ISO 24758-1:2025

International
Standard
ISO 24758-1
First edition
Fine bubble technology —
2025-12
Evaluation method for determining
the reactive oxygen species in
ultrafine bubble dispersions —
Part 1:
Probe based kinetic model
Technologie des fines bulles — Méthode d'évaluation pour
déterminer les espèces réactives de l'oxygène dans les dispersions
de bulles ultrafines —
Partie 1: Modèle cinétique basé sur les sondes
Reference number
© ISO 2025
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms.2
3.2 Abbreviations and chemical formulas .2
4 Principle . 3
5 Apparatus and materials . 3
5.1 Gas chromatography with electron capture detector .3
5.1.1 Headspace vial and clamping machine .3
5.1.2 Carrier gases and column .3
5.1.3 Gas chromatograph .3
5.2 High-performance liquid chromatography–mass spectrometry .3
5.2.1 Vial .3
5.2.2 Carrier gases and column .3
5.2.3 Liquid chromatograph.4
5.3 Reagents .4
5.3.1 Probes .4
5.3.2 Other chemicals .4
6 Requirements . 4
6.1 Sample .4
6.2 Evaluation system .4
6.3 Environment .5
7 Procedure . 5
7.1 General .5
7.2 Introduce probe into the FB system and sample over time .5
7.3 Measurement of the probe compound concentration.6
7.4 Calculation of the probe kinetics model .6
8 Results and calculation . 6
8.1 Commonly used probe for selection .6
8.2 Calibration curve for the probe-concentration measurement .6
8.2.1 High-performance liquid chromatography–mass spectrometry .6
8.2.2 Gas chromatography with ECD .9
8.3 Analysis of the probe with reaction time .10
8.4 Model development . . .11
8.5 Model verification . 12
9 Report .13
9.1 Report of the testing results. 13
9.2 Report of the testing conditions . 13
Annex A (Informative) Commonly used probes for selection . 14
Annex B (Informative) R code used for solving systems of Formulae .18
Annex C (Informative) Example of test results obtained with ozone FB treatment.20
Annex D (Informative) Example of test results obtained with FB combined plasma treatment .26
Annex E (Informative) Example of test results for detecting ROS in quiescent ozone MB water
after H O addition over storage time .31
2 2
Bibliography .34

iii
Foreword
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The procedures used to develop this document and those intended for its further maintenance are described
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of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
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This document was prepared by Technical Committee ISO/TC 281, Fine bubble technology.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
Fine-bubble (FB) technology holds considerable promise for application in water- and wastewater-
treatment processes. Over the past several decades, numerous studies have demonstrated that microbubble
(MB) and ultrafine bubble (UFB) dispersions can accelerate various advanced oxidation processes (AOPs),
such as those using ozone, plasma, ultraviolet (UV), and electrochemical processes, thereby enhancing the
efficiency of pollutant treatment. Although the treatment effects of fine-bubble processes are promising,
their underlying mechanisms have not been fully understood. Understanding the generation mechanism
of reactive species is imperative. Consequently, it is essential to clarify the role of reactive oxygen species
(ROS) in pollutant abatement via MB and UFB treatments.
There are many techniques for detecting ROS in water. Electron paramagnetic resonance (EPR) spectroscopy
stands out as a proficient tool for the direct detection of ROS, specifically those possessing unpaired electrons,
even at concentrations as low as 1 μM. However, its application is limited as EPR falls short in detecting
ROS, such as ozone and hydrogen peroxide (H O ), which are devoid of unpaired electrons. Moreover,
2 2
·− ·−
challenges persist in the detection of the superoxide anion radical (O ) in water. The O radical can stably
2 2
exist in alcohols, such as methanol, where they are readily trapped by 5,5-dimethyl-1-pyrroline N-oxide
·−
(DMPO). In aqueous solutions, however, the addition rate of O to DMPO is comparatively low, whereas the
decomposition of its DMPO-adduct into DMPO–OH occurs at an exceedingly high rate, rendering effective
detection impracticable. Additionally, the EPR technique is predominantly employed for the qualitative or
semi-quantitative analysis of ROS. Determining the cumulative and real-time concentrations of ROS with
precision remains a complex task.
Probe-based kinetic models are useful for optimizing water-treatment processes for efficient pollutant
abatement and elucidating the ROS reaction mechanism driven by fine-bubble technology. By employing
low concentrations (μM scales) of ROS probes, which will not significantly affect the reaction system, we
can more realistically elucidate the reaction mechanisms occurring in water- and wastewater-treatment
processes. With probe-based kinetic models, it is possible to measure the accumulated concentration of these
ROS over time and their real-time concentrations at each treatment interval. However, caution is advised in
the utilization of this method to measure the concentration of H O within systems, as the relatively low
2 2
oxidizing capacity of H O compared to other ROS may lead to inaccuracies due to significant differences in
2 2
reaction rate constants, potentially introducing significant errors in the analytical evaluations.
Fluorescence spectroscopy, in which suitable probes (e.g., 3’-(p-aminophenyl) fluorescein (APF)) are
employed, is an excellent technique for detecting ROS because of its high sensitivity, simplicity in data
collection, and high spatial imaging resolution. The fluorescent response of the APF probe to different ROS
varies significantly. Notably, fluorescence spectroscopy is not a direct measurement method. When multiple
ROS are present in a system simultaneously, it becomes challenging to distinguish them.
This document specifies detection methods for ROS in MB and UFB dispersions. In ISO 24758-1, the
application of probe-based kinetic models for measuring the cumulative concentrations of various ROS over
time, as well as their real-time concentrations at each treatment interval, is described. In ISO 24758-2, the
application of APF to complement the probe kinetic model, which can detect H O in MB and UFB dispersions,
2 2
is described. The establishment of this document will provide substantial value for various industries.
Manufacturers of MB and UFB equipment for environmental remediation can adopt this document to assess
their equipment and wastewater-treatment processes. Companies with wastewater-treatment needs can
use this document as a basis for selecting appropriate processes and instrumentation. This document
will play a proactive role in evaluating the application and research of MBs in fields including wastewater
treatment and disinfection etc.

v
International Standard ISO 24758-1:2025(en)
Fine bubble technology — Evaluation method for determining
the reactive oxygen species in ultrafine bubble dispersions —
Part 1:
Probe based kinetic model
1 Scope
This document specifies evaluation methods for determining the content of reactive oxygen species (ROS)
used in the FB-facilitated advanced oxidation for pollution abatement in the wastewater treatment process.
The probe based kinetic model is applicable to systems that generate ROS in substantial quantities, rather
than at physiological concentrations, and is applicable to short-lived ROS. However, it is not applicable to
long-lived ROS, such as ozone (O ) and hydrogen peroxide (H O ).
3 2 2
The probe based kinetic model method specifies:
— cumulative concentration of different types of ROS during the reaction process;
— concentration of different types of ROS at each time point during the reaction process.
This method does not define the mechanisms of ROS generation, nor the correlation between bubble size
and ROS production.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 3696, Water for analytical laboratory use — Specification and test methods
ISO 14644-1, Cleanrooms and associated controlled environments — Part 1: Classification of air cleanliness by
particle concentration
ISO 20480-1:2017, Fine bubble technology — General principles for usage and measurement of fine bubbles —
Part 1: Terminology
ISO 23015, Fine bubble technology — Measurement technique matrix for the characterization of fine bubbles
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 23015 and ISO ISO 20480-1 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/

3.1 Terms
3.1.1
reactive oxygen species
highly reactive chemicals formed from diatomic oxygen (O ), water, and hydrogen peroxide
·−
Note 1 to entry: Some prominent ROS include ozone (O ), hydrogen peroxide (H O ), superoxide radical (O ), hydroxyl
3 2 2 2
radical (·OH), and singlet oxygen ( O ).
3.1.2
probe
series of specialized chemical agents designed specifically for detecting and quantifying ROS
Note 1 to entry: These probes consist of small organic molecules, and their reactions with ROS are the elementary
processes.
3.2 Abbreviations and chemical formulas
AOPs advanced oxidation processes
FBD fine bubble dispersion
ROS reactive oxygen species
·OH hydroxyl radical
·−
O superoxide anion radical
O singlet oxygen
H O hydrogen peroxide
2 2
O ozone
ECD electron capture detector
PTFE polytetrafluoroethylene
ESI electrospray ionization
r root mean square error
RMSE
p ratio of performance to deviation
RPD
r correlation coefficient
[P] concentration of probe
[R] concentration of ROS
k rate constants between ROS and probe
R, P
t
ROS exposures concentration
[]Rdt
∫
t
the negative rate of change of the probe concentration
dP[]
−
dt
4 Principle
Probe-based kinetic models are developed based on the assumption that pollutants are abated from the
aqueous phase through simultaneous bulk reactions with ozone and various ROS. This approach involves the
use of internal or spiked probe compounds to determine the exposures of the main reactive species in AOPs
systems. Based on the measured exposures, the abatement efficiency of the pollutant can be calculated if the
rate constants for the reaction of the pollutant with the ROS are known. The radicals that can be measured
1 •−
by this method include the hydroxyl (·OH), singlet oxygen ( O ), and superoxide radicals (O ).
2 2
During FB-facilitated advanced oxidation, a probe (P) is eliminated by its reaction with a ROS. The
elimination of P in terms of the logarithmic relative residual concentration of P can be calculated if the ROS
t
rate constants (k ) and the ROS exposures ( []Rdt ) are known.
ROS
∫
t
5 Apparatus and materials
5.1 Gas chromatography with electron capture detector
5.1.1 Headspace vial and clamping machine
— Vial: a 20 mL headspace vial made of glass.
— Cap: made of aluminium.
— Septum: made of silicone or polytetrafluorethylene (PTFE).
— Clamping machine for a flip top cap.
5.1.2 Carrier gases and column
— Carrier gas: nitrogen (N ).
— Gastight plunger syringe: 1 mL in volume.
— Chromatographic column: fused silica capillary column (Ultra Inert Columns, 30 m × 0,32 mm, 1,8 μm
film thickness) or any other column with comparable characteristics.
5.1.3 Gas chromatograph
The gas chromatograph is equipped with an electron capture detector (ECD) for the detection of probes in
the headspace vial.
5.2 High-performance liquid chromatography–mass spectrometry
5.2.1 Vial
— Vial: a 1,5–2 mL vial made of glass or plastic material.
— Cap: a screw-cap or snap-cap type.
— Septum: made of silicone or PTFE for multiple penetrations by the autosampler needle.
5.2.2 Carrier gases and column
— Carrier gas: nitrogen (N ).
— Chromatographic column: C18 column (4,6 × 250 mm, 5 μm) or any other column with comparable
characteristics.
5.2.3 Liquid chromatograph
The system comprises a liquid chromatograph (for separating mixtures of the sample) and a mass
spectrometer (for identifying and quantifying the separated entities).
5.3 Reagents
5.3.1 Probes
The selection of a probe should adhere to the following principles and procedures:
— the first step should involve theorizing based on literature to identity the likely ROS present in the
reaction system and those that contribute most considerably to the oxidation reaction;
— the reaction rate constants of the probe with various types of ROS are known;
— the choice of the probe should be predicated on the principal ROS within the system. For instance, if ·OH
radicals are among the primary ROS, the selected probe shall exhibit a pronounced selectivity toward ·OH
radicals. This is evident in the reaction rate constant of the probe, which should be substantially higher
for ·OH radicals compared to other ROS, such as nitrobenzene. Similarly, if superoxide anions are the
primary ROS, at least one chosen probe should have a reaction rate constant with a strong oxidizing ROS,
such as ·OH radicals, that is comparable to its reaction rate constant with superoxide anions, exemplified
by compounds such as carbon tetrachloride (CCl ) and trichloromethane (CHCl );
4 3
— each type of ROS should react with at least one probe. Commonly used probes for selection are presented
in Annex A; these probes have been previously used in previous studies for ROS measurement;
— the number of probes should exceed the number of ROS being measured in the system. Consequently,
some probes are utilized to detect the accumulative and real-time concentrations of various ROS within
the reaction system, while others are employed to validate the accuracy of the measurement outcomes;
— volatile probes are known for their high sensitivity in gas chromatography, which is essential for
accurately detecting trace amounts of ROS. This exceptional sensitivity, coupled with considerably
affordable equipment cost, makes volatile probes a highly practical and cost-effective option for ROS
measurement. However, for aerated systems, preference should be given to non-volatile probes. Volatile
probes are suitable for detecting ROS in non-aerated systems, such as quiescent ozone MB water.
5.3.2 Other chemicals
— Sodium thiosulfate: Na S O (MW: 158,10 g/mol).
2 2 3
6 Requirements
6.1 Sample
In scenarios involving ROS determination, two main applications shall be considered: treating wastewater
with MB and UFB and cleaning with water containing MB and UFB. In these scenarios, water purity varies
depending on the specific application. For instance, in wastewater treatment applications, water quality
requirements are less stringent, focusing mainly on identifying ROS types and accumulated concentrations
in the system. However, purified water can be necessary for cleaning processes. When purified water is
used, the water shall conform to ISO Grade 1 purity (see ISO 3696) and the air shall conform to ISO Class 5
cleanliness (see ISO 14644-1) for generating fine bubble dispersion (FBD).
6.2 Evaluation system
In ROS determination systems, probes are present at extremely low concentrations. Consequently, high
cleanliness levels shall be maintained within the testing environment to avoid contamination from external
pollutants that can could adversely affect the precision of sample measurements. For example, using
disposable sample tubes for introducing samples in experiments ensures a contamination-free process.

Moreover, using tubing resistant to oxidation in the experimental setup enhances the overall reliability and
integrity of experimental results.
6.3 Environment
The air cleanliness should be considered during measurement to prevent impurity introduction.
Air cleanliness, ambient temperature, and atmospheric pressure depend on the local environment and may
vary. However, as they are important settings and can influence the evaluation process, they should be
recorded before any evaluation takes place.
7 Procedure
7.1 General
The comprehensive protocol encompasses a 3-step methodology:
— step 1, introduce the probe into the FB system and sample over time;
— step 2, probe the compound-concentration measurement;
— step 3, probe the kinetics-model calculation.
A schematic representation of the ROS-detection apparatus is depicted in Figure 1. The detailed processes
are as follows.
Figure 1 — General view of the ROS-determination system
7.2 Introduce probe into the FB system and sample over time
Select a specified number of probes according to the methods and principles described in Clause 4 and 5.3.1.
Typically, the concentration of pollutants in wastewater ranges from tens to hundreds or even thousands
of ppm. Introduce the probes at extremely low concentrations compared with the pollutant concentrations,
thereby ensuring that the presence of the probes does not alter the degradation pathway of the pollutants
within the MB-facilitated advanced oxidation system. Nonetheless, overly low probe concentrations may
induce substantial deviations in measurement accuracy. The probe concentration should be 1–2 orders
of magnitude lower than the pollutant concentration, with a suggested range from 200 μg/L to 1 mg/L.
After probe addition, sampling should be implemented at various time points as the treatment progresses.
The timing of these samplings should be determined based on the reaction rate, with a minimum of 6–8

temporal points recommended to bolster the precision of ensuing model constructions. If substances that
continuously produce ROS, such as ozone, are present in the sample, an excess amount of sodium thiosulfate
solution should be added immediately after sampling to quench the oxidizing processes generating ROS,
thereby halting further ROS production.
In cases where cavitation occurs during the generation of MBs or UFBs, the high temperatures associated
with this process may trigger probe decomposition. To mitigate this risk, conducting a control experiment can
prove beneficial. For instance, employing a nitrogen (N ) UFB generation system, which experiences cavitation
with a relatively small amount of ROS production, allows us to assess whether probes decompose over time
with a relatively small amount of ROS. Comparing these baseline findings with results from the FB system
enhances the ability to accurately determine the extent of probe decomposition attributed solely to ROS.
7.3 Measurement of the probe compound concentration
Volatile probes, such as CHCl , CCl , and C Cl , shall be analysed using a gas chromatograph equipped
3 4 2 4
with an ECD. Non-volatile probes shall be analysed using high-performance liquid chromatography–mass
spectrometry.
7.4 Calculation of the probe kinetics model
By analysing the changes in the probe concentrations over time and the reaction rate constants between
various probes and different ROS, a system of equations for the accumulated concentrations of different
ROS is established. Subsequently, this system shall be solved in a software environment such as R (a
programming language and software environment for statistical computing and graphics). The equations
for the time-dependent change curves of different ROS shall be further simulated. The resulting functions
shall be differentiated to obtain the real-time concentrations of the ROS. Additional probes shall be used
to validate the calculated ROS concentrations; the results shall be accepted as valid when the difference
between the measured and simulated values lies within the 95 % confidence interval.
8 Results and calculation
8.1 Commonly used probe for selection
Table A.1 in Annex A lists some commonly used probes for selection. The rate constant can be obtained from
the NDRL/NIST Solution Kinetic Database (https:// kinetics .nist .gov/ solution/ ).
Researchers may opt to utilize either known probes or organic small molecules that have not been
previously employed in research works as probes. Experimental determinations shall be conducted of the
reaction order and rate constants between the new probe and various ROS before measuring the cumulative
concentrations of the ROS.
8.2 Calibration curve for the probe-concentration measurement
8.2.1 High-performance liquid chromatography–mass spectrometry
Prior to each injection, allow the system to equilibrate for 8-10 min to stabilize the gradient elution’s impact
on the baseline. Throughout the analysis, the pump pressure shall be maintained consistently below 20 MPa
and ensure no liquid leakage occurred from the liquid injection pump. The probe-compound concentrations
were analysed using the built-in analysis tools in LabSolutions.
The recommended run conditions used are as follows:
— injection volume: 20 μL;
— column: C18 column (4,6 mm × 250 mm, 5 μm, GL Sciences).
— mobile phase: solvent A = 10 mM ammonium acetate in water and solvent B =100 % acetonitrile, delivered
as a binary gradient at a flow rate of 0,8 mL/min.

— binary gradient elution: 10 % B should be held for 0,50 min, stepped to 60 % B at 0,51 min, and increased
linearly to 100 % B at 5 min; thereafter, 100 % B should be held for 2 min. A 5-min equilibration step at
10 % B should be employed at the beginning of each run to bring the total run time per sample to 12 min.
— mass spectrometry: The mass spectrometer should be operated in negative electrospray ionization (ESI)
select-ion mode.
— post-analysis chromatographic column rinsing and storage: Upon completion of the analysis, the
chromatographic column should be rinsed with 50 % acetonitrile/water for 30 min, followed by a
30-minute rinse with 95 % acetonitrile/water, followed by storage.
Figures 2 to 6 illustrate examples of calibration curves for selected probes.
Key
X retention time (min);
Y detection response (a.u.);
X’ standard concentration (ppb);
Y’ peak area of the detection response of MTZ (a.u.).
Figure 2 — Calibration curve for metronidazole

Key
X retention time (min);
Y detection response (a.u.);
X’ standard concentration (ppb);
Y’ peak area of the detection response of pCBA (a.u.).
Figure 3 — Calibration curve for 4-chlorobenzoic acid
Key
X retention time (min);
Y detection response (a.u.);
X’ standard concentration (ppb);
Y’ peak area of the detection response of IMI (a.u.).
Figure 4 — Calibration curve for imidacloprid

Key
X retention time (min);
Y detection response (a.u.);
X’ standard concentration (ppb);
Y’ peak area of the detection response of 24D (a.u.).
Figure 5 — Calibration curve for 2,4-dichlorophenoxyacetic acid
Key
X retention time (min);
Y detection response (a.u.);
X’ standard concentration (ppb);
Y’ peak area of the detection response of TA (a.u.).
Figure 6 — Calibration curve for terephthalic acid
8.2.2 Gas chromatography with ECD
Prior to sampling, set the sample temperature to 80 °C, and allow it to equilibrate for 30 min. Draw 0,50 mL
of the gas sample from the headspace vial using a 1,00 mL chromatographic syringe for injection. During the
injection process, take precautions to prevent gas leakage and minimize losses. Utilize a chromatography
data-analysis system to determine the concentration of the probe compound.

The recommended run conditions used are as follows:
— carrier gas: nitrogen gas, constant flow rate mode, 12 mL/min flow rate measured at the column outlet;
— injector: split mode, temperature of 200 °C, nitrogen used as the carrier gas, pressure of 60,5 kPa, total
flow rate of 25,0 mL/min, column flow rate of 2,00 mL/min, purge flow rate of 3,0 mL/min, and a split
ratio of 10,0;
— column: fused silica capillary column (DB-624 Ultra Inert Columns, 30 m × 0,32 mm, 1,8 μm film
thickness);
— temperature program: The initial temperature was set to 40 °C and held for 1 min. Thereafter, the
temperature was increased at a rate of 13 °C/min to 85 °C, where it was held for 6,54 min, resulting in a
total run time of 11 min;
— ECD temperature of 250 °C.
The calibration curve is used for this with known probe concentrations in pure water. Thus, the area of the
probe signal is converted into the concentration using the linear equation of the calibration curve.
Figure 7 shows examples of calibration of selected probes using GC-ECD.
Key
X retention time (min);
Y detection response (a.u.);
X1, X2, X3 standard concentration (ppb);
Y1 peak area of the detection response of CHCl (a.u.);
Y2 peak area of the detection response of CCl (a.u.);
Y3 peak area of the detection response of C Cl (a.u.).
2 4
Figure 7 — Calibration curves for CHCl , CCl , and C Cl using GC-ECD
3 4 2 4
8.3 Analysis of the probe with reaction time
In measurements of the probe concentrations over time, if a volatile probe is selected, control experiments
shall be established. These controls, devoid of any ROS, should assess the changes in the concentration of the
probe over the storage period to serve as background values. The concentrations of the probe obtained from
the experimental treatment group shall be adjusted by adding these background values prior to calculation.

8.4 Model development
The probes are small organic molecules, and their reactions with ROS are elementary processes. Therefore,
the degradation rate of the probes can be characterized using rate Formula (1).
⋅− 1
PR+⋅OH,,OO … →Q (1)
()
2 2
where
P is the probe;
R is the reactive oxygen species (ROS);
Q is the product
Thus, the reaction rate, v , equals the negative change of the reactant (Probe) over time, which is also equal
to the reaction rate constant of the probe with each reactive species multiplied by the concentration product
of the reactants (Formula (2)).
dP
[]
v=− =kP[][]Rk+ []PR[]+kP[][]Rk+ []PR[]+… (2)
PR,,12PR PR,,34PR 4
12 34
dt
where
v is the negative rate of change of the probe concentration
t is the reaction time;
[P] is the concentration of the probe;
[]RR,[]…
are the concentrations of ROS;
k , k …
are the rate constants of probe reaction with each ROS
PR, PR,
1 2
Subsequently, we mathematically transform the Formula (2), resulting in Formula (3).
dP
[]
− = kR +kR +kR +kR +… dt. (3)
[] [] [] []
()
RR12 RR34
12 34
[]P
Thereafter, we integrate the Formula (3) from t to t . The resulting equation emerges as Formula (4):
[]P t t ttt
 
ln =kR[]dt +kR[]dt +kR[]dt +kR[]dt +… (4)
 
R 12R R 3 R 4
  1∫∫2 3∫∫4
P t t t t
[]
0 0 0 0
 
t
In this Formula (4), the left side represents the natural logarithm of the probe’s concentration at time 0
divided by its concentration at time t. This value needs to be determined experimentally.
On the equation’s right side, there are two types of parameters: the reaction rate constants, k, between the
probe and various reactive species, which can be determined from chemical handbooks or literature. The
t
cumulative concentrations of various ROS at time t are expressed by ROSdt , which we aim to calculate
[]
∫
t
(Formulae (5)).
P
[]  tt tt
ln =kR dt +kR dt +k Rdtk+ Rdt,
[] [] [] []
 
PR,,12PR P ,,R 34PR,
∫∫ ∫∫
  11 12 1 3 14
t t t t
P
[]
0 0 0 0
1 ,
 t 
[]P  tt tt
ln =kR[]dt +kR[]dt +k []Rdtk+ []Rdt,
 
PR,,12PR P ,,R 34PR,,
∫∫ ∫∫
  21 22 2 3 24
t t t t
P
[]
0 0 0 0
 t 
[]P  t tt t
ln =kR[]dt +kR[]dt +k []Rdtk+ []Rdt,
 
PR,,12PR PR, 34PR,
∫ ∫∫ ∫
  31 32 33 34
t t tt
P
[]
0 00 00
3 ,
 
t
[]P  tt tt
ln =kR[]dt +kR[]dt +k []Rdtk+ []Rdt. (5)
 
PR,,12PR P ,,R 34PR,,
  41∫∫42 4 3∫∫44
t t t t
P
[]
0 0 0 0
 
t
The cumulative concentrations of the four reactive species at each time point can be determined using the
following matrix equations (Formulae (6)).
 []P 
1 o
t
 
ln
  
R dt
[[]
[]P
∫ 
 1 t 
t
 
o
 
kkk k
 
 
PR,,,PR PR PR,
11 12 13 14
t []P 
 
  2 o
 
ln
[]Rdt
 
 
kkk k  ∫
 
[]P
PR,,,PR PR PR, t
 
21 22 23 24 o 2 t
 
 
⋅ =  (6)
 
t
kk kk 
 []P 
 
PR,,P RRP ,,RP R
3 o
31 3 23 33 4
Rdt
 [] 
ln
 
∫   
t
 o  []P
   
3 t
kkk k  
PR,,,PR PR PR,
 
41 42 43 44
 
t
 
[]P
   
Rdt 4 o
[]
   
∫ ln
t  
   
o
[]
P
  
4 t
The Formula (6) can be efficiently solved using open-source software R which described in Annex B.
[3]
Alternatively, users may perform the calculation using the free ROS_Calculate software .
Additionally, with the derived time-dependent cumulative concentrations of ROS, the concentration of ROS
can be determined at each specific time point as defined in Formula (7).
t
Parameter t is the reaction time ( t , t , t , t … t ); []Rdt represents the cumulative concentration
n 0 1 2 3 n
∫
t
of specific ROS over the time interval of t to t . As defined in Formula (7):
t
Let fx()= Rdt (7)
[]
∫
t
where
t is the reaction time, the units for the reaction time t can be in seconds (s), minutes (min), or
n
hours (h), depending on the experimental setup;
t
[]Rdt is the cumulative concentrations of various ROS at time t;
∫
t
Fit an approximate function, Ft , using tf,,()t tf, ()t , tf, t , tf, ()t ,…, tf, ()t . This
[] [] [] []() [] []
11 22 33 44 nn
approximation is expressed in Formula (8):
t
fx = RdtF≈ t (8)
() [] []
∫
t
where
F(t) the approximate function to fit;
t specific time points ( tt,,tt,,… ) .
i 12 3 n
The value of Rtatpoint istheslopeof thetangent lineat point t forFt .
[] []
i i
8.5 Model verification
Using the data on the accumulated ROS obtained through calculations to further determine the removal rate
of the new probe, conduct a linear regression analysis comparing the theoretically calculated removal rates
with the actual removal rates of the probe measured experimentally.
The accuracy of the model is evaluated by calculating the correlation coefficient (r), the root mean square
error (r ), and the ratio of performance to deviation (p ) of the predicted value. The correlation
RMSE RPD
coefficient, often denoted as r, quantifies the strength and direction of a linear relationship between two

variables. A higher absolute value of r indicates a more reliable linear relationship between the predicted
and measured values.
The r is a conventional metric for assessing the accuracy of the model in predicting quantitative data.
RMSE
It is defined as the square root of the second sample moment of the differences between the predicted and
observed values or the quadratic mean of these discrepancies.
Lastly, the p is applied to assess the efficacy of the model. It is calculated by dividing the standard deviation of
RPD
the observed data using the r . A high p value indicates the superior predictive performance of the model.
RMSE RPD
9 Report
9.1 Report of the testing results
The following information shall be reported based on the testing results.
— Change in the probe concentration with treatment time.
— Accumulated ROS with treatment time.
— Real-time concentration of the ROS with treatment time.
— Model-performance verification.
9.2 Report of the testing conditions
— Date and time of measurement.
— Identification of measuring instruments.
— Identification of measurement officer.
— Identification of apparatus and materials.
— Specification of whether chemical probes were added during the active generation of MB or UFBs or after
completing the generation process. For the latter case, the time after the completion of FB generation
shall be reported.
— Determination of the pH value of the solution.
— Identification of the gas type of MB or UFB.
— Estimation of the concentration of salts in the solution.

Annex A
(Informative)
Commonly used probes for selection
Table 1 below lists some commonly used probes for selection. The rate constant can be obtained from the
NDRL/NIST Solution Kinetic Database (https:// kinetics .nist .gov/ solution/ ).
Table A.1 — Rate constants for the reaction of ROS with probe compounds
Molecu-
k
k
k 1
·−
Probe English Name lar weight Structure k
O
O
3 ·OH O
−1
(g mol )
9 5 4
ATZ Atrazine 215,69 2,3 2,6 × 10 4,1 × 10 <4 × 10
2,4-Dichloro-
9 5
2,4-D phenoxyacetic 221,04 29,1 5,1 × 10 8,3 × 10 a
acid
Chloroform/
7 8
CHCl Trichlorometh- 119,37 <0,1 5,4 × 10 2,3 × 10 a
ane
Carbon tetra-
6 9
CCl 153,81 <0,05 <2 × 10 1,1 × 10 a
chloride
Tetrachloroeth-
9 8
C Cl 165,82 <0,1 2,8 × 10 5 × 10 a
2 4
ylene
9 5 7
IMI Imidacloprid 255,661 3,5 4 × 10 4 × 10 4,8 × 10
9 8
MDE Methylone 207,229 <1 6 × 10 a 1,5 × 10
Terephthalic
9 4 7
TA 166,132 0,04 3,3 × 10 1,1 × 10 1,2 × 10
acid
4-Chlorobenzoic
9 7 7
pCBA 156,57 <0,1 5 × 10 8,6 × 10 1,4 × 10
acid
NOTE 1 a
...