the volume of the nonreactive core, n l is the species density in the reactive layer, V t is the total volume of the droplet, and V l = V t − V c is the volume of the reactive layer. If the species is not initially present in the solution (i.e. the initial mole fraction is zero), the total density is simply n l V l /V t . There is no interaction between the reactive layer and the nonreactive core.
The reaction mechanism includes 112 gas phase species and 123 liquid phase species, listed in table 1. Note that each gas phase species has a liquid phase counterpart, and some species only exist in the liquid. There are 3027 gas phase reactions and 331 liquid phase reactions including reactions involving photons. The gas phase reaction mechanism is based on Van Gaens and Bogaerts [19] with updates to include He made by Norberg [20]. Updates were also made based on branching ratios to produce excited states in recombination of He + and He 2 + from Emmert et al [21]. Two gas mixtures examined include both He and Ar, and their interactions are included and based on [22]. The liquid phase reaction mechanism is based on [23] and [17]. The rates for interaction of He excited states and ions with H 2 O aq were estimated to be fast relative to other reactions and based on branching ratios from [23] and [24].
Additional reactions to address HCOO − aq were included based on the reaction mechanism in Oinuma et al [15]. In this reaction mechanism, HCOO − aq is consumed by OH aq and H aq , producing H 2 O aq or H 2aq and CO 2 − aq . Changes to the liquid phase reaction mechanism relative to Lietz and Kushner [17] are shown in table 2. Henry's law constants are taken from Sander [25] and are listed in table 3. A Henry's law constant greater than 1 indicates that, at equilibrium, the density of the species in the liquid will be larger than that in the gas. A Henry's law constant less than 1 means the density of the species in the gas will be larger than that in the liquid at equilibrium.
Photodissociation and photoionization of H 2 O aq are included in GlobalKin. UV/VUV photons are emitted from resonant states (Ar(1s 2 ), Ar(1s 4 ), Ar(4D), He(2 1 P), He(3P)) and dimer states (Ar 2 * and He 2 * ) of noble gases. Photons are emitted with the natural lifetime of the state and leave the system based on transit time across the plasma. For the resonant states, photons are reabsorbed from the ground state to produce the corresponding resonant state. Using this technique, radiation trapping factors are not explicitly used but naturally result from the reabsorption and residence time of photons in the plasma. Reabsorption does not occur for the radiation emitted by dimers, as the dimers fragment into two ground state atoms upon emitting the photon and so have no absorbing ground state. To account for the small area of the droplet, the gas phase radiation in the plasma is shadowed by a flux that separately interacts with the H 2 O aq in the droplet. Sander et al have shown that, in liquid H 2 O, the threshold for photoionization and photodissociation is lower than in the gas phase [26]. Therefore, all of the UV/VUV photons, including those emitted from Ar states, can interact with H 2 O aq . The UV/VUV photons photoionize H 2 O aq , producing H 2 O + aq and e aq , and photodissociate H 2 O aq , producing H aq and OH aq .
The water droplets were prepared by dissolving equimolar amounts of formic acid HCOOH aq and NaOH aq into distilled water [15]. The initial conditions used in GlobalKin for the liquid includes 2 mM H 3  Simulations using GlobalKin address the volume between the electrodes in the reactor (19.1 mm × 9.5 mm × 2 mm). The flow rate varies from 0.75 slm to 3 slm, and the resulting residence times are shown in table 5 [16]. The base case has a flow rate of 1 slm, corresponding to a residence time in the plasma of 10 ms. The power is specified as nearly a square wave in time, with a 0.1 ms ramp up and ramp down, and the power is kept constant for the residence time. The power varies depending on the gas mixture used, as shown in table 6. The simulation ends after the plasma residence time plus 10 ms; the latter period accounts for the flow of the gas and droplet to the collection surface. The electron temperature is set to 0.025 eV at 0.2 ms after the power has ramped down. Since the vast majority of electrons have recombined or attached by this time, this assignment of electron temperature does not affect the results of the simulation but does eliminate numerical problems. (Electron temperature in the simulation is obtained from dividing electron energy density by electron density. When both electron energy density and electron density trend towards zero, the system becomes numerically stiff.) Each gas mixture includes impurities as measured in Nayak et al (2.3 ppm H 2 O, 1.5 ppm O 2 , and 6.0 ppm N 2 ) [14]. While these impurities were measured in pure He, they were applied to all gas mixtures in this study.

Degradation of HCOO − aq by OH aq
The reaction mechanism in the liquid primarily involves HCOO − aq , OH aq , CO 2 − aq , O 2 − aq , and HO 2 − aq . A schematic representation of the dominant reactions in the mechanism is shown in figure 1. The HCOO − aq dissolved in the droplet undergoes a reaction with OH aq , forming CO 2 − aq and H 2 O aq . This reaction is the dominant consumption mechanism of OH aq in the liquid during the first part of the residence time. While HCOO − aq also reacts with H aq , this reaction is much less important than the reaction with OH aq due to the order of magnitude lower rate coefficient and order of magnitude lower density of H aq due to its smaller Henry's law constant. During the second part of the residence time, OH aq reacts with the byproducts of HCOO − aq degradation. Once the power turns off (or, equivalently, the droplet exits the plasma region), and the source of OH aq from the solvation from the gas phase decreases, the reactions with the byproducts of HCOO − aq degradation will usually consume the remaining OH aq . The CO 2 − aq that is formed from the reaction of OH aq and HCOO − aq then reacts with O 2aq in a charge-exchange reaction, forming CO 2aq and O 2 − aq . As O 2aq is not a reactive species and is instead found in the liquid due to the initial conditions (table 4) or due to solvation of the impurity, the charge-exchange reaction occurs when CO 2 − aq is available.

Reactive layer thickness
Before investigation of the HCOO − aq degradation and reactive species densities, the thickness of the reactive layer was determined. The droplet is divided into two zones: the reactive layer and the nonreactive core. The reactive layer and nonreactive core do not interact throughout the simulation. The thickness of the reactive layer limits the amount of HCOO − aq that can be consumed by OH aq during the transit of the droplet through the reactor. The thickness of the reactive layer was determined by performing simulations varying the thickness from 1 µm to 20.5 µm, where for the maximum thickness the entire droplet is considered reactive. The reactive layer thickness was then chosen to best match the experimental measurements of droplet averaged concentration of 0.76 mM HCOO − aq remaining after plasma treatment. The remaining HCOO − aq concentrations after plasma activation and post-plasma flow for varying reactive layer thicknesses are shown in figure 2. As the reactive layer thickness increases, the volume of the reactive layer increases compared to the nonreactive core, and the total inventory of HCOO − aq in the reactive layer increases. As the amount of HCOO − aq in the reactive layer increases, more HCOO − aq can be consumed by the OH aq during the residence time of the droplet in the plasma. The reactive layer thickness that best matches the experimental measurements is 6 µm, with a remaining droplet averaged HCOO − aq concentration of 0.75 mM. 6 µm was used as the reactive layer thickness at 1 slm, which agrees well with the 1D simulations of Oinuma et al [15]. This reactive layer thickness is similar to the diffusion length in the 10 ms residence time. The diffusion length is proportional to √ tD, where t is the time and D is the diffusion coefficient. The diffusion length in the liquid is 3.8 µm for this system, similar to the 6 µm reactive layer thickness determined to best match experimental measurements.

Plasma properties and reactive species densities
The plasma properties for the base case are shown in figure 3(a). The electron density is initialized at 10 8 cm −3 . As the power ramps up, the electron temperature increases and is maximum at 0.15 µs at 3.7 eV, avalanching the plasma. As the power continues ramping up over 0.1 ms, the electron density increases, and the electron temperature slightly decreases. After about 3.5 ms, a steady state is reached in both the electron temperature and density, 1.8 × 10 11 cm −3 and 2.6 eV. After the power ramps down, the electrons are quickly consumed primarily by dissociative recombination as the electron temperature decreases.
The densities of OH and H 2 O 2 in the gas phase are shown in figure 3(b). When the power first turns on, the density of OH rapidly increases to 1.9 × 10 14 cm −3 due to electronimpact dissociation of H 2 O. At the location of the maximum in the density of OH, the electron temperature is higher than its steady state value, and the electron density is increasing to its steady state value, leading to an increase in OH production. As the electron density and temperature reach their steady state values, the density of OH slightly decreases to its steady state value of 1.5 × 10 14 cm −3 , balancing losses due to gas phase reactions and solvation into the droplet, and the source of OH due to the electron-impact dissociation of H 2 O. Once the power turns off, and the electron temperature and density rapidly decrease, the production of OH by electron-impact dissociation ceases. The remaining OH is rapidly consumed due to reactions that form H 2 figure 3(c). These densities are shown in the reactive layer only and are not scaled to a droplet average as described by equation (1). The density of OH aq increases rapidly during the first 0.2 ms, due to the solvation of gas phase OH. The density of OH aq increases throughout the first 6.4 ms. The gas phase plasma supplies a nearly constant source of OH, and since OH has a moderately high Henry's law constant of 620, OH readily solvates into the droplet. Photodissociation is not an important source of OH aq due to the low densities of emitting He states, which are quenched by reactions with H 2 O and impurities. In the first 5.5 ms, the main consumption mechanism of OH aq in the droplet is its reaction with HCOO − aq . As the HCOO − aq density decreases in the reactive layer due to reactions with OH aq , the OH aq density increases because its rate of consumption decreases while having a nearly constant source due to solvation of gas phase OH. The density of OH aq reaches a maximum at 6.4 ms, or 3.7 ms before the power begins ramping down, at a value of 9.3 × 10 13 cm −3 . At this point, much of the HCOO − aq in the reactive layer has been consumed.  The results from the model are compared to the experimental measurements in table 7. The electron density and temperature are reactor averaged values, while the experimental values result from optical emission measurements emphasizing properties where the He atoms are excited [13]. Given these differences, agreement is good. The OH density and HCOO − aq concentration are also shown in table 7. The HCOO − aq concentration predicted by the model is averaged over the reactive layer and nonreactive core, as described by equation (1). The model underpredicts the measured OH density by a factor of 2. In the global model, any OH in the gas phase can solvate into the droplet. Since OH does not reach Henry's law equilibrium in the droplet, OH in the gas phase constantly solvates into the liquid phase in the model. However, in the experiments, OH must be near the droplet to solvate into the droplet, resulting in local depletion of the OH. This limits the amount of OH that can solvate into the droplet and increases the OH in the gas phase relative to the model. The HCOO − aq concentration predicted by the model matches the experimental measurements well, as the reactive layer thickness was chosen to match the measured HCOO − aq concentration.

OH, OH aq , and HCOO − aq variation with liquid and plasma properties
The decomposition of HCOO − aq in the droplet depends on the properties of the droplet and the plasma. In this section, the properties of the droplet (diameter and initial HCOO − aq concentration) and of the plasma (gas flow rate, power deposition, gas mixture) are varied, and the effects on the densities of OH, OH aq , and HCOO − aq are discussed. The reactive layer thickness was kept constant at 6 µm at all flow rates of 1 slm.

Droplet diameter
Varying the droplet diameter varies the total inventory of HCOO − aq in the droplet and therefore also varies the time required to consume HCOO − aq . The reactive layer thickness was kept constant at 6 µm regardless of the diameter.
The variation of the density of OH with droplet diameter and SVR is shown in figure 4. OH density was recorded at 10.1 ms, the time that the power begins to ramp down, corresponding to the time the droplet exits the plasma. The OH density does not significantly vary with droplet diameter or SVR and is nearly constant at 1.5 × 10 14 cm −3 . Therefore, increasing the droplet diameter does not significantly affect the gas phase plasma. In particular, the droplet diameter does not affect the H 2 O density in the gas phase. This is because the majority of H 2 O in the gas phase does not come from evaporation of the droplet; rather, it comes from the 0.2% H 2 O in the gas mixture.
While the gas phase OH does not vary with droplet diameter or SVR, OH aq and HCOO − aq do vary with droplet diameter and SVR, as shown in figure 4. Both the OH aq density and HCOO − aq concentration are averaged over the reactive layer and nonreactive core, as described by equation (1). OH aq density was recorded at 10.1 ms, and HCOO − aq concentration in the droplet was calculated after an additional 10 ms corresponding to flow to the collector. For all droplet diameters, HCOO − aq density in the reactive layer was low, decreasing to 6.3 × 10 16 cm −3 for an 81 µm diameter droplet and 1.7 × 10 16 cm −3 for a 21 µm diameter droplet at the time of collection. The HCOO − aq density in the nonreactive core of the droplet remains constant at 1.2 × 10 18 cm −3 . With small droplet diameters, the reactive layer constitutes most of the volume of the droplet (i.e. at 21 µm, the reactive layer is 92% of the total droplet volume). However, as the droplet diameter increases, the reactive layer is progressively a smaller fraction of the volume of the droplet, decreasing to 38% of the total droplet volume at a diameter of 81 µm. Therefore, as the diameter increases (SVR decreases), the HCOO − aq concentration remaining in the droplet becomes more dependent on the concentration in the core and therefore increases. This variation is in fact linear with SVR.
OH aq is only present in the reactive layer and not in the nonreactive core of the droplet. Therefore, its density is scaled by the volume of the reactive layer over the total volume. As the diameter increases, OH aq in the reactive layer peaks later and at smaller densities during the power-on period. However, as the power begins to turn off at 10.1 ms, OH aq in the reactive layer increases as the diameter increases. This increase occurs because O 2 − aq in the reactive layer decreases as the diameter increases, consuming less OH aq . However, when averaged over the reactive layer and nonreactive core, as shown in figure 3, OH aq decreases as the diameter increases. As the diameter increases, the relative volume of the nonreactive core compared to the reactive layer increases, decreasing the droplet-averaged density. This variation is again linear with SVR.
The HCOO − aq concentrations in the droplet are compared to the experimental measurements in table 8 for three different droplet diameters. At 36 µm and 41 µm, the HCOO − aq concentrations predicted by the model match the measurements within uncertainty. However, at 56 µm, the model predicts 1.02 mM of HCOO − aq remaining, while the measurements show 1.61 mM of HCOO − aq remaining. This discrepancy may be a consequence of the effective reactive layer thickness being smaller for a diameter of 56 µm, as can be deduced from HCOO − aq diffusion profiles calculated by a 1D model [15]. Varying the initial concentration of HCOO − aq in the droplet varies the total inventory of HCOO − aq in the droplet and the time required to consume HCOO − aq for otherwise constant plasma conditions. The initial concentration of HCOO − aq also changes the initial mole fractions of HCOO − aq , Na + aq , and HCOOH aq , as shown in table 4.
The variation of the density of OH with initial HCOO − aq concentration is shown in figure 5 as the power begins to ramp down (10.1 ms) when the droplet leaves the plasma. The OH density does not significantly vary with initial HCOO − aq concentration, demonstrating that gas phase plasma is not strongly affected by the initial composition of the droplet. In order for the composition of the droplet (of a fixed diameter) to affect the gas properties, the rate of solvation of a gas phase species (or desolvation of an aqueous species) would need to significantly change with initial concentration. This would require that the aqueous analogue of a gas species becomes saturated (or supersaturated) in the droplet in a manner that is sensitive to the initial concentration. This would likely occur only for species with small Henry's law constants. Since the gas phase species of interest (i.e. OH, H 2 O 2 ) have moderate to large Henry's law constants and do not saturate in the droplet, gas phase properties are not sensitive to the initial HCOO − aq concentration.
While the gas phase density of OH does not vary with initial HCOO − aq concentration, OH aq at the time the power begins to ramp down (10.1 ms) or exit from the plasma and HCOO − aq after an additional 10 ms of flow time do vary, as shown in figure 5. The densities of OH aq and HCOO − aq were averaged over the droplet, as described in equation (1). At low initial For initial HCOO − aq concentrations of 2 mM and 3.5 mM, the density of HCOO − aq decreases in the reactive layer by at least 75%, but O 2 − aq has a density at least 33% of the HCOO − aq concentration before the power turns off and begins consuming OH aq . As the initial HCOO − aq concentration increases, more HCOO − aq remains in the reactive layer after plasma treatment. In fact, at 10 mM initial HCOO − aq concentration, the remaining density in the reactive layer is 4 × 10 18 cm −3 (initial density is 6 × 10 18 cm −3 ). Therefore, the total HCOO − aq concentration is not only due to the nonreactive core; the reactive layer still has a significant amount of HCOO − aq remaining. Above an initial HCOO − aq concentration of 5 mM, at least 2 mM of HCOO − aq is degraded by OH aq . Since HCOO − aq is not depleted in the reactive layer at high initial HCOO − aq concentrations, the density of OH aq density is low, as it is still actively being consumed in the reaction with HCOO − aq . The density of O 2 − aq is over a factor of 3 lower than HCOO − aq , implying that the consumption of OH aq by O 2 − aq is not dominant.

Gas flow rate
Varying the gas flow rate changes the residence time of the droplet in the plasma. At low gas flow rates, the residence time of the droplet in the plasma is long; at high gas flow rates, the residence time of the droplet in the plasma is short. The flow rates and corresponding residence times are listed in table 5 and are primarily taken from the experimental work in Nayak et al [16]. The residence time also affects the diffusion of reactants in the droplet and therefore changes the reactive layer thickness. Since the diffusion length is proportional to √ t, the reactive layer thickness was scaled by the square root of the residence time relative to that for 1 slm. The values for the reactive layer thickness are also listed in table 5.
The OH density as the power begins to ramp down (droplet exiting the plasma) is shown in figure 6(a). Note that this time varies depending on the flow rate. The gas phase OH density  [16]. Aqueous quantities are averaged over the droplet.
does not depend on the flow rate. As shown in figure 3(b), the density of OH reaches a near steady state after 2 ms. This steady state value will not depend on flow rate or residence time unless the water density is depleted.
The OH aq density averaged over the droplet as the power begins to ramp down is shown in figure 6(a), and the HCOO − aq concentration at the residence time plus 10 ms averaged over the droplet is shown in figure 6(b). These aqueous densities are averaged over the droplet, as described by equation (1). The OH aq density increases from 0.75 slm to 2.5 slm. At 0.75 slm (13.5 ms residence time), the OH aq density reaches a maximum near 6.8 ms. However, at 0.75 slm, the maximum occurs 6.8 ms before the power begins to ramp down (end of the plasma channel), and the density of OH aq decreases due to consumption by O 2 − aq . At 1 slm, the maximum in OH aq density occurs 3.7 ms before the power ramps down, and so the decrease in the density OH aq due to competing reactions is less in the remaining 3.7 ms. As the flow rate continues increasing to 2 slm, the maximum in OH aq occurs closer to when the power ramps down. At 2.5 slm, the maximum in OH aq density occurs just as the power begins to ramp down, and so the density of OH aq does not decrease.
The droplet averaged HCOO − aq concentration increases from 0.75 slm to 2.5 slm. This increase in HCOO − aq concentration is due to the decrease in the reactive layer thickness and decrease in residence time. The OH aq has less HCOO − aq to interact with as the reactive layer thickness decreases, which increases the remaining inventory when averaged over the entire droplet. The OH aq also has less time to interact with the HCOO − aq in the reactive layer, leading to a small increase in HCOO − aq density. As the flow rate increases beyond 2.5 slm (residence time decreases below 5.7 ms), the OH aq density decreases and HCOO − aq density increases. As the residence time decreases, the HCOO − aq density in the reactive layer increases both as a result of there being less time for the OH aq to react with HCOO − aq as well as the decrease in reactive layer thickness. Therefore, the OH aq density decreases, as it is consumed in the reaction with HCOO − aq , and, to a lesser extent, O 2 − aq . The measured HCOO − aq concentrations are also shown in figure 6(b), increasing as the flow rate increases. The HCOO − aq concentrations predicted by the model follow the same trend. At low flow rates (<1.5 slm), the HCOO − aq in the reactive layer is depleted to less than 5% of its initial value. However, the decrease in the reactive layer thickness with increasing flow rate (smaller residence time) means less HCOO − aq in the droplet is in the reactive layer and available to react with the OH aq . In the experiments, HCOO − aq at the surface of the droplet is depleted but may be replenished by diffusion from the interior of the droplet. At lower flow rates (longer residence times), HCOO − aq has more time to diffuse from the center of the droplet to the surface, resulting in more HCOO − aq being consumed. While this process is not directly included in the model, the change in reactive layer thickness with flow rate approximates this process.

Power deposition
Power deposition in the He/H 2 O plasma was increased and decreased from the base case of 14.3 W. As the power deposition increases, the electron density increases, leading to more electron-impact collisions and more reactive chemistry. The OH and H 2 O densities in the gas phase are shown in figure 7 as the power begins to ramp down (10.1 ms). At low power (<14.3 W), the OH density increases as the power increases as the steady-state electron density increases while the density of H 2 O is not significantly depleted. Therefore, the rate of electron-impact dissociation of H 2 O, the dominant source of OH, increases. However, as power increases beyond 14.3 W, the OH density decreases in spite of the steady-state electron density increasing. This decrease in OH density is due to the depletion of H 2 O in the gas phase by electron-impact reactions, as shown in figure 7. With H 2 O being the primary precursor to OH, the depletion of H 2 O leads to a reduction in OH density.
The OH aq density as the power begins to ramp down (10.1 ms) and the HCOO − aq concentration after an additional 10 ms (time of collection) are also shown in figure 7, both averaged over the droplet, as described in equation (1). Below 10 W, the HCOO − aq concentration decreases as power increases, as expected. As the HCOO − aq concentration decreases, the OH aq concentration increases because the consumption of OH aq by reaction with HCOO − aq decreases. As the power increases above 10 W, the decrease in HCOO − aq slows because a substantial amount of O 2 − aq has been produced to consume OH aq at rates larger than the reaction with HCOO − aq . As the power increases above 25 W, the HCOO − aq concentration remains constant. This is because the HCOO − aq in the reactive layer is almost completely consumed, and the droplet-averaged density of HCOO − aq is determined by the initial concentration in the core. When including diffusion from the core to the reactive layer, we expect that there will be some increasing consumption of the droplet-averaged HCOO − aq . At 25 W, the OH aq density increases significantly. While OH aq is consumed by reactions with O 2 − aq after the density of HCOO − aq decreases, OH aq increases once O 2 − aq is consumed due to solvation of OH. Experimentally, increasing the power at the same gas flow rate will likely increase the droplet evaporation rate and reduce the droplet diameter. The smaller size of the droplet will lead to rapid diffusion of HCOO − aq from the nonreactive core to the reactive layer, leading to increased consumption of HCOO − aq by OH aq .

Gas mixtures
When the plasma is sustained in different gas mixtures, different reaction pathways and possible radical species are formed in the plasma. For example, in plasmas with high concentrations of O 2 , O and O 3 are the dominant reactive species, while in plasmas with high concentrations of H 2 O, OH is the dominant radical reactive species. The degradation of HCOO − aq has been investigated for different gas mixtures [13][14][15][16] O can be found in the gas phase due to impurities and evaporation of the droplet, the main source of H 2 O is in the initial gas mixture and flow. The He/O 2 = 99.8/0.2 mixture has the next highest density of OH in the gas phase due to reactions of HO 2 and O. The other three gas mixtures The OH aq density as the power begins to ramp down (10.1 ms) and HCOO − aq concentration at the time of collection are also shown in figure 8, both averaged over the droplet. Where OH density was high in the gas phase, OH aq density is also relatively high, since solvation of OH from the gas is its dominant source. However, since OH aq is consumed by O 2 − aq , the density of OH aq is lower than the density of OH. In the He/O 2 mixture, the OH density is relatively low, and the OH aq density is the highest of all gas mixtures examined. In this case, OH aq is formed not in the gas phase but in the liquid phase by O aq + H 2 O aq → OH aq + OH aq [17]. Since the He/O 2 mixture has an abundance of O to solvate into the droplet, OH aq is readily formed within the droplet. Therefore, the decomposition of HCOO − aq is due to the OH aq formed by O aq instead of by solvation of gas phase OH. However, this value for OH aq may be sensitive to the Henry's law constant of O. With the He/O 2 mixture, the rate of OH aq production by O aq is higher than the consumption of OH aq by O 2 − aq , and OH aq does not significantly decrease over the power-on period. For the He/H 2 O, He/O 2 , and He/Ar/H 2 O mixtures, the density of HCOO − aq in the reactive layer is depleted to below 4% of the initial HCOO − aq concentration, leading to a relatively constant HCOO − aq concentration (averaged over the droplet). For the He, He/Ar, and He/H 2 mixtures, the HCOO − aq is decreased by less than 0.5 mM from its initial concentration of 2 mM. In the He and He/Ar mixtures, OH aq is formed both by the solvation of gas phase OH as well as O aq + H 2 O aq → OH aq + OH aq . The rate of OH aq formation by UV/VUV radiation is at least four orders of magnitude lower than the rate of formation by O aq + H 2 O aq in the He mixture and nearly three orders of magnitude lower in the He/Ar mixture. The total density of the radiating states is below 2 × 10 9 cm −3 in the He mixture and below 5 × 10 11 cm −3 in the He/Ar mixture due to their being quenched by H 2 O and impurities. Without the UV/VUV radiation, HCOO − aq increases by less than 0.02 mM across all gas mixtures, with the largest difference in the He/Ar mixture. Therefore, in this system, UV/VUV radiation does not play a large role in OH aq production and HCOO − aq degradation. In the He/H 2 mixture, the H density is three orders of magnitude larger than the OH density. However, H has a low Henry's law coefficient (6.48 × 10 −3 ) compared to OH (620), leading to H aq only being a factor of 1.7 larger than OH aq . While H aq has a higher density than OH aq , the rate coefficient of H aq reacting with HCOO − aq is an order of magnitude lower than that of OH aq reacting with HCOO − aq . Therefore, HCOO − aq is still consumed primarily through OH aq . Since OH aq is not abundant, HCOO − aq is not depleted. The results from the model are compared to the experimental measurements in table 9. As discussed in section 3.2, in the He/H 2 O plasma, the model underpredicts the OH density by a factor of 2 while matching the HCOO − aq density. For the He/O 2 plasma, the OH density was not measured, but the model predicts a density of 2. Species in addition to OH aq and H aq could also play a role in HCOO − aq depletion. In Nayak et al, it was argued, based on the work of Jirasek and Lukes [27], that O aq could directly interact with HCOO − aq [16]. UV/VUV photodissociation and photoionization of H 2 O aq was shown to not play a large role in OH aq production and subsequent HCOO − aq degradation due to the low density of radiating states. However, in other systems with larger densities of radiating states, UV/VUV photodissociation could play an important role, particularly when large amounts of OH are not produced in the gas phase. Additionally, photodetachment of electrons from negative ions (OH − aq , HCOO − aq ) may be important. As electron affinities of typical negative ions are in the order of 1 eV, most radiation is energetically able to produce photodetachment. In this system, photodetachment could increase OH aq through detachment from OH − aq or could degrade HCOO − aq directly.

Water percentage
While different gas mixtures produce varying levels of OH and OH aq , varying the H 2 O percentage in the He/H 2 O mixture can also change the OH and OH aq levels, allowing the OH density to be tuned to the desired amount. Note that, to compare with experiments, the results in this section are with a flow rate of 1.5 slm, compared to 1 slm in previous sections. As discussed in section 4.3, the flow rate changes the reactive layer thickness due to the shorter (or longer) time for transport of solvating species into the droplet. Therefore, the reactive layer thickness is decreased to 5.5 µm to match that at 1.5 slm. The OH density as the power begins to ramp down (8.4 ms, exit of the plasma channel) is shown in figure 9(a) at a flow rate of 1.5 slm. As the H 2 O percentage in the initial gas mixture