Characterization and Treatment Performance of an Atmospheric Pressure Plasma Jet-Operated Spinning Disc Reactor for the Treatment of Rhodamine B Dye

A spinning disc reactor is a design widely adopted in chemical process industries because of its capability to produce thin fast-moving films, which enhance the diffusive and convective transport of solutes. However, this configuration has yet to be explored for plasma-based water treatment, where mass transport limitations in the bulk liquid often limit reactor degradation efficiency. This study presents a novel plasma spinning disc reactor (PSDR) for degrading rhodamine B dye and characterizes its performance. The impact of discharge power, gas flowrate, liquid flowrate, disc rotational speed, and bulk liquid concentration on dye degradation was investigated. The results indicate that mass transport limitations within the fluid were the primary limitation to efficient degradation. Higher degradation rates were achieved primarily through changes in the plasma area, fluid velocity across the disc, and increased bulk liquid concentration, resulting in enhanced contact between the solute and the plasma. Residence time, a function of plasma area and fluid velocity, was used to describe and predict degradation rates on the PSDR using a 1-D fluid element model, which indicated that lower residence times favored dye degradation, especially for systems limited by small plasma areas.


Introduction
Efficient wastewater treatment is a growing concern due to the ubiquity of novel organic contaminants in drinking water and groundwater such as dyes, surfactants, and pharmaceuticals.These compounds often cannot be degraded using conventional treatment methods such as UV and chlorine, posing a risk to humans and aquatic ecosystems.Advanced oxidation processes (AOPs), which generate highly oxidative hydroxyl radicals ( • OH), have successfully degraded a range of emerging and legacy contaminants [1,2].One such AOP is low-temperature plasma (LTP) technology, which produces large quantities of oxidizing species, including • OH, H 2 O 2 , • O, O 3 , and other reactive agents/species such as (V)UV photons and solvated electrons, all of which work individually and synergistically to degrade even the most recalcitrant compounds without the need for additional chemicals [3][4][5][6].
More than a hundred plasma reactor designs are used in water treatment today.They differ in electrode arrangements, discharge phases, and power source characteristics, giving rise to various treatment efficacies.The most effective are gas discharge reactors in which plasma is generated in the gas phase over the surface of the liquid target [7,8].These systems have successfully degraded dyes and surfactants.However, their strong performance can largely be attributed to the tendency of these surfactant compounds to accumulate at the gas (plasma)-liquid interface-a thin (~ tens of nm) region of chemical reactivity [9][10][11].When applied to the treatment of non-surfactant compounds, the same reactors exhibit a significantly diminished performance.
The optimization of gas-liquid discharge reactors is extremely challenging.The heterogeneous nature of the system requires that solutes from the bulk liquid and short-lived species generated on the plasma side be effectively transported to the interface.To ensure high contaminant removal rates, the contact area between the plasma and the treated liquid (i.e., surface area to volume treatment ratio) must be maximized, and the treated fluid under the plasma must be rapidly renewed [12].This is often achieved through plasma reactor design, modifications in the electrode arrangement, and the introduction of bubbling [13][14][15].In this study, an alternative reactor design is developed to maximize plasma-liquid contact and minimize bulk liquid mass transport limitations: the PSDR [16][17][18].This reactor also offers unprecedently high fluid renewal rates, making it an attractive bench-scale solution for plasma reactor scaleup.
In the PSDR, liquid is introduced onto the surface of a rotating disc from its center, from which it flows radially outward to the sides of the disc.The centrifugal acceleration of the disc causes the liquid to be sheared into a thin layer, the thickness of which can be adjusted by the rotational speed of the disc and the rate at which the liquid is introduced to its surface.This study focuses on characterizing the PSDR driven by an atmospheric pressure plasma jet (APPJ) and assessing its performance in degrading a model contaminant, rhodamine B (RhB) dye.Parameters such as discharge power, disc rotational speed, gas flowrate, liquid flowrate across the disc, and initial dye concentration were investigated.The key mechanisms that drive dye degradation were identified and integrated into a onedimensional model adapted for the PSDR to describe dye degradation at the plasma-liquid interface.

Plasma Spinning Disc Reactor Design and Plasma-Generating Network
The spinning disc reactor shown in Fig. 1a consists of a circular stainless-steel disc (i.d.= 1.2 cm, o.d.= 7.4 cm, l = 1.3 cm) mounted onto a hollow stainless-steel rod (i.d.= 0.2 cm, o.d.= 4.1 cm, l = 28.5 cm) which acted as both the inlet for the liquid flow to the disc surface and the ground electrode.The surface of the disc was covered by a 1 mm thick Teflon sheet of the same diameter to facilitate an even spread of the discharge.
The spinning disc was enclosed in a custom-designed cylindrical acrylic chamber consisting of two fused cylinders; a "narrow" one (i.d.= 8.8 cm, o.d.= 10.2 cm, l = 14 cm) and a "wide" one (i.d.= 8.8 cm, o.d.= 15.9 cm, l = 5 cm), the latter of which contained four built-in quartz tube windows for optical measurements.The wide cylinder was fitted concentrically to the center of the narrow cylinder to form a T-shaped chamber.The spinning disc was positioned in the center of the chamber, so the accelerated fluid coming off the disc was collected and directed to the bottom.The chamber was mounted on a square acrylic base (20.5 cm × 20.5 cm × 6.0 cm) which collected and directed (via an opening) the liquid leaving the disc to an external solution reservoir (Fig. 1b).The top of the chamber was covered with an airtight acrylic square lid (20.5 cm × 20.5 cm × 3 cm) adapted to accommodate the plasma source and gas outlets.
The plasma source used in the study (Fig. 2a) was an argon-driven APPJ featuring a high voltage (HV) tungsten electrode (d = 1.0 mm, l = 50.0mm) inserted into the center of a dielectric (quartz) tube (i.d.= 2.8 mm, o.d.= 3.0 mm, l = 66 mm), and connected to the HV power supply.A middle tube (i.d.= 5.0 mm, and o.d.= 6.4 mm, l = 50.0mm), made of electrically insulating garolite was glued to the quartz tube on one end and connected to a push-to-connect manifold tube fitting on the other end.The back end of the push connector was connected to a digital mass flow controller, which was connected to the main gas inlet-an argon gas tank.The APPJ was suspended above the spinning disc by an XYZ-axis linear stage (XR25C, Thor Labs) mounted on the chamber lid, which enabled the adjustment of the distance between the HV electrode and the disc surface.The APPJ was positioned 25 mm above the spinning disc and off-centered ~ 18 mm from the liquid inlet.Figure 2b shows an image of the jet in operation.The entire acrylic assembly shown in Fig. 1a was mounted on an aluminum-reinforced acrylic encasement which housed the mechanism for the disc rotation, a control panel for adjusting the disc rotational speed, and the liquid inlet and outlet lines (Fig. 1b).
Electrical discharges were created by an AC power supply (PVM-500/DIDRIVE10, Information Unlimited, Amherst, NH) with a maximum voltage of 40 kV (peak-to-peak, V P-P ) and frequency of 70 kHz.The maximum voltage and frequency for the dye degradation experiments were 5.5 kV (V P-P ) and 22.05 kHz, respectively.Voltage was measured on the HV side using a North Star PVM-1 high-voltage probe, and the current was measured on the ground electrode side using a Tektronix P6021 current probe (Fig. 1b).Both probes were connected to a Tektronix MDO 3032 oscilloscope.Example voltage and current waveforms are shown in Fig. 3. Discharge power was calculated by integrating the product of voltage and current within a single wave period, as shown in Eq. ( 1).
where V(t) and I(t) are the measured voltage and current respectively, and T = 1/f where f = 22.05 kHz, a single wave period.The discharge power ranged between 0.9 W and 30 W.

Experimental Procedures
Rhodamine B solutions (RhB, ≥ 95.0%, Sigma-Aldrich) ranging from 0.01 mM to 0.2 mM with solution conductivity adjusted to 100 µS/cm using sodium chloride (NaCl, ≥ 99.0%, Sigma-Aldrich) were introduced onto the spinning disc at various liquid flowrates (0.32-0.92 LPM) from a continuously stirred 250 mL solution reservoir using a peristaltic pump (Fig. 1b).At the disc's surface, thin layers of a fast-moving liquid briefly contacted the plasma and were accelerated towards the chamber walls, from which the liquid trickled to the base of the chamber and out of the reactor.The outlet was connected to the inner tube of a Liebig condenser, where the treated solution was cooled by water at 5 °C passing through the outer tube.The Liebig condenser dispensed the cooled solution into the reservoir from which it was recirculated back into the reactor.
Disc rotational speed varied between 200 and 1000 rpm, argon (jet) flowrate between 2 and 10 LPM, and the total treatment time was 60 min.The interaction of the discharge with ambient air was minimized by purging the PSDR chamber with argon gas for 15 min prior to the start of each experiment.Reference operational treatment conditions were chosen (1)

Analytical Methods
The concentration of RhB was determined spectrophotometrically (UV-1800, Shimadzu) by measuring its absorbance at 554 nm.The concentration of H 2 O 2 was determined colorimetrically using the reaction between H 2 O 2 and titanium (IV) sulfate reagent (159.93M, ~ 15% by weight in dilute sulfuric acid 99.9%, Sigma-Aldrich).The absorbance of the resulting yellow peroxotitanium complex was measured spectrophotometrically at 410 nm.The H 2 O 2 measurements were carried out using deionized water only for all conditions investigated.The plasma-liquid contact area (i.e., the APPJ discharge spread on the disc's surface, mm 2 ), as well as the length of the plasma in the radial direction (mm), was obtained from discharge images taken with a digital single-lens reflex camera (Nikon D5200).Images were modified to a standard amplification of 1000 pixels/inch using known reactor dimensions with a custom code written in MATLAB.The plasma length and area were then estimated from the scaled images based on the observed area covered by the streamers.An average of at least three images per operating condition were used to estimate the plasma area and length.
Surface tension measurements of 0-3 mM RhB solutions were carried out by the bubble drop method using a SITA dyno-tester plus tensiometer (Future Digital Scientific Corp.).The tensiometer has type I & II PEEK capillary tips that transfer an airstream into the liquid to create a bubble.To measure the equilibrium surface tension, the bubble lifetime was adjusted to 15 s, and the instrument took an average of three readings for each solution.The RhB equilibrium surface excess was calculated using the Langmuir equation [19]: (2) where Г eq is the equilibrium surface excess (mol•cm −2 ) corresponding to the bulk RhB concentration C b (M), Г m is the maximum (saturated) surface excess (mol•cm −2 ), and K eq is the equilibrium interface partitioning constant (M −1 ).Г m was calculated by plotting the measured surface tension (γ) as a function of bulk RhB concentration (C b ) on a log scale, and fitting the slope of the linear portion of the dependence into the Gibbs adsorption equation: where n is the number of particles associated with the solute (n = 2 for RhB), R is the gas constant, T is the temperature, γ is the measured surface tension (dyn•cm −1 ), and Г is the Gibbs surface excess (Г = Г m in the constant slope saturated regime).To determine K eq , surface tension data were fitted to the Szyszkowski equation: where П is the surface pressure (dyn•cm −1 ) and γ 0 is the surface tension of the solution without RhB (pure water).

Plasma Diagnostics
Plasma diagnostics was carried out at the Princeton Collaborative Research Facility (PCRF) to determine the rotational gas temperature (T g ) and plasma electron density (n e ) at selected experimental conditions.The light emission from the plasma plume was recorded using a monochromator (HRS PRO750 with gratings 1200 g/mm and 2400 g/mm) coupled with an ICCD camera (PI-MAX 3) that served as a detector.To obtain spatially resolved spectral data in the axial direction, the emission of the jet plume (from the jet nozzle to the plasma-liquid interface) was imaged on the entrance slit (10 μm) of the monochromator.Spectral resolution and instrumental broadening, which corresponds to the gratings, were measured using a calibration lamp (Oriel Hg-Ar pencil lamp) and were determined to be Δ instr ~ 0.065 nm (for 1200 g/mm) and ~ 0.024 nm for 2400 g/mm.

Rotational Temperature (T g )
The rotational temperature was estimated from OH A-X (1-1) emissions and OH A-X (0-0) transitions in the wavelength range of 305-313 nm.It can be assumed that the rotational temperature of OH is equal to the gas temperature since at atmospheric pressure the excited states undergo many thermalizing collisions during their radiative lifetime, allowing the excited OH molecules to thermalize.The rotational temperature was estimated by simulating the theoretical rotational spectra with the Lifbase 2.2.1 software [20] and comparing it with experimental spectra.An example of a comparison between experimental and theoretical spectra is shown in Fig. 4.

Electron Density (n e )
The electron density at the plasma-liquid contact interface was obtained by measuring and analyzing the full width at half area (FWHA) of broadening of the H α spectral line.The major source of line broadening originates from the Stark broadening due to the Coulomb interaction between the light-emitting atom and the charged particles.
However, for low-ionized plasmas produced at high pressure, broadenings are apparent as several broadening mechanisms take place such as resonance broadening, and Van der Waals (VdW) broadening due to collisions with neutral particles [21].Thus, the broadening of spectral line profiles is generally characterized by Voight profile (i.e., convolution of Gaussian and Lorentzian), where the Doppler broadening and instrumental broadening have a Gaussian profile while the VdW, resonance, and Stark broadening have Lorentzian profiles.In this study the resonance broadening of the H band is negligible due to the low H density. VdW broadening of H α can be estimated in terms of plasma gas temperature for argon plasmas and is given as [22]: where T g is the gas temperature in K.The Doppler broadening can be expressed as [22]: where T g (K) is the gas temperature, M (a.m.u.) is the atomic mass of the emitter, and λ (nm) is the wavelength of H α .Stark broadening of spectral lines as a function of electron density (n e ) is conveniently tabulated especially in the case of hydrogen Balmer lines in the work by Gonzales et al., [23].Because it has been shown that FWHA is a more stable parameter, in the present work the electron density was obtained by locating the FWHA of H α and finding the corresponding electron density.The FWHA is the Stark broadening obtained by deconvoluting the Gaussian (Doppler broadening and instrumental broadening) and Lorentzian (VdW, resonance and Stark broadening) simulated profiles from the experimental line profile.An example of the fitted spectral line for FWHA calculation is given in Figure S1 of the Online Resource.

Results and Discussion
The Effect of Discharge Power on Reactor Performance Figure 5a shows the dependence of the H 2 O 2 production rate and plasma area on discharge power ranging from 0.9 W to 9.5 W. Time-dependent concentration profiles for H 2 O 2 generation (not shown) revealed zero-order kinetics, as reported for many other plasma systems [7,24].The observed (linear) increase in the H 2 O 2 production rate with discharge power has also been reported previously and is explained by the increase in OH intensity which occurs with larger energy deposition into the plasma; H 2 O 2 is assumed to be produced exclusively in the gas phase by the recombination of OH radicals [25].
In contrast to previous studies which reported no changes in the plasma contact area of APPJs with changes in discharge power [26][27][28], here discharge power scaled linearly with area.This trend was attributed to the increase in discharge current that occurs when discharge power is increased (Figure S2, Online Resource), which allowed plasma to propagate further over the surface of the liquid [29,30].An increase in plasma area enhances liquid evaporation in the vicinity of the streamers, and therefore the production of OH and, subsequently H 2 O 2 increases [31].Indeed, our previous work with pulsed DC gas-liquid discharges, where the plasma area was controlled by either the size of the grounded electrode, the discharge power, or both demonstrated that when plasma area expansion is controlled by discharge power and area is allowed to undergo unrestricted expansion (e.g., by using a large ground electrode size), the H 2 O 2 production correlated linearly with plasma area.In contrast, when the expansion of plasma area was restricted (e.g., by using a small ground electrode size), an increase in discharge power yielded lower amounts of H 2 O 2 and the correlation was not linear [32].In this present study, the ground electrode size was not a limiting factor (ground size:area ≈ 140:1), and the observed results are consistent with those previously reported for an unconstrained area expansion.
The results of spectroscopic measurements presented in Fig. 5b reveal that the electron density remains relatively constant in the range 1.85 × 10 21 to 1.92 × 10 21 m −3 for 8 W to 30 W discharge power, which is higher than that reported for similar argon APPJs [13,[33][34][35].This discrepancy can be attributed to the presence of a conductive liquid target in Fig. 5 The dependencies of a the H 2 O 2 production rate and plasma area on discharge power (0.9 to 9.5 W) and b gas temperature and electron density on discharge power (8.5 to 30 W). Experimental conditions: 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc, and 1000 rpm disc rotational speed 1 3 contact with the plasma discharge.It is important to note that the spectroscopic data were obtained at discharge powers ranging from 8 to 30 W, which is considerably higher than the range used in the degradation experiments (0.9 to 9.5 W).The dependence of plasma density on the power delivered to an RF-powered plasma argon jet interacting with water was investigated in [36] where electron density and gas temperature were measured via Thomson scattering.The results demonstrated that the electron density (n e ) decreased by a factor of ~ 1.53 when the power was reduced from 50 to 20 W (n e = 7.8 × 10 21 m −3 and 5.1 × 10 21 m −3 , respectively).Based on these results, the density results shown in Fig. 5b are not expected to decrease below 10 21 m −3 even for P < 1 W. Gas temperature generally exhibits a stronger dependence on the power, as was shown in [36] and subsequently in [37], using the same RF-powered argon jet, by means of Rayleigh scattering.In this study, as a result, the gas temperature is also expected to follow the trend shown in Fig. 5b and decrease at lower discharge powers.The lack of significant variation in electron density with discharge power can be attributed to the relatively constant power density of the discharge (~ 3 × 10 5 W/m 2 ) arising from changes in plasma area.The observed increase in gas temperature with discharge power, as shown in Fig. 5b, is due to Joule's heating, which has been reported in previous studies [38][39][40][41].Furthermore, the increase in gas temperature between 8 and 13 W indicates that the increase in plasma area following power deposition is associated with increased OH production.Both phenomena are responsible for the linear increase in H 2 O 2 production shown in Fig. 5a.However, it is important to note that experiments on dye degradation and H 2 O 2 production were not conducted at high powers due to the transition of the discharge into an arc, which introduces additional effects that may influence bulk liquid processes, such as UV photolysis.
The impact of discharge power on the degradation of multiple starting concentrations of RhB dye is presented in Fig. 6a.Considering that the main mechanism of RhB degradation is OH radical attack, the degradation follows pseudo first order kinetics [26,42,43].Consequently, the degradation rates recorded for each parameter correspond to the initial rates derived from fitting RhB concentration profiles to the first-order rate equation: The impact of discharge power on degradation becomes more pronounced at high dye concentrations and diminishes as the initial dye concentration decreases.To explain these results, surface tension measurements were carried out to calculate the equilibrium surface excess of RhB (i.e., RhB interfacial concentration) at each concentration investigated.Although it is acknowledged that the highly non-equilibrium conditions of a 22 kHz discharge prevent the RhB interfacial concentration from reaching its equilibrium values, it is presumed that the established correlations between the bulk and interfacial concentrations remain valid.Figure 6b illustrates a comparison between the RhB interfacial concentration, representing the equilibrium surface excess, and the corresponding dye degradation rates for varying initial bulk liquid concentrations.Increasing the bulk liquid concentration initially augments the interfacial dye concentration and subsequently its removal rate.However, when the bulk concentration reaches approximately 0.1 mM, the interface becomes saturated with RhB molecules, causing no further increase in the interfacial concentration or the dye removal rate.The interfacial concentration of RhB is controlled by the diffusion and subsequent adsorption of RhB molecules to the interface until maximum adsorption is attained.Increasing the bulk liquid dye concentrations results in significantly greater diffusion fluxes, which in turn leads to higher RhB degradation rates, as observed for bulk liquid concentrations greater than 0.01 mM.The RhB removal rate, nevertheless, increases with discharge power for each concentration.The variation in discharge power can impact dye degradation in two ways: (1) an increase in OH radical production rate with discharge power, as observed in Fig. 5a, and (2) the impact of discharge power on plasma area, which subsequently influences the plasma-liquid contact time.The residence time of the fluid, defined as the ratio of the characteristic plasma length (i.e., the length of the plasma plume in contact with the liquid surface in the radial direction of flow) to the fluid's surface velocity (v r,max ), can be used to evaluate the impact of discharge power (and other operational parameters) on plasma-liquid contact time: where τ (s) is the residence time, L p (m) is the plasma length obtained from images of the plasma's spread on the liquid surface, and v r,max (m/s) is the surface velocity of the fluid across the disc.As discharge power does not affect the fluid velocity, changes to the residence time via discharge power are due solely to its effect on the plasma area.As a result, the relationship between discharge power and the fluid's residence time on the PSDR will be linear (Figure S3, Online Resource).The correlation between residence time and dye degradation will be addressed in Section "Residence Time and Dye Degradation Rate" once all other operational parameters have been introduced.

The Effect of Disc Rotational Speed on Reactor Performance
Figure 7a shows the dependence of the hydrogen peroxide production rate and the plasma area on the disc rotational speed between 400 and 1000 rpm.Varying the disc rotational speed had a negligible effect on both the H 2 O 2 production and the plasma area.This can be attributed to the fact that changes in the rotational speed affect the radial and tangential (7) velocities of the fluid on the disc surface, as well as the thickness of the liquid layer, but have little to no impact on the plasma properties.As shown in Fig. 7b, the gas temperature and electron density exhibit only minor changes with varying rotational speeds.
Figure 8 shows the effect of disc rotational speed on the degradation rate of a 0.2 mM RhB solution.The relationship between rotational speed and degradation rate is complex, with the lowest measured degradation rates observed at zero rotational speed, where the discharge contacts a motionless bulk liquid.The zero rotational speed experiments were carried out using a beaker with the same inner diameter as the spinning disc.In these experiments, no additional mixing was applied to the treated solution.All other experimental conditions were identical to those of the PSDR mentioned in Fig. 8, including the plasma source.One notable difference between the two reactor systems was the grounded electrode which in the beaker case was a copper tape placed at the bottom of the vessel.Without bulk liquid mixing introduced by the spinning disc, degradation rates are limited by the renewal of interfacial fluid elements via diffusion and eddy currents initiated by the discharge impinging on the liquid surface.However, introducing transport through the spinning disc (rpm > 0) enhances the rate at which solute-rich fluid elements are introduced under the plasma, leading to an initial increase in the degradation rate.Beyond 300 rpm however, the degradation rate decreases.
Figure 9a demonstrates the variation in surface velocity and liquid layer thickness with disc rotational speed.The calculation of these parameters was performed using the hydrodynamic analysis of fluid flow on a rotating disc method developed by Aoune and Ramshaw [44].Further details are provided in Text S1, Online Resource.Disc rotational speed has a direct impact on fluid velocity, which subsequently affects the fluid's residence time under the plasma (Eq.8). Figure 9b demonstrates that an increase in rotational speed results in a reduction in the time that fluid remains under the plasma.Since plasma area is unaffected by rotational speed, this decrease is solely attributed to the increase in fluid velocity caused by the disc's rotational speed.Our previous work has shown that high fluid renewal rates reduce the formation of a diffusive barrier that hinders the replenishment of contaminants at the interface, which occurs when fluid under the discharge is overtreated [12].The decrease in the dye degradation rate observed at rotational speeds greater than 300 rpm was initially attributed to the reduction in liquid layer thickness that occurs with increased rotational speed.In this study, the liquid layer thicknesses ranged from 2 mm at 100 rpm to 0.45 mm at 1000 rpm.However, since the penetration depths of OH radicals are on the order of a few µm [45,46], the liquid layer on the disc's surface can be considered a semi-infinite bulk.Hence, changes in the liquid layer thickness may not necessarily affect the degradation processes at the interface.An alternative explanation for the decrease in dye degradation at higher rotational speeds could be the impact of the Coriolis acceleration on fluid velocity at the interface.As rotational speed increases, the Coriolis force acting on the liquid also increases.While it can be assumed to be negligible at lower speeds, at higher speeds, the Coriolis force may substantially reduce the radial velocity of the fluid across the disc by moving it in a perpendicular direction.This effect would be more pronounced as thinner layers are formed on the disc with increasing rotational speed, allowing for the Coriolis force to have a greater impact on the fluid velocity.Consequently, the fluid velocity at the interface could be significantly lower than reported by our calculations.

The Effect of Liquid Flowrate on Reactor Performance
Figure 10 shows the relationship between the hydrogen peroxide production rate and plasma area (Fig. 10a) and gas temperature and electron density (Fig. 10b) as a function of liquid flowrate.The results indicate that decreasing the liquid flowrate increases the plasma area, which, in turn, results in a slight increase in the H 2 O 2 production rate.The gas temperature also increases as liquid flowrate is reduced while the electron density remains statistically unchanged, consistent with previous observations for discharge power and rotational speed.As with the rotational speed, the liquid flowrate affects the hydrodynamic Figure 11a and b show the relationship between liquid layer thickness, fluid velocity, and residence time with respect to liquid flowrate.The calculation methods for these parameters are provided in Text S1 of the Online Resource.While the previous analysis in Fig. 9a suggested that the liquid layer thickness was of minimal importance for film thicknesses greater than 0.4 mm, the current study found that films less than 0.4 mm in thickness underwent a breakdown as they propagated from the disc inlet to the periphery.This resulted in a significant reduction in the electrical resistivity of the liquid layer, leading to an increase in the plasma area.Consequently, the increase in plasma area affected the plasma gas temperature and H 2 O 2 production.Furthermore, Fig. 11a demonstrates a decrease in fluid velocity across the disc as liquid flow rate decreases, which, in combination with the increase in plasma area, resulted in a noticeable increase in residence time, as shown in Fig. 11b. Figure 12 shows the correlation between dye degradation and liquid flowrate, where it is observed that a reduction in flowrate yields higher degradation rates.This finding can be attributed to the increase in OH radical production and plasma area as a consequence of reduced liquid flowrate.Although higher flowrates allow for improved fluid renewal rates under the plasma, the degradation rate increases with residence time, as was previously reported for discharge power.The observed trend is associated with the changes in plasma area that occur with variations in discharge power and liquid flowrate.Hence, it can be concluded that higher contact time between discharges and the solution leads to an increased degradation rate within a certain residence time range, subject to the parameters employed to achieve higher contact times.In order to deconvolute this complex relationship, a fluid element model developed to elucidate degradation mechanisms at the plasma-liquid interface of the PSDR is presented in Section "Residence Time and Dye Degradation Rate".

The Effect of Gas Flowrate on the Reactor Performance
Figure 13 shows the impact of argon gas flowrate on plasma area and H 2 O 2 production rates.Plasma characterization measurements were not carried out for these experiments.Flowrate exhibited a significant effect on the production of H 2 O 2 and a smaller effect on the plasma area.Gas flowrate did not affect the discharge power (data not shown).
The increase in H 2 O 2 production rates with gas flowrate could be attributed to the increased water vapor content in the gas phase, which could have originated from either the humid gas or from the evaporation or sputtering induced by the (turbulent) gas flow [25,28,47].High gas velocities could also reduce OH radical losses and enhance H 2 O 2 formation by minimizing mixing between the plasma plume and surrounding residual air [48].The slight increase in plasma area with gas flowrate (< 3 mm 2 increase) was hypothesized to be the result of the reduced liquid layer resistivity, similar to what was observed for lower liquid flowrates.
Figure 14 shows the degradation rates of 0.2 mM RhB for different gas flowrates, which generally show an increase in removal with flowrate as reported previously in literature Fig. 14 RhB degradation rate as a function of gas flowrate for 0.2 mM RhB solution.Experimental conditions: 5 LPM argon gas flowrate, 1000 rpm rotational speed, and 5 W discharge power [47,49].However, the trend observed in Fig. 14 does not quite follow that of hydrogen peroxide observed in Fig. 13, which could be explained by a transition from laminar to turbulent gas flow that occurs as the gas flowrate increases from 2 LPM (Re = 1171) to 10 LPM (Re = 5857).The turbulent gas flow at 10 LPM introduces other effects which improve dye degradation, although these are currently unknown.Figure S4 in the Online Resource shows that gas flowrate has a minimal effect on fluid surface velocity and residence time.However, gas phase turbulent flows may disrupt the liquid layer thickness and fluid velocity near the discharge, potentially impacting dye removal.

Residence Time and Dye Degradation Rate
Figure 15 shows degradation rates of RhB dye as a function of liquid residence time, which was determined from the changes in discharge power, disc rotational speed, and liquid Fig. 15 Degradation rates of 0.2 mM RhB solutions obtained from individual investigations into the effects of discharge power, liquid flowrate, rotational speed, (while keeping all other parameters constant), as a function of the residence time Fig. 16 Schematic diagram of the surface of a spinning disc highlighting the plasma-liquid interface, subsurface, and bulk liquid phase as well as the processes and reactive species important for the degradation of RhB flowrate.Gas flowrate was not included in the analysis as it had no effect on the residence time.The data indicate that irrespective of the parameter used to calculate the residence time, the dye removal rate increases with an increase in residence time up to about 18 ms, beyond which it either plateaus or decreases.
The observed relationship between the degradation rate and residence time highlights the importance of RhB mass transport in the degradation process.In order to gain a deeper understanding of the impact of mass transport on degradation, a 1-D diffusion-reaction model was adapted from [12].This model was used to investigate the processes occurring in the vicinity of the plasma-liquid interface and to describe the mass transport of RhB and other reactive species within a fluid element of depth δ which is in contact with plasma.The fluid element described in Fig. 16 is an infinitesimally small volume of RhB solution with a cross-sectional area approaching zero and a height equal to the liquid layer thickness (δ).Within this fluid element, three distinct zones can be identified.
The interfacial zone, which spans only a few nm, has the highest concentration of hydroxyl radicals, and contains RhB at concentrations equal to their equilibrium surface excess.The subsurface zone extends from the plasma-liquid interface (z = 0) to approximately 500 μm, while the bulk liquid zone extends from 500 μm to the disc surface.The RhB concentration in the bulk liquid zone is the initial solution concentration and decreases gradually due to RhB degradation at the interface and subsurface.As the degradation of RhB is assumed to occur via hydroxyl radical attack, the relevant species considered in this model are RhB, hydroxyl radicals, and hydrogen peroxide.
The concentration profiles of RhB, hydroxyl radicals, and hydrogen peroxide as a function of residence time were obtained by numerically solving the diffusion-reaction equation: where C i (M) is the local solute concentration, D i (m 2 /s) is the diffusion coefficient of solute i, and R i (M/s) is a source term representing the solute's local rates of chemical reactions: The diffusion-reaction Eq. ( 9) was solved by applying appropriate boundary conditions for all three species in the subsurface and bulk liquid regions, as described next.The interfacial concentration of RhB was represented by its equilibrium surface excess, Γ, which depends on the underlying subsurface RhB concentration.Therefore, by assuming mass flux continuity between the subsurface and interface, a relation between the surface excess concentration of RhB at the interface a subsurface RhB concentration can be established [47]: The concentration of hydroxyl radicals and other reactive species (electrons, excited gas molecules and ions) at the interface is several orders of magnitude higher than the RhB (9) As a result, every discharge is capable of producing enough OH radicals to remove all the RhB at the interface.The flux of •OH from the interface into the subsurface, F OH, was assumed to be produced in the exact stoichiometric relationship with measured H 2 O 2 as a function of the discharge power: The assumption that a constant influx of reactive species approximates the periodic nature of the discharge is justified by noting that at the operational frequency of 22.05 kHz, the discharge timescales are significantly smaller than those of mass transport.
For hydrogen peroxide, a no-flux condition was imposed at the subsurface through the equation: For the bulk liquid region, the RhB concentration was set to 0.2 mM, consistent with the initial bulk RhB concentration used in degradation experiments.No-flux boundary conditions were imposed for hydroxyl radicals and hydrogen peroxide.To determine the concentration profiles of RhB, hydroxyl radicals, and hydrogen peroxide in the subsurface region, Eq. ( 9) was solved under these conditions for the duration of τ seconds.
Figure 17a shows species distribution in the fluid element immediately following a single plasma period of duration τ = 1 µs.The high flux of hydroxyl radicals during this period results in a substantial concentration of hydroxyl radicals at the subsurface, in the range of mM.This leads to a significant decrease in the RhB concentration (by an order of magnitude), which begins to limit further degradation.As a result, a large portion of the OH radicals recombine to form H 2 O 2 , leading to high subsurface concentrations of H 2 O 2 in the mM range.However, the effect of the single plasma period is limited to the immediate subsurface (10 -7 m) due to its short duration.Although the effect of a single plasma period is limited, the concentration gradient established between the immediate subsurface region and the rest of the liquid layer drives diffusion of RhB molecules to replenish the subsurface and interface, and H 2 O 2 to diffuse into the rest of the liquid layer.Figure 17b shows the concentration profiles after 45 µs, which show the redistribution of stable species.The RhB subsurface concentration has been replenished to more than 99% of its bulk liquid level, and the H 2 O 2 has been redistributed over a depth of 1 µm.This process of degradation and redistribution continues over multiple plasma periods, leading to a slow decline in RhB concentration at the subsurface and a slow accumulation of H 2 O 2 throughout the fluid element.Figure 17c presents the concentration profiles after 399 discharge periods (τ = 18 ms), where the RhB concentration at the subsurface is extremely low, and a significant diffusive boundary layer of 1 µm is observed, which limits further degradation.Further treatment beyond this point does not result in a substantial increase in degradation but only leads to higher levels of H 2 O 2 .Note that the thickness of the liquid layer on the disc (δ = 3 × 10 -4 to 1.2 × 10 -3 m) obtained from experiments did not affect the observed concentration profiles, as correctly assumed in the rotational speed in Section "The effect of disc rotational speed on reactor performance".The RhB degradation on the reactor scale is a cumulative result of the continuous plasma treatment of multiple fluid elements that exit the disc, mix with the rest of the bulk liquid, and are recirculated back, resulting in a decrease in the RhB concentration in the bulk liquid.The experimental degradation rate of RhB can, therefore, be expressed as the product of the fluid element transport under the plasma (v r,max •w p ) and the degradation within a single fluid element, n RhB : Figure 18 compares the predicted and measured rates of RhB degradation in the PSDR, normalized by the measured plasma-liquid contact area as a function of residence time.The area-normalized degradation rate deconvolutes the effect of plasma area from that of fluid velocity to observe the influence of residence time on RhB degradation.The measured RhB degradation rates were found to be an order of magnitude higher than those predicted For a fixed plasma area, the model predicts a weak correlation between degradation rate and residence times longer than 5 ms because each discharge period instantaneously degrades all of the interfacial RhB, and a diffusive distance begins to develop from the subsurface at z = 0 towards the bulk through which RhB molecules have to travel to replenish the interface.As the fluid element spends more time contacting the discharge, this diffusive distance grows, and at longer residence times (τ > 5 ms), a diffusive barrier to RhB replenishment at the interface develops, limiting the degradation rate by the rate of diffusive transport of RhB from the bulk to the interface.The experimental results showed the same weak correlation between degradation rate and residence time, as the lowest residence time tested was ~ 5 ms.At shorter residence times (τ < 5 ms), the model predicts much higher removal rates of RhB because degradation occurs primarily at the interface and within a short diffusion distance into the subsurface before the fluid element is removed from under the plasma, and a new solute-rich fluid element is introduced.Therefore, degradation at short residence times is controlled by the rate of convective transport of fluid elements to the plasma discharge region.Such short contact times, however, were not tested due to experimental setup limitations (i.e., strong interfacial hydrodynamic instabilities were observed at rotational speeds required for sub-millisecond contact times).Thus, the dependence of degradation rate on residence time observed in Fig. 15 is largely due to changes in the plasma area resulting from changes in certain operational parameters.Therefore, for constant or limited plasma area systems, shorter residence times favor higher degradation rates.
The PSDR has demonstrated remarkable efficacy in degrading RhB, despite its limited plasma area.As shown in Table 1, the energy efficiency achieved for treating a 0.2 mM RhB solution is 5.39 g/kWh under optimal conditions of 5 W discharge power, 1000 rpm rotational speed, 0.92 LPM liquid flowrate, and 10 LPM gas flowrate.This value compares where C 0 (M) is the initial concentration, V 0 (L) is the volume treated, M (g/mol) is the molecular weight of RhB, P (W) is the discharge power, and t 50 (s) is the time required for 50% degradation [ In-liquid -50/0.100.202 d favorably to the energy efficiencies reported for other plasma treatment systems including the plate-to-plate dielectric barrier discharge [49], an APPJ discharge contacting the surface of a stationary liquid in a beaker [26], a multiple point-to-plane corona discharge [50], and an in-liquid point-to-plane pulsed discharge [51].For a 0.1 mM solution (50 mg/L) in the PSDR the calculated energy efficiency is ~ 3.00 g/kWh (at optimal conditions).Considering the size of the treatment volume applied, this value is still competitive.However, making a direct comparison across different systems in a true "apples to apples" manner presents challenges due to variations in experimental conditions, especially starting concentrations of the target compound, treatment volumes and discharge gas types.

Conclusions
The aim of this study was to characterize and evaluate the performance of a plasma spinning disc reactor for rhodamine B dye degradation by investigating the impact of various operational parameters.The effect of initial bulk liquid concentration, discharge power, liquid flow rate, gas flow rate, and rotational speed on RhB degradation was studied.Results showed that mass transport of RhB molecules to the interface where degradation occurred was the primary limitation of the treatment process.Higher degradation rates were achieved by reducing diffusional limitations through a higher initial RhB concentration and thinner liquid layers, or by improving contact between the solute and the plasma through changes in plasma area and fluid velocity across the disc.Plasma area was controlled by discharge power and liquid layer thickness, while fluid velocity was controlled by liquid flow rate and rotational speed.Residence time, which is a function of plasma area and fluid velocity, was used to characterize changes in operational parameters and correlated well with observed degradation.A 1-D model, which describes degradation in a plasmaliquid system based on a fluid element contacting the discharge, was adapted to predict degradation trends on the PSDR.It was found that plasma area had the most significant influence on the degradation rate for all starting dye concentrations.Furthermore, shorter contact times favored RhB degradation in cases where the plasma area was fixed.Overall, the results of this study suggest that the PSDR is a promising technology for plasma-based water treatment applications.However, to increase its throughput capacity, it may be necessary to use larger area plasmas that are not generated by atmospheric pressure jets.

Fig. 1
Fig. 1 Schematics of the a PSDR and b overall experimental setup

Fig. 2 a
Fig. 2 a Schematic of the APPJ (plasma source) and b Picture of an argon-driven discharge contacting the surface of a 0.1 mM RhB solution on the spinning disc.Experimental conditions: 5 W discharge power, 5 LPM argon gas flowrate, 0.32 LPM liquid flowrate across the disc, and 1000 rpm disc rotational speed

Fig. 3
Fig. 3 Representative current and voltage waveforms recorded at 5 W discharge power, 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc, and 1000 rpm disc rotational speed

1∕2Fig. 4
Fig. 4 OH spectra fit between the experimentally measured and simulated values.Experimental conditions: 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc, and 1000 rpm disc rotational speed

Fig. 6 a
Fig. 6 a RhB degradation rate as a function of discharge power for different initial concentrations of RhB and b RhB equilibrium interfacial concentrations and RhB degradation rates as a function of the initial bulk liquid concentration at 5 W discharge power.Other experimental conditions: 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc, and 1000 rpm disc rotational speed

Fig. 7 Fig. 8
Fig.7 The dependencies of a the production rate of H 2 O 2 and the plasma area on disc rotational speed at 5 W discharge power and b gas temperature and electron density on rotational speed at 30 W discharge power.Experimental conditions: 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc

Fig. 9 a
Fig. 9 a Calculated liquid layer thickness and fluid surface velocity as a function of disc rotational speed between 200 and 1000 rpm.b Residence time (calculated using Eq.8) as a function of rotational speed between 200 to 1000 rpm.Experimental conditions: 5 LPM argon gas flowrate, 0.92 LPM liquid flowrate across the disc, and 5 W discharge power

Fig. 10 Fig. 11 a
Fig. 10 The dependencies of the a production rate of H 2 O 2 and the plasma area on liquid flowrate at 5 W discharge power and b gas temperature and electron density as a function of liquid flowrate at 30 W discharge power.Experimental conditions: 5 LPM argon gas flowrate, 1000 rpm rotational speed, and 5 W discharge power

Fig. 12 Fig. 13
Fig. 12 RhB degradation rate for 0.2 mM initial RhB concentration as a function of liquid flowrate.Experimental conditions: 5 LPM argon gas flowrate, 1000 rpm rotational speed, and 5 W discharge power

Fig. 17
Fig. 17 Concentration profiles of RhB, H 2 O 2 , and OH radicals as a function of distance from the interface for a immediately after the first discharge (τ = 1 µs), b after 45 µs, and c just before the 400th period (τ = 18 ms)

( 15 )Fig. 18
Fig.18 Experimental and predicted RhB removal rates in PSDR as a function of residence time.The initial concentration of RhB was 0.2 mM, the value of hydroxyl radical influx was taken as 1.9 × 10 -3 mol/m 2 /s, as calculated from the measured hydrogen peroxide production rates

Table 1
Comparison of the RhB degradation efficiency of the plasma spinning disc reactor to those of other gas and liquid discharge reactors a Initial RhB concentration and treatment volumes influence energy efficiency, therefore view comparisons as approximations b Energy efficiency for 50% degradation of RhB calculated as G 50 = 1.8×10 6 ×C 0 ×V 0 ×M P×t 50