Quantifying Radical Pathways in a 425 kHz Sonoreactor: Coupled Calorimetric–Multidosimetric Assessment and Process Variable Impacts in Sunset Yellow FCF Degradation

Abstract

This study quantifies radical pathways and the influence of process variables in a 425 kHz sonoreactor through a coupled calorimetric and multidosimetric approach during Sunset Yellow FCF degradation. Reactive oxygen species were mapped with four complementary dosimeters. Potassium iodide (KI) tracked interfacial hydroxyl radicals (^•OH). KI with ammonium heptamolybdate (AHM) captured ^•OH radicals together with hydrogen peroxide (H₂O₂). Bulk H₂O₂ accumulation integrated the recombination branch. Hydroxylation of 4-nitrophenol to 4-nitrocatechol acted as a selective near-interface ^•OH probe. Calorimetry showed that acoustic power density increased with set power and decreased with liquid height. All four dosimeters rose coherently with this variable, indicating that stronger driving elevated ^•OH generation while channeling a larger fraction into H₂O₂ through recombination. Process studies linked energy delivery to performance across operating conditions. Higher power accelerated pseudo-first order dye decay. Increasing initial dye concentration reduced fractional removal at fixed power, consistent with a radical-limited regime. Acidic media enhanced degradation by maintaining a stronger hydroxyl radical to water redox couple and by improving H₂O₂ persistence. Near neutral and alkaline media exhibited carbonate and bicarbonate scavenging of hydroxyl radicals and faster peroxide loss. Dissolved gas identity strongly modulated activity. Oxygen and argon outperformed air and carbon dioxide due to the combined thermophysical and chemical roles of the bubble gas. The calorimetry anchored and multidosimetric protocol provides a general route to compare reactors, optimize conditions, and support scale-up based on delivered energy density. Ultrasonication-driven degradation is a robust, practical technology for advanced treatment of dye-laden waters.

1. Introduction

Ultrasonic advanced oxidation is governed not by nominal electrical settings but by the energy that couples into the liquid and by how that energy partitions into reactive oxygen species near cavitating bubbles [1]. Much of the sonochemistry literature still reports input power and reactor make or model without establishing a quantitative bridge from energy delivery to radical pathways, which limits reproducibility and scale-up across geometries and fills. Temperature-rise calorimetry provides that bridge by measuring delivered acoustic power and, when normalized by volume, an energy density variable that is portable across reactors and operating points. Although community guidance recommends this practice, it is rarely integrated with a mechanistic readout of radical speciation in the same system.

Ultrasonic advanced oxidation is regulated by acoustic cavitation dynamics and by mass transport at the bubble–liquid interface. Transient bubble collapse generates primary radicals through water ultrasonication and produces pyrolytic fragments when reactive gases are present. The interfacial region sustains rapid reactions and transfers hydrogen peroxide into the bulk solution, so the accessible oxidant pool depends on both in-bubble chemistry and near-interface scavenging processes [2]. The principal regulatory levers are as follows. First, acoustic parameters govern radical formation. Frequency determines bubble size and lifetime and thereby the balance between radical pathways and pyrolysis, while delivered power density controls bubble number density and collapse intensity. Reported trends across tens to thousands of kilohertz and across reactor volumes demonstrate strong sensitivity to both variables [3]. Second, reactor geometry, standing wave structure, and liquid path length determine the fraction of the volume that resides in active zones. Third, temperature modifies vapor pressure and the cavitation threshold, so moderate liquid temperatures favor violent collapse and higher radical yields [2]. Fourth, gas composition and saturation regulate both thermophysical and chemical effects. Argon and oxygen commonly enhance activity through hotter collapse or direct oxidative participation, whereas carbon dioxide tends to suppress activity through carbonate radical formation and collapse cushioning [4]. Fifth, solution chemistry sets radical fate and persistence. Acidic media strengthen the hydroxyl radical to water redox couple and reduce scavenging, while bicarbonate and chloride can divert hydroxyl radicals or shorten oxidant lifetime. Finally, hybrid routes intensify oxidation by converting cavitation energy into additional oxidants. Ultrasonication activates persulfate or peroxymonosulfate to generate sulfate radicals and also enhances ozonation and Fenton-based schemes, thereby extending the effective pH window and increasing oxidant flux [4]. Recent works clarified how delivered acoustic power, reactor mapping, and complementary dosimetry enabled reproducible sonochemistry and demonstrated the growing use of ultrasound in hybrid oxidation routes [5,6,7,8].

This study introduces a calorimetry-anchored multidosimetric strategy that quantifies both energy delivery and the distribution of oxidizing equivalents under high-frequency irradiation at 425 kHz. Calorimetric maps establish the volumetric acoustic power density, while a four-probe panel consisting of potassium iodide, potassium iodide with ammonium heptamolybdate, bulk hydrogen peroxide accumulation, and hydroxylation of 4 nitrophenol to 4 nitrocatechol triangulates where the delivered energy is directed. The probes capture interfacial hydroxyl radicals, hydroxyl radicals combined with hydrogen peroxide, the recombination branch that forms hydrogen peroxide, and pollutants like aromatic oxidation at the bubble–liquid boundary. The design leverages standard iodide dosimetry and established mechanistic frameworks for cavitation chemistry, but advances them by co-registering energy density and reactive oxygen species inventories under identical conditions, thereby converting qualitative trends into quantitative budgets that are actionable for process engineering.

The choice of 425 kHz is deliberate. At these frequencies, cavitation clouds and path length effects make sonochemical efficiency highly sensitive to fill height and standing wave structure, so comparisons that rely on nameplate power are especially misleading [2]. By coupling calorimetry to iodide-based probes and to organic and Fricke-type readouts, the study resolves the long-standing ambiguity of whether performance gains arise from stronger collapses, greater bubble number density, or a shift from radical to molecular oxidants with increasing drive. The approach also reveals how classical process variables, including power, volume, dissolved gas, pH, and substrate loading, modulate the energy to chemistry link. In particular, the method shows why oxygen or argon feeds outperform air by combining favorable collapse thermodynamics with oxidative participation of the bubble gas, and why carbonate buffering and base-catalyzed hydrogen peroxide loss depress activity at neutral and alkaline pH.

Sunset Yellow FCF is used as a representative azo dye to demonstrate how a single unified metric, delivered energy density, organizes multiscale observations from calorimetry, dosimetry, and kinetics into predictive operating maps. The result is a practical recipe for selection of working volume, gas feed, and pH at fixed hardware, together with a transferable basis for scale-up that aligns with reactor design guidance on reporting delivered energy rather than nominal settings. The framework is compatible with diverse sonochemical platforms and complements recent efforts to model and optimize ultrasonication energy with calorimetric calibration, extending those ideas from probes to reactors and from energy accounting to radical pathway quantification.

By merging standardized calorimetry with orthogonal and concurrently applied dosimeters, the study delivers a quantitative map from acoustic power density to oxidant speciation and pollutant loss, enabling rigorous comparison across fills and geometries and offering a reproducible template for sonochemical water treatment.

Reporting of nominal electrical settings without quantifying the acoustic energy delivered to the liquid has hindered comparison across reactor geometries and fill volumes. Single-probe dosimetry remains common and often yields divergent estimates of hydroxyl radical production and peroxide formation. The balance between peroxide generation and peroxide decomposition under strong drive at high frequency has rarely been quantified directly in the same reactor. Operating windows for gas feed, pH, and substrate loading have frequently been presented qualitatively and without normalization to energy delivered per volume.

This study addressed these gaps by introducing a calorimetry-anchored framework in which volumetric acoustic power density was mapped, and four complementary dosimeters were applied concurrently in the same 425 kHz reactor. The iodide test with and without ammonium heptamolybdate resolved the respective contributions of hydroxyl radicals and hydrogen peroxide at the bubble–liquid interface. Independent bulk peroxide accumulation, Fricke chemistry in acidic medium, and selective 4-nitrophenol hydroxylation triangulated short-lived interfacial radicals and longer-lived molecular oxidants. This combined design converted qualitative trends into quantitative oxidant budgets linked to delivered energy. The approach identified process windows in volume, gas identity, and pH that maximized radical availability and explained performance changes at higher substrate loading. The framework provides a transferable basis for reactor comparison and scale-up using delivered energy density rather than nominal electrical settings.

2. Materials and Methods

Sunset Yellow FCF (SSY; disodium 6-hydroxy-5-[(4-sulfophenyl)azo]-2-naphthalenesulfonate; 90% purity) was obtained from Sigma-Aldrich. All other reagents were analytical grade and used as received. Solutions were prepared with Milli-Q water (18.2 MΩ·cm resistivity).

Experiments were carried out in a double-jacketed cylindrical glass vessel (internal Ø 6 cm). A 4 cm piezoelectric ceramic transducer, bonded to the vessel base and operated at 425 kHz, provided ultrasonication; the electrical input was adjusted to the desired setpoints. Liquid temperature was regulated by recirculating water through the external jacket and continuously logged with an immersed thermocouple.

The acoustic power delivered to the liquid was quantified calorimetrically from the temperature rise during 5 min of ultrasonication [9,10,11]. For this power calibration, Milli-Q water served as the working fluid, and the jacket was drained to minimize heat loss to the thermostat, improving the accuracy of the energy balance.

The formation of reactive oxygen species (ROS) during ultrasonication was quantified using potassium iodide (KI) dosimetry, both in the absence and presence of ammonium heptamolybdate (AHM) as a catalyst. In the classical Weissler test, hydroxyl radicals (^•OH) generated by acoustic cavitation oxidized iodide ions to iodine, which was rapidly converted to triiodide (I₃⁻). The accumulation of I₃⁻ was monitored spectrophotometrically at 351 nm using a 1 cm path length cuvette and an extinction coefficient of 2.63 × 10⁴ L/mol·cm [12]. The slope of I₃⁻ concentration versus time was taken as the ^•OH radical production rate. To account for oxidants formed by ^•OH recombination, namely H₂O₂, the KI test was repeated in the presence of ammonium heptamolybdate. The molybdate catalyst promoted the reaction between H₂O₂ and iodide, producing iodine that was subsequently converted to I₃⁻. Thus, the KI–molybdate system provided a combined measure of ^•OH and H₂O₂ yields, with the specific H₂O₂ contribution estimated by subtracting the uncatalyzed rate from the catalyzed rate [13].

Hydrogen peroxide was quantified iodometrically [14]. During ultrasonication, 200 µL of the reaction solution was withdrawn and transferred into a quartz cuvette with a 1.0 cm path length. Subsequently, 20 µL of 0.01 M ammonium heptamolybdate and 1.00 mL of 0.10 M KI were added [12]. In the molybdate-catalyzed medium, H₂O₂ oxidized iodide (I⁻) to iodine, which is rapidly converted to triiodide (I₃⁻), forming a stable complex. The mixture was allowed to stand for 5 min at room temperature before analysis. The absorbance of I₃⁻ was then recorded at 351 nm using a UV7 Mettler Toledo UV–Vis spectrophotometer. The H₂O₂ concentration was calculated via the Beer–Lambert law. Reagent blanks and replicate measurements were routinely performed to ensure baseline stability and analytical precision. The accumulation of H₂O₂ was found to be linear with time, consistent with zero-order kinetics, and the formation rate was determined from the slopes of the concentration–time plots [13,15].

A classical Fricke dosimeter containing acidic ferrous sulfate was employed to quantify the total oxidizing capacity generated during ultrasonication. In this system, ^•OH and hydrogen peroxide were produced in situ and contributed to the oxidation of ferrous ions. Specifically, in a solution composed of 0.4 M H₂SO₄, 1.0 mM ferrous ammonium sulfate (Mohr’s salt), and 1.0 mM air-saturated NaCl, ^•OH directly oxidized Fe²⁺ to Fe³⁺. In parallel, hydrogen peroxide participated in the Fenton reaction (Fe²⁺ + H₂O₂ → Fe³⁺ + ^•OH + OH⁻), generating additional hydroxyl radicals that further oxidized Fe²⁺. As a result, the ferric ion yield reflected the aggregate oxidant production, which under ideal conditions corresponded to the rate of [Fe³⁺] formation. The concentration of Fe³⁺ was monitored spectrophotometrically at 303 nm using a 1-cm path-length quartz cuvette and an extinction coefficient of ε = 2197 L/mol·cm. The oxidant formation rate was then calculated via the Beer–Lambert law.

Hydroxyl radicals generated during ultrasonication were quantified via their aromatic substitution on 4-nitrophenol (4-NP), yielding 4-nitrocatechol (4-NC). A 200 mL solution of 4-NP (1.0 mM, pH adjusted to 5.0 to suppress base-catalyzed side reactions) was irradiated in the ultrasonic reactor. At defined intervals, 0.5 mL aliquots were withdrawn and immediately mixed with 0.5 mL of 0.20 M NaOH in a quartz cuvette. The alkaline medium converted the product into its strongly absorbing phenolate, enabling photometric detection. The concentration of 4-NC was determined spectrophotometrically at 510 nm (ε = 12,500 L/mol·cm). The accumulation of 4-NC was linear with irradiation time within the sampling window, consistent with zero-order kinetics, and the slope of [4-NC] versus time provided the ^•OH production rate.

For SSY degradation experiments under various process conditions, 200 mL of freshly prepared dye solution at a fixed concentration was subjected to ultrasonication. The progress of SSY degradation was monitored using a UV–visible spectrophotometer at 482 nm by analyzing 1.2 mL aliquots. After measurement, each aliquot was promptly returned to the bulk solution in order to maintain the acoustic power density applied to the system.

Each experiment was carried out in three independent replicates. Unless noted otherwise, values were reported as the mean of three runs. Differences between conditions were evaluated with two-tailed Student’s t-tests, with statistical significance defined as p < 0.03.

3. Results and Discussion

The performance of the 425 kHz sonoreactor was first evaluated through calorimetric studies to establish the actual acoustic power delivered to the liquid phase and to provide a reliable basis for comparing experimental conditions. To complement this energy-based characterization, a suite of chemical dosimeters, including potassium iodide (with and without catalyst), hydrogen peroxide, Fricke, and 4-NP probes, was employed to quantify radical generation and to map the oxidative environment within the sonoreactor. These combined approaches enabled a mechanistic understanding of cavitation activity and radical pathways under varying process variables. Building on this reactor characterization, the ultrasonic degradation of SSY was systematically investigated, allowing the correlation of sonochemical reactivity with operational parameters and providing insights into the efficiency and pathways of SSY sono-oxidation.

3.1. Calorimetric Studies

Figure 1a illustrates the correlation between calorimetric acoustic power density (i.e., calorimetric acoustic power divided by liquid volume) and working volume across input powers ranging from 20 to 100 W. As the working volume increased from 200 to 500 mL, the calorimetric acoustic power density systematically decreased at each power setting: by approximately 2.2, 2.2, 2.3, 2.2, and 1.6-fold for input powers of 100, 80, 60, 40, and 20 W, respectively. This inverse trend was expected because distributing energy into a larger liquid volume decreased the energy density available to nucleate and drive transient cavitation events for a given transducer output. This diminishes hot-spot formation and sonochemical potency. The small confidence intervals highlighted good reproducibility of the calorimetric readout from run to run. These results aligned with cavitation theory, which stated that chemical effects scale with the local acoustic energy available per unit volume. The results also support the long-standing recommendation to treat calorimetric acoustic power density as a primary scale variable in sonoreactor design.

Figure 1b showed how calorimetric acoustic power density changed across different volumes (200–500 mL) as set power increased from 20 to 100 W. As the set power increased, the calorimetric acoustic power density rose nearly monotonically with each volume increase. For example, at 300 mL, the values were 29.26, 56.01, 72.94, 96.56, and 126.03 W/L for set powers ranging from 20 to 100 W. However, the increase became sublinear at larger volumes because attenuation and dispersion of the ultrasound field increased as the liquid path lengthened.

Figure 1a,b together emphasize two ways to intensify sonochemistry: decreasing the volume (or, equivalently, the liquid height/path) and increasing the delivered power. Both methods are expressed compactly through calorimetric acoustic power density. Therefore, maintaining a comparable calorimetric acoustic power density when changing scales should preserve the cavitation activity map and radical production to a first approximation.

Delivered acoustic power was quantified by calorimetry (temperature-rise method), an accepted approach for power calibration in sonochemistry and sonoprocessing [9,10,11]. Reporting calorimetric acoustic power density provided a normalized metric that could be compared directly across reactor fills and geometries. Since radical generation rates and pollutant degradation kinetics typically increased with acoustic power density, these calorimetric maps can be used to interpret trends in dosimetry (e.g., with potassium iodide, hydrogen peroxide, Fricke reagent, and 4-NP) and SSY oxidation. In short, volumes and powers that maximized calorimetric acoustic power density were expected to maximize measurable dosimeter yields and SSY removal.

3.2. ROS Dosimeters

To complement calorimetry and determine the formation of ROS at 425 kHz, the sonoreactor using a set of well-established dosimeters that detect various aspects of cavitation chemistry was profiled. Potassium iodide measured the local oxidizing environment by forming I₃⁻ from I⁻. This process is initiated by ^•OH/HO₂^• and promoted by in situ H₂O₂. The strong absorbance of KI at 351 nm enables high sensitivity to interfacial radical fluxes. Bulk H₂O₂ accumulation integrated ROS production in the liquid phase, primarily the recombination of ^•OH. This provides a volumetric marker that scales with acoustic energy input. The Fricke system provided a quantitative standardized measure of hydroxyl radical yield under acidic conditions via Fe²⁺ conversion to Fe³⁺ with a defined response factor. Finally, 4-NP acted as an organic probe that was rapidly consumed by electrophilic ^•OH attack. This links dosimetric signals to pollutant-like reactivity. Together, KI, H₂O₂, the Fricke system, and 4-NP triangulated ROS generation across bubble–liquid regions and chemistries. This approach showed a relation between volumetric acoustic power density and specific oxidative pathways and enabled systematic evaluation of process variables.

A working volume of 200 mL was selected because calorimetry demonstrated that, at a fixed electrical set power, the delivered acoustic power was essentially volume independent, so the volumetric acoustic power density decreased as the fill increased. Under typical conditions, this corresponded to nearly twice the power density at 200 mL compared with 500 mL, representing the strongest energy density achievable without hardware modification. From a reactor physics standpoint, at 425 kHz, a smaller working volume shortened the liquid height, reduced attenuation, and better aligned the bulk with antinode regions. At the same time, 200 mL avoided the drawbacks of very small fills, such as rapid heating, evaporation, and field distortion, while still delivering the high power density required to resolve kinetics over extended runs.

3.2.1. KI Dosimeter

To identify the primary ROS at 425 kHz ultrasonication, the formation of triiodide in 0.1 M KI in the absence and presence of AHM was examined. In KI solution, the ^•OH radical oxidized iodide through a short chain (I^•/I₂^•−) to form I₂, which rapidly converted to I₃⁻. The I₃⁻ concentration was measured and found that its linear increase over time corresponded to the zero-order ^•OH production rate during steady ultrasonication. In the presence of AHM, H₂O₂ formed from ^•OH recombination was catalytically converted with I⁻ to I₂ (H₂O₂ + 2I⁻ → I₂ + 2OH⁻). Thus, the measured I₃⁻ slope reflects the total oxidant flux (^•OH + H₂O₂). Subtracting the KI-only slope yields the H₂O₂ formation rate. These procedures are commonly used to distinguish between radical and molecular oxidants produced by cavitation [13].

Figure 2 showed that the formation rate of I₃⁻ from KI dosimetry increased monotonically with input power, regardless of the presence of AHM. When the KI-only slopes were interpreted as ^•OH-equivalent production rates, the ^•OH flux increased nearly linearly with input power. Specifically, it increases by a factor of 3.13 from 40 to 100 W (from 1.50 to 4.70 µM/min). This trend aligns with calorimetric power density scaling, wherein greater acoustic energy delivered per unit volume results in more violent collapses and higher ^•OH production rates. As power increased, so did the fraction of the oxidant captured as H₂O₂ (21%, 46%, 53%, and 52% at 40, 60, 80, and 100 W, respectively). This suggested that, at higher acoustic intensities, a greater percentage of nascent ^•OH species combined before reacting with solutes. This outcome is expected because the bubble number density and coalescence increase, thereby enhancing recombination pathways (^•OH + ^•OH → H₂O₂). H₂O₂ is a stable molecular product that primarily forms through radical recombination in and around collapsing bubbles. The yield of H₂O₂ increases with ultrasonication power and acoustic path length.

In the presence of AHM, the enhancement increased from 1.3-fold at 40 W to 1.8-fold at 60 W to 2.1-fold at 80–100 W. This showed that H₂O₂ became a more significant sink for ^•OH at higher power settings. AHM mechanistically accelerates iodometric capture of H₂O₂ (H₂O₂ + 2I⁻ → I₂ + 2OH⁻), enabling real-time observation of the growing H₂O₂ pool. Without AHM, KI cannot practically detect H₂O₂ within the measurement timescale.

The production rate of ^•OH established the upper limit of pollutant transformation via direct radical attack, scaling with calorimetric acoustic power density. The H₂O₂ share indicates the proportion of the radical inventory diverted to non-radical oxidant pools. This information is crucial when coupling ultrasound with a process for which H₂O₂ is a useful co-reagent rather than a radical sink. Along with calorimetric maps, the results of the KI dosimeters (with and without AHM) provide a quantitative link between energy input, ROS speciation, and expected reactivity. These results will be used to interpret the behavior of the other dosimeters and the kinetics of SSY oxidation. KI (with and without AHM) remains a reliable method for determining the contributions of ^•OH and H₂O₂ in high-frequency reactors.

3.2.2. H₂O₂ Formation

The production rate of H₂O₂ increased monotonically with input power (40 to 100 W), ranging from approximately 0.75 to 3.5 µM/min (Figure 3). Since hydrogen peroxide in pure water primarily arose from hydroxyl radical self-recombination and, to a lesser extent, from hydroxyl radical pathways formed from hydrogen/oxygen reactions, its accumulation indicated net ROS generation under acoustic cavitation. Thus, increasing the delivered acoustic energy raises the number of active bubbles and their collapse intensity, thereby boosting primary water sonolysis (H₂O → ^•OH + ^•H) and subsequent ROS coupling to H₂O₂.

As expected, the scaling is not perfectly linear because the measured H₂O₂ rate reflected the balance between production and concurrent losses. At higher powers, ultrasound attenuation, bubble–bubble interactions, and local heating can reduce collapse severity (shielding), while H₂O₂ itself can be consumed by further sonolysis and radical reactions (e.g., H₂O₂ + ^•OH → HO₂^• + H₂O), moderating net accumulation. Thus, the sublinear gain at the highest settings likely reflects physical (acoustic) and chemical (secondary ROS) limitations superimposed on the primary power effect.

Notably, the power-response profile aligned with earlier calorimetric mapping results. Increasing acoustic power density increases H₂O₂ productivity. This finding further establishes calorimetry as a meaningful normalization method for comparing reactor fills and geometries. Since H₂O₂ integrates ROS generated across hot spots and interfacial regions, these maps provide a useful baseline for interpreting the behavior of more selective dosimeters, such as KI, Fricke, and 4-NP. Ultimately, these maps clarify the trends in SSY abatement reported below.

To reconcile iodometric and hydrogen peroxide dosimeters, KI assays performed with and without AHM were compared to independent bulk H₂O₂ measurements, thereby quantifying how ROS are formed and evolve in the 425 kHz sonoreactor. In neat KI, I₃⁻ originates primarily from the Weissler reaction, in which interfacial ^•OH oxidizes I⁻. AHM addition generates catalytic species that rapidly oxidize I⁻ using freshly formed H₂O₂ (H₂O₂ + 2 I⁻ + 2 H⁺ → I₂ + 2 H₂O; I₂ + I⁻ → I₃⁻). Because this catalytic pathway is both fast and selective, the increment in I₃⁻ production (ΔKI = with − without AHM) serves as a proxy for the instantaneous H₂O₂ formation rate near the bubble–liquid interface, before peroxide undergoes back-decomposition or diffusion losses.

A minimal kinetic framework rationalizes the divergence between KI without AHM, KI with AHM, and bulk H₂O₂ at high power. Let r_•OH denote the volumetric formation rate of ^•OH radicals near the interface. Loss of ^•OH radicals occurs by recombination, with second-order rate constant k₂, and by first-order scavenging, with effective rate constant k_S, which represents reactions with solutes and the liquid matrix. Under quasi-steady-state conditions:

r_•OH = k₂ [^•OH]² + k_S [^•OH]

(1)

Solving gives:

$$\left[{\mathrm{H}\mathrm{O}}^{•}\right]={\displaystyle \frac{-{\mathrm{k}}_{\mathrm{S}}+\sqrt{{\mathrm{k}}_{\mathrm{S}}^2+4{\mathrm{k}}_2{\mathrm{r}}_{•\mathrm{O}\mathrm{H}}}}{2{\mathrm{k}}_2}}$$

(2)

The instantaneous interfacial H₂O₂ formation rate is then

r_H2O2 = k₂ [^•OH]²

(3)

Two limiting regimes follow:

• When the ^•OH radical concentration scales linearly with r_•OH, and the H₂O₂ formation rate scales with $r_{•\mathrm{O}\mathrm{H}}^2$. In this regime, most oxidative capacity remains with short-lived radicals.
• When the ^•OH radical concentration scales as $\sqrt{r_{•\mathrm{O}\mathrm{H}}/k_2}$, and the H₂O₂ formation rate approaches r_•OH, oxidative capacity is transferred largely through molecular oxidants.

Representative aqueous constants support this shift. The reaction ^•OH + ^•OH → H₂O₂ has k₂ = 5.5 × 10⁹ M⁻¹·s⁻¹ at 25 °C. The reaction H₂O₂ + ^•OH → HO₂^• + H₂O has k = 2.7 × 10⁷ M⁻¹·s⁻¹, providing a significant back reaction at elevated radical levels. Hydroperoxyl self-reaction, HO₂^• + HO₂^• → H₂O₂ + O₂, proceeds with k = 8 × 10⁵ M⁻¹·s⁻¹. The acid–base pair HO₂^•/O₂^•− has pKa = 4.8, so conversion to superoxide increases with pH and alters secondary sinks.

These values explain the growing KI + AHM increments and the sublinear bulk H₂O₂ gains at the highest powers by showing that bimolecular termination accelerates strongly as r_•OH increases and that secondary loss of H₂O₂ becomes non-negligible at elevated radical concentrations.

KI dosimetry without AHM gave triiodide formation rates of approximately 1.50, 2.28, 3.36, and 4.70 µM/min at 40, 60, 80, and 100 W, respectively. With AHM, the rates increased to about 1.91, 4.20, 7.18, and 9.85 µM/min, corresponding to boosts of nearly 27–110% as power increased. The AHM-induced increments (ΔKI) of nearly 0.41, 1.92, 3.82, and 5.15 µM/min thus reflect a growing peroxide contribution at higher acoustic powers. Independent bulk H₂O₂ accumulation assays yielded approximately 0.77, 1.73, 2.61, and 3.53 µM/min over the same power range. At powers of 80−100 W, these bulk rates fell below the corresponding ΔKI values, indicating that net peroxide destruction (via sonolysis inside/near bubbles and secondary radical reactions) increasingly offsets formation as the ultrasound field intensifies. This divergence is consistent with the dual role of H₂O₂ as both a product of ^•OH recombination and a substrate for further sonochemical degradation.

Because two hydroxyl radicals recombine to form one H₂O₂, the observed bulk accumulation provides a lower-bound recombination sink of 1.54, 3.46, 5.21, and 7.05 µM/min at 40–100 W. Adding these values to the KI without AHM rates (^•OH captured by I⁻) yields minimum total ^•OH generation estimates of approximately 3.04, 5.74, 8.57, and 11.75 µM/min, respectively. Expressed as fractions, the share of ^•OH lost to recombination rises from about 51% at 40 W to 60% at 60−100 W, showing that stronger fields not only increase absolute radical production but also favor radical–radical coupling. This trend aligns with the expected behavior of high-frequency cavitation clouds, where higher power expands the active bubble population and shortens radical diffusion paths, thereby promoting bimolecular ^•OH loss to H₂O₂.

As an ensemble, the observations reveal that the two dosimetric approaches bracket the actual ROS dynamics. KI without AHM emphasizes interfacial ^•OH capture, KI with AHM approximates the combined flux of ^•OH and freshly formed H₂O₂ near bubbles, and bulk H₂O₂ accumulation reports the net peroxide that survives mixing and secondary chemistry in the sonoreactor volume. The internal consistency of these trends, and their systematic dependence on acoustic power, confirmed that power primarily scaled ^•OH generation while shifting a larger fraction toward H₂O₂ via recombination. The KI/AHM trap is thus valuable for capturing all oxidizing equivalents produced at the cavity interface, and using both KI and H₂O₂ readouts provides complementary bounds on ROS budgets that can be directly related to calorimetric acoustic power density for sonoreactor optimization and scale-up.

3.2.3. Fricke Dosimeter

Figure 4 showed a monotonic increase in oxidizing capacity with acoustic power, as quantified by the Fricke dosimeter. As the input power rose from 40 to 100 W, the Fe³⁺ formation rate increased from 2.39 to 11.58 μM/min. This scaling is expected, since stronger driving enhances both cavitation number density and collapse intensity, thereby increasing radical generation in the bubble–liquid interfacial zone and the surrounding liquid. In acidic Fricke solution, the primary oxidant is ^•OH, with a smaller contribution from HO₂^•/H₂O₂ via Fenton-type secondary chemistry. Each ^•OH (and HO₂^• under these conditions) oxidizes one Fe²⁺ to Fe³⁺, making the Fe³⁺ formation rate a reliable indicator of the total oxidizing radical flux in the bulk liquid. Two features of the response are noteworthy. First, the rate–power curve becomes slightly superlinear at higher powers, consistent with the growth of nonlinear cavitation activity at elevated acoustic power densities. Second, absolute Fe³⁺ formation rates are substantially higher than measured H₂O₂ production rates (Figure 3), consistent with the Fricke system integrating contributions from both primary ^•OH and secondary oxidants such as HO₂^•/H₂O₂ in strongly acidic media.

The KI (Weissler) dosimeter corroborates the power dependence but also reveals chemistry-specific differences. The triiodide formation rate rises from 1.50 to 4.70 µM/min without AHM and from 1.91 to 9.85 with AHM as the power increases from 40 to 100 W. This enhancement stems from the well-established Mo(VI)-catalyzed oxidation of I⁻ by H₂O₂ in the Weissler reaction. H₂O₂, formed by the recombination of ^•OH, enters a catalytic cycle that swiftly converts I⁻ to I₃⁻. This enables the KI assay to detect direct ^•OH attacks on I⁻ and the H₂O₂ pathway. Consequently, the KI+AHM system reports a larger fraction of the overall ROS budget than the uncatalyzed KI system, and its rates approach those of the Fricke system.

Bulk H₂O₂ accumulation increased with power, rising from 0.77 to 3.52 µM/min over a range of 40 to 100 W. Because H₂O₂ is predominantly formed by radical recombination (2^•OH → H₂O₂), the lower-bound ^•OH production rates are approximately twice the H₂O₂ rates (1.54, 3.46, 5.21, and 7.05 µM/min). These values remain lower than the Fricke Fe³⁺ and KI+AHM rates at the same powers. This outcome is consistent with the fact that H₂O₂ reflects only the recombination branch of ^•OH chemistry, is subject to back reactions and loss processes, and undergoes additional Fe²⁺ oxidation pathways in the Fricke solution. The qualitative ordering observed across all powers (Fricke ≥ KI+AHM > KI without AHM > H₂O₂) is therefore mechanistically coherent. Fricke dosimeter integrates ^•OH and secondary oxidants in an acidic environment, KI with AHM directly senses ^•OH and the H₂O₂ formed from ^•OH. Uncatalyzed KI primarily detects interfacial ^•OH, and H₂O₂ alone reflects only the recombination sink of ^•OH.

Synthesizing these findings, the three dosimeters provide a consistent picture of ROS generation at 425 kHz. Increasing power elevates acoustic power density, amplifying ^•OH formation and H₂O₂ yields downstream. The AHM-promoted KI response confirms that a significant portion of the oxidative capacity originates from the H₂O₂ produced by ^•OH recombination. Meanwhile, Fricke rates demonstrate that the total oxidizing equivalents accessible to the bulk liquid increase due to the efficient conversion of ^•OH and peroxy species into Fe³⁺ under acidic conditions.

3.2.4. 4-Nitrophenol Dosimeter

Figure 5 showed that the formation rate of 4-NC increased monotonically with input power. The formation rate ranged from approximately 0.51 µM/min at 40 W to 2.02 µM/min at 100 W. This behavior is consistent with cavitation theory, which states that greater acoustic driving increases the frequency and intensity of transient collapses. These collapses increase the flux of ^•OH at the interface and the likelihood of electrophilic aromatic substitution on 4-NP, yielding 4-NC, the canonical hydroxylation product. Since 4-NP reacts with ^•OH via a high second-order rate constant (k = 3.8 × 10⁹ M⁻¹·s⁻¹ [16]) and a selective ring-substitution pathway, its response depends more on the presence of short-lived radicals at the bubble–liquid interface than on bulk oxidants. Consequently, 4-NP acts as a stringent process probe for ROS generated directly by cavitation. The nearly linear increase in product formation with power indicates that interfacial ^•OH production scales with acoustic power density in this sonoreactor.

Collectively, the observations demonstrate that the four dosimeters provide complementary yet internally consistent information. 4-NP (or 4-NC) primarily responds to interfacial, extremely short-lived ^•OH radicals. KI without AHM captures rapid radical oxidation but is less sensitive to H₂O₂ accumulation. KI with AHM converts stored H₂O₂ into I₃⁻, thereby reflecting the combined contributions of immediate ^•OH radicals and accumulated peroxides. The Fricke dosimeter, in contrast, quantifies the total pool of oxidizing equivalents under acidic conditions.

3.3. SSY Sono-Oxidation

This section examines how operating conditions affect cavitation chemistry and, consequently, the sonochemical oxidation of SSY at 425 kHz. Acoustic power governs bubble population and collapse intensity. Although increases in acoustic power typically increase ^•OH/H₂O₂ production, attenuation and decoupling effects prevent additional increases. SSY loading influences radical demand and interfacial availability, often altering the apparent reaction order as the substrate competes for ^•OH in the boundary layers. pH alters the speciation of the dye, the lifetimes of ROS, and the balance between bulk and interfacial reactions. These changes lead to systematic alterations in degradation kinetics. Dissolved gas composition and sparging determine bubble thermodynamics and hot-spot temperatures. In aggregate, power, dye loading, pH, and the gas environment provide the mechanistic framework through which SSY decay behavior is understood.

3.3.1. Power Impact

Figure 6a showed how ultrasonication power affected SSY degradation at initial dye concentrations of 5 and 10 mg/L. Increasing the electrical input power from 40 to 100 W accelerated SSY decay at both concentrations. The normalized concentration profiles (C/C₀ vs. time) consistently rank the power levels as follows: 100 W > 80 W > 60 W > 40 W. The largest differences emerge beyond the 60–90 min mark. At a fixed power level, the 10 mg/L solutions decay more slowly than the 5 mg/L solutions, reflecting stronger competition for ROS and higher radical demand per unit volume. Steeper apparent slopes emerge as power increases, and modest but systematic rate suppression occurs when the initial dye concentration doubles. Fitting over the main ultrasonication window gives apparent pseudo-first-order rate constants that grow with power (Figure 6b). For 5 mg/L SSY, k increases from 2.5 × 10⁻³ to 1.09 × 10⁻² min⁻¹ as the power rises from 40 to 100 W, and for 10 mg/L, k increases from 2.1 × 10⁻³ to 0.99 × 10⁻² min⁻¹. The slight suppression of k at 10 mg/L relative to 5 mg/L reflects stronger competition for short-lived oxidants (primarily ^•OH) at higher solute loading, a common feature of sonolytic dye abatement where steady-state radical assumptions lead to apparent first-order kinetics with respect to the dye. At a given ROS flux, a higher bulk SSY level increases competition for ^•OH in the interfacial reaction zone and consumes a larger share of the H₂O₂ pool. This results in lower fractional conversion at equal irradiation times. Since solute levels are low (in the mg/L range), acoustic attenuation by the dye is minimal. Thus, radical demand is the dominant factor rather than changes in cavitation hydrodynamics. Overall, power is the primary factor governing SSY sono-oxidation. Higher acoustic power densities result in higher radical and peroxide yields and faster dye decay. Increasing the initial SSY concentration uniformly shifts the curves toward slower kinetics by increasing ROS consumption.

Calorimetric mapping in this sonoreactor showed that delivered acoustic power and, by normalization, the volumetric acoustic power density increased systematically with the set power, providing a device-independent scale variable for comparing fills and operating points. In parallel, all four dosimeters confirmed that higher power drove larger oxidant fluxes. KI (Weissler) without AHM tracks interfacial ^•OH production and rises nearly linearly with power, while the KI with AHM variant captures both ^•OH and H₂O₂, rising more steeply and indicating that the peroxide fraction of the oxidant budget grows with power. Bulk H₂O₂ accumulation also increases but remains below KI with AHM at the highest powers, consistent with in situ H₂O₂ losses through back decomposition and radical reactions in dense cavitation fields. Complementary Fricke measurements, which integrate ^•OH and peroxy species in acidic media via Fe²⁺ to Fe³⁺ oxidation, likewise increase with power and provide an upper bound on accessible oxidizing equivalents. The 4-NP to 4-NC hydroxylation, a selective probe for near-interface ^•OH, shows the same trend. The consistent ranking with power aligns with calorimetric delivered-power mapping and with established sonochemistry: stronger acoustic driving increases active bubble density and collapse severity, raising both ^•OH flux and the fraction diverted to H₂O₂ via recombination.

The coherent power response across SSY, KI with and without AHM, H₂O₂, Fricke, and 4-NP was consistent with cavitation theory [1]. Stronger acoustic driving increases both the number density of active bubbles and the intensity of their collapse, thereby enhancing primary water sonolysis and, in turn, promoting both direct radical attack and radical recombination to H₂O₂.

Figure 6a,b, together with calorimetric and dosimetric data, established a clear linkage between energy input and chemical output. Increasing the calorimetric acoustic power density enhances both ^•OH and H₂O₂ generation, which in turn monotonically accelerates SSY removal.

3.3.2. SSY Loading Impact

Figure 7a illustrates the influence of initial SSY loading on its degradation, with dye concentrations varied between 2.5 and 20 mg/L. When the acoustic input remains constant (100 W), SSY degradation exhibits an inverse relationship with the initial concentration. A concentration of 2.5 mg/L decays the fastest, reaching complete removal within 210 min. Concentrations of 5, 10, and 20 mg/L, on the other hand, exhibit progressively slower fractional losses within the same irradiation period. The accompanying pseudo-first-order fits quantify this trend (Figure 7b): the apparent rate constant (k) decreases from 1.63 × 10⁻² to 1.09 × 10⁻², 0.99 × 10⁻², and 0.88 × 10⁻² min⁻¹ as the initial SSY concentration increases from 2.5 to 5, 10, and 20 mg/L, respectively. In normalized coordinates (C/C₀), the initial degradation slopes systematically decrease with increasing dye concentration, indicating that the system operates in a radical-limited regime. In this regime, the flux of ROS is essentially fixed by the acoustic field and must be distributed over a larger number of dye molecules as the initial SSY concentration rises. At higher loadings, two additional effects reinforce this behavior. First, saturation of the bubble–liquid interfacial layer, where most ^•OH is generated, limits the frequency of encounters between radicals and individual dye molecules. Second, aromatic transformation products accumulate over time and compete for ROS, progressively scavenging oxidants. Together, these effects account for the observed curvature in the degradation profiles and the pronounced slowdown at later stages of reaction.

These concentration trends are consistent with the established power dependence observed at 5 and 10 mg/L (Figure 7a,b). Increasing the input power from 40 to 100 W markedly steepened the C/C₀ decay curves at both concentrations, demonstrating that higher acoustic input accelerates ROS formation. Calorimetry confirmed this energy delivery: the acoustic power density rose significantly with input power, reflecting a larger population of active bubbles and more violent collapses. Dosimetry provided the chemical correlate. The KI assay showed a linear increase in ^•OH production with power, while the KI/AHM assay, which also detects H₂O₂, exhibited an even steeper rise. Together, these results indicate that both primary ^•OH and secondary H₂O₂ increase with acoustic intensity. Accordingly, the degradation curves at 100 W represent the outcome of the highest available ROS flux, while increasing initial SSY concentration simply imposes a larger stoichiometric demand and intensifies radical competition against this fixed flux.

Overall, the data set reveals a coherent link between energy, chemistry, and performance. Calorimetry demonstrates that higher input power delivers greater acoustic power density, dosimeters show that this translates into higher ^•OH and total oxidant generation, and kinetics confirm faster SSY loss at a fixed initial dye concentration. At constant power, fractional conversion slows as the initial SSY concentration increases. In practical terms, lower influent dye concentrations are removed more efficiently on a fractional basis when treatment volume and power are fixed, whereas higher loadings require extended residence times or increased acoustic power density to achieve comparable conversion.

3.3.3. pH Impact

SSY removal was strongly pH-dependent (Figure 8a,b). The fastest decay occurred under strongly acidic conditions. At pH 1, the normalized concentration drops to zero within 150 min, and the apparent pseudo-first-order constant is the largest in the series. The next most effective condition is pH 3. As the medium shifts to mildly acidic/near-neutral (pH 4.8–6.9) and moderately alkaline (pH 9), the curves flatten and the fitted rate constants decrease, indicating slower fractional conversion. At pH 11, the early-time loss is the slowest, yet the time-averaged rate constant is higher than at pH 4.8–9 due to a late-stage acceleration. This explains why its bar is elevated in Figure 8b, even though Figure 8a shows an initially sluggish trajectory.

Under acidic conditions, the oxidizing strength of the ^•OH radical was higher, and the potential shifted negatively with increasing pH according to Nernstian dependence. This favored aromatic hydroxylation and cleavage of the azo bond in SSY. In addition, ^•OH remains in its protonated form at low pH; only at very high pH does partial deprotonation occur (pKa 11.9), producing the oxyl radical anion O^•−. This species is more nucleophilic and far less prone to aromatic addition, thereby suppressing dye-bleaching pathways. Acidic media also stabilize H₂O₂ against base-catalyzed decomposition (maximal stability at pH < 4), allowing it to persist as both a secondary oxidant and a precursor of ^•OH.

In neutral to alkaline water, background anions such as bicarbonate and carbonate efficiently scavenge ^•OH (e.g., k_{•OH+HCO3−} = 8.5 × 10⁶ M⁻¹·s⁻¹ [16]), diverting the radical flux toward less reactive species such as CO₃^•− and reducing the oxidant budget available for SSY degradation. Base also accelerates H₂O₂ disproportionation, further diminishing oxidant persistence. These effects explain the slower kinetics observed at pH 4.8–9. The elevated average rate constant at pH 11 reflects a different balance: although early-time scavenging and ^•OH to O^•− deprotonation suppress aromatic addition initially, prolonged sonolysis at high pH accumulates substantial oxidant pools and can alter SSY speciation or aggregation. This leads to a late-stage acceleration, producing a low early-loss curve but a higher global fit.

Quantitative stability context supports the observed pH trend. H₂O₂ has a pKa of 11.62 at 25 °C, so alkaline conditions shift speciation toward the conjugate base HO₂⁻. At pH 10, 11, 11.62, and 12, the calculated HO₂⁻ fractions are approximately 0.02, 0.19, 0.50, and 0.71, respectively, consistent with faster base-promoted decomposition relative to the neutral species. In alkaline solution, HO₂⁻ reacts with neutral H₂O₂ to yield oxygen, water, and hydroxide, and the reaction of ^•OH radicals with HO₂⁻ proceeds about two orders of magnitude faster than with neutral H₂O₂. In addition, ^•OH radicals react with H₂O₂ with a second-order rate constant of 2.7 × 10⁷ M⁻¹·s⁻¹ at 25 °C [16], so elevated radical levels also limit net accumulation. Field and laboratory measurements indicate representative half-lives of 8–31 h in fresh water and 50–70 h in filtered seawater, whereas wastewater exhibits decay on the order of minutes to hours due to catalytic metals and enzymes [17]. These quantitative points explain the reduced peroxide persistence as pH increases and under strong acoustic drive.

The pH trends aligned with ROS measurements. KI (Weissler) tracks interfacial ^•OH and increases with driving power. KI/AHM captures both ^•OH and H₂O₂, rising even more steeply and reflecting enhanced peroxide formation and persistence at low pH. The Fricke assay integrates oxidizing equivalents in acidic media and likewise increases with power. Together, these protocols support the conclusion that acidic operation provides a larger effective oxidant budget at the same delivered acoustic power density, directly accounting for the steeper C/C₀ decays at pH 1–3.

When power and volume were fixed, operation under acidic conditions (pH 1–3) minimized the residence time or delivered energy required for a given SSY conversion. Near-neutral and weakly basic conditions are hindered by radical scavenging and faster H₂O₂ loss, while strongly basic conditions (pH 11) exhibit slow initial kinetics but composition-dependent late gains.

3.3.4. Gases Impact

Figure 9a,b illustrates the effect of saturated gases on SSY degradation. The kinetic curves and fitted rate constants followed the order O₂ > Ar >> Air ≈ No saturation >> CO₂. Oxygen produces the steepest decay (k = 6.72 × 10⁻² min⁻¹), followed by argon (5.07 × 10⁻² min⁻¹). Air and the unsparged condition cluster near ≈ 0.011 min⁻¹, whereas CO₂ essentially suppresses removal over the same ultrasonication window. This hierarchy reflects the combined influence of thermophysical control of collapse intensity and chemical participation of the bubble gas.

The observed order (O₂ > Ar >> Air ≈ No saturation >> CO₂) provides direct guidance for treatment design. Oxygen represents a practical default for dye removal because it combines vigorous collapse conditions with in-bubble participation that enhances oxidant formation and accelerates decay. Argon can generate very strong activity through hotter collapses, but its use is generally suited to small-volume studies or polishing steps rather than large-scale continuous operation. Air or no sparging results in lower activity, and the sonicated liquid progressively loses dissolved gas during operation; therefore, continuous sparging is advisable to maintain steady performance. Carbon dioxide should be avoided for oxidation of aromatics because collapse cushioning and diversion of hydroxyl radicals into carbonate chemistry reduce effective oxidant availability. For all gases, placement of the sparger close to the active acoustic zone and adjustment of flow rate to refresh dissolved gas without excessive stripping of cavitation nuclei are practical operational levers.

Ar is monatomic with a high heat capacity ratio (γ = 1.67) and low heat capacity, so adiabatic compression produces very high hot-spot temperatures. Replacing a fraction of Ar with a polyatomic gas sharply lowers the estimated collapse temperature. Stronger collapses enhance primary water sonolysis (^•OH, ^•H) and thereby increase oxidative capacity. Oxygen, with a lower γ of about 1.4, slightly cushions the collapse relative to Ar, but it also participates chemically inside the bubble or plume. Pathways such as O₂ → O^• and HO₂^•, ^•H + O₂ → HO₂^•, and HO₂^• → H₂O₂ contribute to oxidant yields, generating HO₂^•, H₂O₂, and additional ^•OH through secondary reactions.

Air contains O₂ and N₂, the latter being chemically less reactive and lowering the heat-capacity ratio (γ). As a result, both collapse intensity and in-bubble chemistry are diluted compared with pure O₂ or Ar. In addition, ultrasound progressively degasses solutions, so without continuous sparging, the dissolved gas content decreases during operation, reducing cavitation activity toward the unsparged condition. This explained why the air and no-saturation traces converged.

In the presence of CO₂, two effects act in the same unfavorable direction. First, collapses are weaker because CO₂ is polyatomic with a lower heat-capacity ratio and a higher effective heat capacity, which reduces peak collapse temperatures compared with Ar or O₂ and depresses primary radical formation. Second, dissolved CO₂ establishes H₂CO₃/HCO₃⁻/CO₃²⁻ buffers that divert radicals into carbonate chemistry. Hydroxyl radicals react rapidly with HCO₃⁻ and CO₃²⁻ to form CO₃^•−, a much less reactive oxidant toward many aromatics, with reported rate constants on the order of 10⁶–10⁷ M⁻¹·s⁻¹ [16]. The CO₃^•− radical is a more selective and generally less reactive oxidant toward many aromatics. The suppression observed under CO₂ saturation is consistent with this kinetic framework, although CO₃^•− radical formation was not directly confirmed in this study.

4. Conclusions

A coupled calorimetric and multidosimetric framework was established to quantify radical pathways in a 425 kHz sonoreactor and to link energy delivery with chemistry and performance in SSY degradation. Temperature-rise calorimetry provided the delivered acoustic power, which, when normalized by working volume, yielded the acoustic power density as a device-independent scale variable. Across fills and set powers, higher acoustic power density reproducibly translated into stronger cavitation activity and faster pollutant removal, confirming calorimetry as the anchor for reactor comparison and scale-up. Four complementary dosimeters, KI, KI/AHM, bulk H₂O₂ accumulation, and 4-NP to 4-NC hydroxylation, enabled triangulation of oxidant formation across bubble–liquid regions and mapping of ROS. KI isolated interfacial ^•OH attack. KI/AHM captured ^•OH combined with H₂O₂. Bulk H₂O₂ integrated the recombination branch. 4-NP to 4-NC selectively reported near-interface ^•OH. The four readouts rose coherently with acoustic power density, demonstrating that stronger driving both increased ^•OH generation and shifted a larger fraction into H₂O₂ through recombination.

Process variable studies rationalized SSY kinetics through this energy-to-chemistry linkage. Power was the primary lever. Increasing set power increased apparent pseudo-first-order rate constants and steepened C/C₀ trajectories in step with higher dosimeter signals. Substrate loading modulated fractional removal at fixed power, with higher pollutant concentration imposing greater radical demand and competition in the interfacial zone. pH tuned oxidant strength and persistence. Acidic media maximized bleaching by maintaining a stronger ^•OH/H₂O redox couple and stabilizing H₂O₂. Near-neutral and alkaline media suffered from carbonate and bicarbonate scavenging of ^•OH and base-catalyzed H₂O₂ loss. Dissolved gas identity controlled both collapse thermodynamics and in-bubble chemistry. Oxygen and argon gave the fastest removal by combining violent collapses with oxidative participation, while carbon dioxide suppressed activity through collapse cushioning and diversion of ^•OH to carbonate radicals.

The calorimetry-anchored multidosimetric strategy provides a generalizable protocol for quantifying cavitation-driven radical pathways and diagnosing process variables in other aqueous systems. Reporting delivered power and standardized dosimetry enables future studies to construct comparable datasets across reactor geometries and operating frequencies, accelerate process optimization, and support the advanced treatment of dye-contaminated water.

Lower frequencies generate larger cavitation bubbles with more violent collapses, producing stronger mechanical effects but lower radical yields per unit volume. Our dosimetric framework enables quantification of these differences and can guide reactor design when mechanical disruption is prioritized. At higher frequencies, cavitation produces smaller bubbles with gentler collapses, favoring chemical effects and more uniform radical generation, and the methodology presented in this study provides a basis for evaluating efficiency and reproducibility under such conditions. More broadly, normalizing results by delivered energy density and dosimetric parameters establishes a transferable framework for comparing sonoreactors across frequency ranges despite inherent differences in cavitation dynamics.

The proposed framework has direct implications for real-world water treatment practice. By linking delivered acoustic power density with radical speciation, the method provides a transferable basis for scaling laboratory reactors to pilot and industrial units. The approach enables rational selection of operating parameters such as working volume, gas feed, and pH to maximize oxidant yield under given hardware constraints. In practical scenarios, this allows treatment plants to predict performance across variable influent loads, to minimize energy consumption per unit pollutant removed, and to integrate ultrasound with complementary advanced oxidation processes. The strategy also supports regulatory compliance by providing a standardized and reproducible metric for reporting energy delivery and oxidative capacity, thereby facilitating comparison across technologies and installations. These features make the method suitable for deployment in textile effluent treatment, pharmaceutical wastewater abatement, and other industrial sectors where dye and aromatic contaminants are prevalent.