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\DOI{10.5802/crchim.244}
\datereceived{2023-02-03}
\daterevised{2023-07-06}
\dateaccepted{2023-07-11}
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\dateposted{2023-09-13}
\begin{document}

\begin{noXML}

%\makeatletter
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%\def\cdr@specialtitle@english{CNRS Cavitation Research Network}
%\def\cdr@specialtitle@french{GDR Cavitation}
%\makeatother

\RubricEF{Review article}{Article de revue}

\title{Experimental evidences of radicals production by hydrodynamic
cavitation: a short review}

\alttitle{Preuves exp\'erimentales de la production de radicaux par
cavitation hydrodynamique : une br\`eve revue}

\author{\firstname{Julius-Alexander} \lastname{N\"{o}pel}\CDRorcid{0000-0002-5690-2201}}
\address{Institute of Fluid Mechanics, Faculty of Mechanical Science
and Engineering, Technische Universit\"{a}t Dresden, 01062 Dresden,
Germany}
\email[J.-A. N\"{o}pel]{julius-alexander.noepel@tu-dresden.de}

\author{\firstname{Fr\'{e}d\'{e}ric} \lastname{Ayela}\CDRorcid{0000-0002-8807-1334}\IsCorresp}
\address{Laboratoire des Ecoulements G\'{e}ophysiques et Industriels,
Univ. Grenoble Alpes, C.N.R.S., 38000 Grenoble Cedex, France}
\email[F. Ayela]{frederic.ayela@legi.cnrs.fr}

\def\thanksname{Note}

\thanks{This article is part of the CNRS Cavitation Research Network
project. More information at \url{https://gdr-cavitation.cnrs.fr/}
(available in several languages).}

\begin{abstract}
The presence of induced radicals and of chemical reactions, in liquids
processed in ultrasonic reactors producing acoustic cavitation, has
been widely demonstrated and is known as sonochemistry. Otherwise, the
number of publications related to chemical reactions caused by
hydrodynamic cavitation arising in a liquid flowing out, is more
limited. Most of these articles have exposed qualitative results and
empirical attempts in order to increase a primary weak efficiency. As
the physics of collapsing bubbles in a flow is more complex than the
monitoring of acoustic bubbles at a fixed frequency, it was largely
assumed, until shortly, that hydrodynamic cavitation has inherent
limitations preventing from getting relevant radical yields. However,
new efforts have been recently performed to evolve from qualitative to
quantitative measurements, in order to be able to know whether
hydrodynamic cavitation could become a reliable process for wastewater
treatment or not. This short review focuses on recent progresses that
have made possible experimental evidences of radical production in
hydrodynamic cavitation, and on forthcoming orientations.\vspace*{-1pt}
\end{abstract}

\begin{altabstract}
La pr\'esence de radicaux et de r\'eactions chimiques, dans des liquides
trait\'es dans des r\'eacteurs ultrasoniques produisant de la cavitation
acoustique, a \'et\'e largement d\'emontr\'ee et est connue sous le nom de
sonochimie. Mais par ailleurs, le nombre de publications consacr\'ees aux
r\'eactions chimiques provoqu\'ees par la cavitation hydrodynamique dans un
\'ecoulement est plus limit\'e. La plupart de ces articles exposent des
r\'esultats qualitatifs et des tentatives empiriques visant \`a accroître
une efficacit\'e intrins\`equement faible. Comme la physique de
l'effondrement d'une bulle dans un \'ecoulement est plus complexe que
celle d'une bulle excit\'ee \`a une fr\'equence acoustique fixe, on supposait
jusqu'\`a pr\'esent que la cavitation hydrodynamique \'etait intrins\`equement
incapable de produire des radicaux avec un rendement significatif.
Cependant, de nouvelles d\'emarches ont \'et\'e r\'ecemment suivies pour
\'evoluer vers des mesures quantitatives, afin de savoir si la cavitation
hydrodynamique pouvait devenir, ou pas, un processus fiable pour le
traitement des eaux us\'ees. Cette br\`eve revue souligne les progr\`es
r\'ecents qui ont permis d'obtenir des preuves exp\'erimentales de la
production de radicaux en cavitation hydrodynamique, et sur les futures
orientations \`a suivre.
\end{altabstract}

\keywords{\kwd{Hydrodynamic cavitation}
\kwd{Hydroxyl radicals}
\kwd{Dosimetry}
\kwd{Chemiluminescence}
\kwd{Luminol}}

\altkeywords{\kwd{Cavitation hydrodynamique}
\kwd{Radicaux hydroxyles}
\kwd{Dosim\'etrie}
\kwd{Chimiluminescence}
\kwd{Luminol}}

\maketitle

\vspace*{-2pt}

\twocolumngrid

\end{noXML}

\section{Introduction}

Cavitation is related to the growth and the collapse of vapor bubbles
or vapor clouds in a liquid. The vaporization of the liquid and the
condensation of the vapor are thermodynamic changes of phase of the
fluid, involving absorbed and emitted latent heat respectively.
Mechanical effects induced by the collapses are also likely to occur.
Cavitation differs from boiling in the fact that cavitation results
from a pressure drop below vapor pressure at a fixed temperature, when
boiling results from an increase of temperature above the temperature
of saturation, at a fixed pressure.

Acoustic cavitation occurs when oscillating vapor bubbles are induced
by acoustic excitation, and monitored at ultrasonic frequencies ranging
from 20~kHz to 1 MHz. A global rectified diffusion of matter from the
surrounding liquid toward the bubble, during the expansion phases,
enhances an increase of the average size of the bubble until a critical
radius, that depends on the frequency and on the acoustic pressure, and
above which the collapse of the bubble occurs. The consequences of the
collapse depend on the frequency, on the intensity of the pressure
field, on the presence of dissolved gases, and on the temperature.
Imploding cavities often involve the formation of high-pressure shock
waves, and extreme temperatures and pressure may be reached. This might
not necessarily result in the formation of a supercritical fluid inside
the bubble, therefore supercritical oxidation is not a typical outcome
in imploding cavities. Low frequency cycles produce large sized
bubbles, giving way to violent collapses. As a consequence, some
uncondensed water molecules are splitted and produce hydroxyl radicals
${\cdot}$OH. High frequency cycles induce smallest bubbles that
collapse with a weaker intensity, but they generate more events and
they can help for diffusion of radicals toward the liquid. Hydroxyl
radicals can recombine and produce
H$_{2}$O$_{2}$. In contrast, when adding
H$_{2}$O$_{2}$ in the liquid, reaction rates
increase~\cite{1}. Depending on the hydrophilic or hydrophobic nature
of a possible pollutant, the optimum working frequency should be a
balance between low or high acoustic frequency. Sonoluminescence is
another consequence of the collapse, that is caused by the ionization
of rare gases present in the core of the bubbles. It should be noted
that the best conditions to observe sonoluminescence are not similar to
those enhancing sonochemical activity.\looseness=-1

Hydrodynamic cavitation is the consequence of the Bernoulli law, when a
flowing liquid passes through a local constriction. The increase of the
dynamic pressure $1/2\cdot\rho u^{2}$, where
${\rho}$ is the density of the fluid and $u$ its average velocity, goes
with a decrease of the static pressure $p$, as illustrated in Figure~\ref{fig1}.
Downstream the constriction, where the velocity of the flow recovers a
lower value, the static pressure increases but reaches a smaller level
than upstream, because of the singular pressure loss due to the
constriction. Inception of cavitation becomes possible if the pressure
value falls below a threshold value, which is generally the vapor
pressure $p_{\mathrm{vap}}$. Vapor bubbles and vapor clouds, which
arise in the low pressure area, collapse downstream where the static
pressure has raised above $p_{\mathrm{vap}}$.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Sketch of the pressure line evolution along a
liquid flow encountering a constriction.}
\end{figure}

Different flow regimes can induce cavitation: around an emerging liquid
jet, around a hydrofoil, through an orifice or a diaphragm, through the
throat of a venturi. Shear cavitation is induced in low pressure
vortices in shear flows; sheet cavitation appears as a vapor pocket
emitting bursts of vapor clouds at a shedding frequency that has no
relation with the frequency monitored in ultrasonic cavitation
(Figure~\ref{fig2}). \looseness=-1

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}Snapshots of shear (up) and sheet (down) cavitating flows.}
\end{figure}

Hydrodynamic cavitation is simple to execute. However, the physics of
the growth and collapse of multiple cavitating bubbles in a
hydrodynamic flow is drastically more complex than in ultrasonic
reactors. A cavitation number, noted ${\sigma}$, is a dimensionless
parameter that can be used to quantify the possibility for cavitation
to occur in a fluid flow system. With the notations of Figure~\ref{fig1},
${\sigma}$ is defined here by: 
{\begin{equation*}
\sigma =\frac{p_{{\mathrm{downstream}}}-p_{\mathrm{sat}}}{{0.5}\varrho
{u}^{{2}}}
\end{equation*}}\unskip
The condition $\sigma < 1$ is required for the cavitation to become
possible. In the literature, some alternative definitions of the
cavitation number may be found, but all agree with the fact that
${\sigma}$ can be expressed as a function of the ratio of the output
pressure $p_{\mathrm{out}}$ divided by the flow rate. The cavitation
number only means that a cavitating flow regime is reachable by
increasing the flow rate and/or by lowering the output pressure and
that no cavitation should occur when $\sigma > 1$. In
microfluidic systems, we have calculated that the critical cavitation
number below which the pressure falls under $p_{\mathrm{sat}}$ depends
on the size of the constriction~\cite{2}. More recently, Sarc \etal\ 
have highlighted, that describing the hydrodynamic cavitation by the
solely value of ${\sigma}$ was inadequate~\cite{3}. Moreover, some
factors affecting chemical reactions, such as turbulence, dissolution
of gas, mass transfer rates, are not relevant with the cavitation
number. So, it is suggested~\cite{3} to consider several parameters, in
order to address the issue of different experiments. We consider that
the cavitation number, the maximum average velocity and the hydraulic
power, that is the product of the total pressure drop (in J/m$^{3}$) by
the volumetric flow rate of the liquid phase (in m$^{3}$/s), are the
quantities that allow comparison between hydrodynamic flows. But the
frequency, which is a crucial parameter in acoustic cavitation, has no
obvious peer in hydrodynamic cavitation. Such a lack of a parameter
able to evaluate an average shape or size of the bubbles may result in
the fact that the experimental attempts to study chemical effects
induced by hydrodynamic cavitation could not be based on a firm model.

\section{Chemistry induced by hydrodynamic cavitation}

Twenty-five years ago, Suslick and co-workers underlined that reports
on chemistry induced by hydrodynamic cavitation had been extremely
limited~\cite{4}. They tested the Weissler reaction, as a dosimeter for
chemical reactions, with a solution passed through a high pressure
microfluidizer in which cavitation was likely to occur, with working
pressures running from 100 bars to 1300 bars. The tri iodide formation
rate increased linearly with the upstream pressure. The respective
influence of dissolved gases and liquid temperature were also
considered, and led to evolutions similar as those observed in acoustic
\mbox{cavitation.} That was the first firm demonstration of chemical
similarities between acoustic and hydrodynamic cavitation.
Unfortunately, the flow rates were not expressed in the paper, and it
is not possible to evaluate the hydraulic powers involved in these
experiments. Later, Kalumuck and Chahine tested the degradation of
p-nitrophenol aqueous solutions in both acoustic and hydrodynamic
reactors~\cite{5}. They compared the power of the hydraulic set up to
the calorimetric power of the acoustic reactor, and concluded to a
better efficiency of the hydraulic reactor. Temperature and pH effects
highlighted the same trends, in acoustic and hydrodynamic cavitating
regimes. The cavitating jet was monitored up to 65 bars. Comparing the
application of cavitation reactors for water disinfection,
Gogate~\cite{6} enhanced an empirical arrangement of multiholes on a
plate, taking into account the relative free area offered to the flow.
General conclusions were not supported by quantitative values of
parameters such as inlet pressure or average maximum velocity. Perhaps
in order to treat flow rates higher than what is reachable with high
pressure fluidizers, the subsequent efforts, which were consacred, used
mild experimental conditions. Wang \etal\ studied the degradation of
rhodamine B using swirling jet-induced cavitation, at an
inlet pressure of 6 bars and a hydraulic power of around 600
W~\cite{7}. Brauetigam \etal\ used a design inspired by the multiholes
scheme~\cite{8, 9} working on a very limited inlet pressure range (from
1.4 bars to 2.6 bars~\cite{8}, and then up to 10 bars~\cite{9}), with
hydraulic powers between 60 W and 80 W. They noticed that the
centrifugal pump present in the loop could be a source of cavitation,
in competition with the reactor. Capocelli \etal\ undertook simulation
and experimental comparison of chemical effects of hydrodynamic
cavitation in a Venturi reactor~\cite{10}. They conducted degradation
tests on p-nitrophenol between 2 bars and 6~bars, and observed a
maximum efficiency around 4.5~bars. That optimum was correlated to
similar trends obtained by other groups, but with other reactors and
other pollutants. Zupanc \etal\ performed a broad study of
shear-induced hydrodynamic cavitation as a tool for pharmaceutical
pollutants removal~\cite{11}. They stated that the amount of free
radicals is related to the aggressiveness of the cavitation, and that
shear induced cavitation is more aggressive than sheet cavitation that
is formed in the throttle of a Venturi. That conclusion is not shared
by Rajoriya \etal~\cite{12} who have observed a higher degradation
rate of orange-G dye when using slit Venturi at an optimum pressure of
3 bar. The authors state that cavitation in a Venturi profile results
into a large magnitude collapse, as long as a choked cavitation regime
is not reached. The authors present also an overview of experimental
results devoted to waste water treatment by hydrodynamic cavitation
through Venturi and orifice nozzles.

A larger spectrum of references may also be found in a short review
article published by Tao \etal\ in the same year of 2016~\cite{13}, and
more recently by Das \etal~\cite{14}. The authors review the possible
reactors geometries and list the main operating parameters that are
inlet pressure, bulk liquid temperature, effect of pH and of initial
pollutant concentration, effect of the initial radius of the nuclei,
effect of the surface tension. They agree that qualitative results have
been obtained, but they underline the lack of quantitative analysis.
Each research team has developed a self-made reactor used to degrade a
given pollutant, and it is difficult to draw general conclusions for
such a set of data. Similar conclusions have been drawn in most recent
review articles~\cite{15, 16}. Ciriminna \etal\ stress that the
chemical effects of hydrodynamic cavitation are the consequence of
hydroxyl radical formation, and that a direct measurement of such a
concentration is hardly possible due to their high
reactivity~\cite{15}. Hydroxyl radicals are short-lived oxidants that
degrade within nanoseconds~\cite{17}. Therefore, it is difficult to
detect them directly. The dosimetry of hydroxyl radicals comes from
indirect measurement, funded on chemical reactions involving new
products, or on the emission of light. 

\section{Dosimetry of hydroxyl radicals produced by hydrodynamic cavitation}

Different dosimetry methods have been developed in sonochemistry in
order to quantify the chemical activity and the amount of hydroxyls
radicals produced by cavitation. Most of them have then been tested in
hydrodynamic cavitating flows. The reliability of these techniques,
that can only detect radicals which have not been involved in
recombination, is still an open question in sonochemistry~\cite{18}.
The data concerning dosimetry of hydrodynamic cavitating flows are
equally scattered.

Iodide dosimetry has been largely used as a test reaction. It has been
inspired by the Weissler reaction, where the yield of iodine is
proportional to the time of ultrasonic irradiation. When potassium
iodide KI is initially present in the solution submitted to cavitation,
iodide can scavenge the hydroxyl radicals ${\cdot}$OH and form the tri
iodide ${\mathrm{I}_{3}}^{-}$, which is detected by UV visible absorbance at
$\lambda = 353$ nm~\cite{19, 20}. Otherwise, a part of the processed
solution may be withdrawn and mixed with a KI solution. The oxidation
of iodide to tri iodide ${\mathrm{I}_{3}}^{-}$ is then caused by hydroxide
peroxide H$_{2}$O$_{2}$ resulting from the recombination of hydroxyl
radicals~\cite{21}.

But iodide dosimetry is non-specific to ${\cdot}$OH radicals, since
iodide ions may be oxidised by other radicals and by hydrogen peroxide.
The presence of saturated oxygen in the cavitating liquid is likely to
help the formation of peroxide hydrogen, and to overestimate the amount
of hydroxyl radicals generated by cavitation. Moreover, in a global
study devoted to compare the respective efficiencies of acoustic and
hydrodynamic cavitation, Morison and Hutchinson enlightened the
presence of a consumption reaction in hydrodynamic flows, leading to a
limit of the ${\mathrm{I}_{3}}^{-}$ concentration~\cite{20}. That
could explain why experiments of Suslick \etal~\cite{4} could detect
tri-iodide only above very high input pressures. Such a consumption of
tri iodide ions occurred even if the flow was driven below the onset of
cavitation, but was not present in acoustic cavitation. Their
conclusion stated that the Weissler reaction is not reliable in order
to know the effectiveness of hydrodynamic cavitation as an advanced
oxidizing process.

The Fricke dosimetry is funded on the oxidation of Fe$^{2+}$ to
Fe$^{3+}$~\cite{22}. As for the Weissler reaction, other species than
${\cdot}$OH radicals may be responsible for the oxidation reaction.
Terephtalic acid TA has been used as an ${\cdot}$OH radical
scavenger~\cite{23, 24}. The reaction forms hydroxyterephtalic acid
(HTA), which is strongly fluorescent and stable for hours. Terephtalic
acid dosimetry is presented as specific for hydroxyl
radicals~\cite{23}. Matthews, working on the radiation chemistry of the
terephtalic dosimeter, observed that the yield of HTA is affected by
the oxygen concentration~\cite{25}. Oxygenation increases HTA, but in a
solution sparged with nitrogen gas, the yield of HTA falls. In acoustic
cavitation, the fact that a very low ${\cdot}$OH yield is obtained by
this dosimetry method is still an open question~\cite{18}. In
hydrodynamic cavitation, Wang \etal~\cite{7} used TA dosimetry to
conclude to a synergetic effect between cavitation and H$_{2}$O$_{2}$
for the degradation of rhodamine B, with fluid pressures ranging from 2
to 6 bars.

{\advance\baselineskip by -.2pt
Arrojo \etal\ proposed the application of salicylic acid dosimetry to
characterize both ultrasonic and hydrodynamic cavitation~\cite{23}. The
reaction with ${\cdot}$OH produces mainly 2,5 DHB (dihydroxybenzoic
acid), that is fluorescent. The reactor was a venturi, developing a
hydraulic power around 500 W at a maximum inlet pressure of 4.7 bars.
The authors underlined that as salicylic acid is hydrophobic, molecules
should migrate toward the bubbles interface. That would enhance the
trapping efficiency, as the life time of ${\cdot}$OH is very short. A
new question then arises, that is to know the ratio between the real
number of hydroxyl radicals initially present inside collapsed bubbles,
and the effective number of radicals able to react with a hydrophobic
or with a hydrophilic molecule present in the liquid phase. Salicylic
acid dosimetry was also used by Amin \etal~\cite{26}, who tested
different shapes of orifices (circular, ellipsoidal, rectangular). But
unfortunately, there is a lack of hydrodynamic data (such as pressure
drop/flow rate relationships, critical pressure drop above which the
onset of cavitation occurs), that cannot be related to chemical
activity and to the related measurements. More recently, Zupanc and
co-workers~\cite{27} used salicylic acid dosimetry with a Venturi
equipped with a rectangular slit. They highlighted the fact that an
excessive concentration of salicylic acid should negatively affect the
surface tension and, as a matter of fact, the violence of the collapse.
Care must be taken, so that the scavenger should not affect the radical\break
production.

Coumarin dosimetry has been recently used in cavitation. After an
exposition to ultrasound waves at 500 kHz, an aqueous coumarin solution
has produced hydroxylated products and has presented a decrease of the
absorbance of coumarin, that are the consequence of reactions with
hydroxyl radicals~\cite{28}. Among these products, umbelliferone (also
named hydroxylated 7-hydroxycoumarin, 7-OHC) is fluorescent. Coumarin
was then used by Srinivas \etal~\cite{29} and by De-Nasri 
\etal~\cite{30} to quantify the ${\cdot}$OH radical generation in
hydrodynamic cavitating vortex diode reactors. Coumarin was also used
for the detection of radicals in irradiated solutions~\cite{31}. Once
again, it is not obvious to know the exact relationship between the
amount of ${\cdot}$OH molecules involved in the reaction producing the
fluorescent 7-OHC component, and the total number of ${\cdot}$OH
radicals.

A variety of other methods have been published. For example, the
transformation of benzene into phenol due to the reaction with hydroxyl
radicals can be used as a dosimeter~\cite{32}. The correlation between
dye degradation experiments, with Congo red used as a reference
substance, and chemiluminescence of luminol was used to evaluate
degradation effects and cavitation intensity~\cite{33}. 
}

\section{Chemiluminescence of luminol}

The above dosimetry methods require a regular extraction of the liquid
under test, and do not provide any information neither about the fluid
mechanism conditions nor about the localization of the chemical
activity. An indirect determination of the presence of ${\cdot}$OH
hydroxyl radicals and an in-situ visualisation of their localization,
may be performed with luminol aqueous solutions. It is known for a long
time that aqueous solutions of luminol emit light when exposed to
acoustic waves, which are strong enough to generate cavitation, and
that such a chemiluminescence results from reactions with hydroxyl
radicals~\cite{34}. Chemiluminescence of luminol has also been enhanced
in single bubble sonoluminescence experiments~\cite{35}. The method of
chemiluminescence of luminol gives a statement about the spatial
distribution of the reaction area and is suitable as a marker for the
spatial characterization of the hydroxyl radical concentration, which
is also quantifiable for measurements. The observation of the intensity
of the radical production becomes possible inside devices equipped with
optically transparent walls, because when cavitation occurs and
hydroxyl radicals are formed, the decomposition of luminol emits
visible blue light above the UV-spectrum. 

Surprisingly, using luminol as the working fluid in hydrodynamic
cavitating experiments has been firstly presented only six years
ago~\cite{36}. Gathering relatively high volumes of solution together
with transparent reactors able to withstand high pressure levels, is
perhaps the reason why there has been such a delay between acoustic and
hydrodynamic cavitation experiments using luminol. The measurement of
chemiluminescence of luminol is now a well-established proof for
hydroxyl radical production by hydrodynamic cavitation even if the
number of papers dealing with luminol cavitating flows remains up to
now limited. On the one hand, several experiments have been performed
under moderate pressure drops through microchannels \mbox{(hydrodynamic}
cavitation ``on a chip'')~\cite{37,38,39} and mini channels~\cite{40};
on the other hand, another set of experiments at macroscale and under
inlet pressures up to 40 bars have been published~\cite{33, 41, 42}.

The existence of luminescent scavengers of hydroxyl radicals makes
possible to count emitted photons directly. However, the relationship
between the number of radicals reacting with luminol and the number of
collected photons is not obvious. Chemistry of the oxidation of luminol
is complex and the emission of light requires both the presence of
hydroxyl radicals together with superoxide anion
${\mathrm{O}_{2}}^{-\circ}$~\cite{43, 44}. As a matter of fact, the deficit
of superoxide ${\mathrm{O}_{2}}^{\circ -}$, even if ${\cdot}$OH
are still present, will stop the luminescence, and one should
underestimate the number of ${\cdot}$OH radicals. Moreover, when using
a photomultiplier tube (PMT) as a photon detector, one has to take into
account the correction due to the collection solid angle, the global
quantum efficiency of the photocathode of the PMT for the
chemiluminescent spectrum, the quantum yield of the luminol
chemiluminescence reaction. Whatever the size of the reactor is, the
test rig must be completely darkened in order to capture the relatively
weakly emitted light. The knowledge of a number of radicals detected
during one second, and the knowledge of the hydraulic power required to
drive the flow make possible the calculation of the so-called $G$-value,
that is the number of ${\cdot}$OH moles produced per Joule of consumed
energy. By working with hybrid silicon-Pyrex micro channels with a
micro diaphragm inside, Podbevsek \etal\ calculated a minimum radical
production of $\approx 6 \times 10^{6}$\ ${\cdot}$OH/s for a
hydraulic power of ${\approx}$ 0.4 W, that corresponds to 
\mbox{$G \approx
2.50 \times 10^{-17}$~mole/J~\cite{37}.} Similar $G$-values were
also recorded with another opto-electronic set up and with other micro
reactors (microdiaphragms and micro steps profiles) developing shear
rate cavitation~\cite{38}. Recently, the chemiluminescence emitted from
a larger set of micro- and mini hydrocavitating reactors has been
investigated~\cite{40}. The devices presented semi convergent--divergent
constrictions, with hydraulic diameters ranging from 100 ${\upmu}$m to
540~${\upmu}$m. For the largest diameter, the maximum recorded flow
rate was 50~L/h under a driving pressure of 10~bars. The flow dynamics
was rather different from that inside micromachined silicon-Pyrex
devices, because cloud shedding was present at frequencies ranging from
150~Hz to 1400 Hz. It is noteworthy to find that the \mbox{$G$-values}
calculated from the reactive oxidising species production were similar
($3.6 \times 10^{-17}$~moles/J~$< G < 6 \times 10^{-17}$~moles/J)
to those calculated from former experiments. Moreover, the
radical production exhibits a linear evolution as a function of the
hydraulic power, and no scale effect was noticeable: the $G$ values of
the microreactors were roughly similar to the $G$ values of the
minireactors. For a small as for a large device, the $G$-value was the
highest for the smallest constriction under test. To our knowledge,
only Arrojo \etal\ had up to now calculated a $G$-value from
hydrocavitation experiments, and found $G \approx
10^{-12}$~mole/J with salicylic acid as a scavenger used
in a Venturi~\cite{23}. There are five orders of magnitude between
these respective $G$-values. The microfluidics experiments of Podbevsek
\etal~\cite{37,39} and of Perrin \etal~\cite{38} were mainly devoted
to demonstrate the effective presence of hydroxyl radicals inside
cavitating flows, and they were performed just above the critical flow
rate corresponding to the inception of cavitation, when the cavitating
flow was not fully developed. But the recent results obtained at larger
scale confirm the former $G$ values~\cite{40}. Possible explanations are
as follows: the value of the quantum yield of luminol is under
evaluated; the luminescence is limited by the superoxide anion
production; the hydrophobic salicylic scavenger react with a larger
number of radicals, which have disappeared when using luminol. Anyway,
complementary experiments at micro and miniscale, with complementary
geometries, are scheduled in order to draw firm findings.\looseness=-1

\begin{figure*}
\vspace*{-2pt}
\includegraphics{fig03}
\vspace*{-2pt}
\caption{\label{fig3}Local repartition of emitted photons per second
(up) compared to a snapshot of the corresponding cavitating flow (down)
recorded on a microdiaphragm. The fact that the coloured area oversizes
the channel area is the consequence of the diffusion of light, and of
the lack of filters removed in order to increase the sensitivity.}
\vspace*{-2pt}
\end{figure*}

Even if chemiluminescence of luminol cannot provide the real number of
hydroxyl radicals, it makes possible a mapping of the chemical activity
together with a mapping of the two-phase liquid-vapor flow. Supporting
the fact that cavitation occurs inside a ``lab on a chip'', Podbevsek
\etal\ used a confocal microscope set up to draw a local mapping of the
chemiluminescent intensity, enhancing local gradients of intensity.
Such mappings could be compared to void fraction mappings, also
obtained from confocal microscopy with fluorescent hydrophilic
nanotracers~\cite{39}. An example of a chemiluminescent mapping is
presented in Figure~\ref{fig3}, with a snapshot of the corresponding two-phase
flow. The main\break conclusion was that the area where the maximum chemical
activity was recorded (due to the presence of both ${\cdot}$OH and
${\mathrm{O}_{2}}^{-\circ}$ radicals) is located just downstream the area
where the cavitation clouds collapse.

A correlation between the volume of chemiluminescence due to luminol
and the volume of cavitation has been studied by Deggelmann 
\etal~\cite{42} and N\"{o}pel \etal~\cite{33, 41}, but on a larger
scale. The authors applied the method of chemiluminescence of luminol,
which occurs in the visible range of light due to the reaction with
hydroxyl radicals. The emitted light was then recorded with a digital
SLR camera.

The investigations about the luminescent area and the cavitating vapor
cloud were performed initially in a cylindrical reactor with an inner
diameter of 15 mm and a length of 100 mm~\cite{41, 42}. The flow was
accelerated through a circular orifice with diameter sizes of $d = 1$~mm
or $d = 1.7$~mm. In~\cite{33} same orifice diameters were adapted, but
the configuration changed to a rectangular reactor with a
cross-sectional area of $15 \times 15$~mm$^{2}$, leading to less light
distortion due to curved surfaces. The measurement configuration of
recording the chemiluminescence consisted of a digital SLR camera and a
light sensitive lens, which was aligned orthogonally to the\break reactor
walls. 

The experimental setup with the reactor was shielded from external
light influence. In this darkened room, blue light emission from the
chemiluminescence of luminol was recorded by long exposure times of
5~min~\cite{41} to 10~min~\cite{42}. This method is relatively
inexpensive and straightforward to perform. The solution here consisted
of 2~g/l luminol and 7.5~g/l sodium hydrogen carbonate, which are both
dissolved in deionised water by stirring. The solution has a pH value
of pH $=$ 9.3~\cite{41}. 

{The method of measuring the chemiluminescence of luminol involved the
digital single lens camera recording an integral value of the blue
light emission over the exposure time and space. Figure~\ref{fig4} shows the
distribution of vapor bubbles (top) and the distribution of light
emission of chemiluminescence by luminol reacting with hydroxyl
radicals~\cite{33}. In N\"{o}pel \etal~\cite{33, 41} the exposure time
was set to 5~min without additional substances. A camera with a light
sensitive lens ({Canon EOS 650D, EF 50 mm 1:1.8 STM)}
{was used for this purpose. A different camera
and lens (}{Canon EOS 1100D, EF-S 18--55~mm IS
II}) was used in~\cite{42} and exposure time
was set to 10~min resulting in different area sizes. Also a low amount
$V = 1$~ml of hydrogen peroxide solution (30\%) of was added
in~\cite{42}, which enhanced the reaction. The changes towards smaller
areas were noted in~\cite{42}. This was due to the different
measurement equipment.} 

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Inside the cavitation reactor with nozzle $d=1$~mm
at $\Delta p = 30$~bar. Flow from left to right. Top: Time averaged
spatial distribution of vapor bubbles representing area of cavitation.
Acquired by side illumination with high power lighting and a camera
with exposure time of 11~${\upmu}$s. Bottom: Time averaged
spatial distribution of chemiluminescence of luminol (blue light)
representing the reaction area. Original image is
brightened~\cite{33}.}
\end{figure}

The original images are first brightened and binarized, all similarly,
using a threshold for evaluation. From the binary images, the pixel
area of the blue light emission can be determined, which represents
two-dimensional information about the \mbox{reaction} area. Based on this
information, the length extent of the area is used to calculate an
approximate volume in which reactions are assumed to be
occurring~\cite{41}.

Figure~\ref{fig5} displays the dependency of the reaction volume marked by
chemiluminescence over hydraulic power input. The inception of
cavitation occurred at $\Delta p = 7$~bar for $d = 1$~mm. For pressure
differences below 10~bar, no light was recorded since the cavitation
area was short and vapour density optically low. From 10~bar to 30~bar
the optically visible volume of chemiluminescence increases nearly\break
linear.

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5}Volume of chemiluminescent part emerging from
orifice $d = 1$~mm normalized with reactor volume over hydraulic power
P in W starting from $\Delta p = 0$ bar up to 30 bar in steps of 10
bar~\cite{41}.}
\end{figure}

The higher the pressure difference $\Delta p$ or the hydraulic power
P, the greater the cavitation volume of gas bubbles. A larger volume of
cavitating bubbles leads to a higher implosion rate, which must tend to
produce more radicals. However, the pressure difference increases the
fraction of vapour and air bubbles. This may result in differences in
the spatial extent of the recorded area of chemiluminescence due to
scattering and reflexion of light by the gas fraction. This causes a
certain limitation for the application of measuring the strength of
cavitation for degradation. In~\cite{33} the method is used to proof
the occurrence of oxidation as the leading mechanism of\break degradation.

\section{Conclusion}

The production of hydroxyl radicals in cavitating flows has been
attested by an amount of experiments, each of them performed with a
specific hydraulic set up and with a fixed chemical scavenger. Compared
with ultrasonic cavitation, that involves a relatively limited number
of parameters, hydrodynamic cavitation may be monitored in a lot of
kinds of devices, under different complex flow regimes. The number of
publications related to chemical activity in hydrodynamic flows has
increased these past last years, because possible applications to
wastewater treatments are timely. Concerning the hydroxyl radical
production, the pros and cons of related scavengers have been now
assessed. Recent progresses with luminescent scavengers have made
possible live and in-situ observations, facilitating coupled studies
between chemistry and fluid mechanics. If the rare quantitative data
published up to now agree with the fact that hydrodynamic cavitation
could display a low radical efficiency, it is nevertheless believed
that any further research programs should develop an experimental,
structured and multidisciplinary strategy, in order to reach a full
understanding of the physics inside collective collapsing bubbles. For
each kind of hydraulic device, the largest number of scavengers should
be used and compared, for different cavitating flow regimes.
Reciprocally, each scavenger should be tested in different devices, at
different scales, and submitted to shear and to sheet cavitation.
Ideally, every experiment could be managed in order to rise a
quantifiable radical efficiency, expressed in ${\cdot}$OH moles/J, that
would be a common reference for any comparison.

\section*{Conflicts of interest}

Authors have no conflict of interest to declare.

\section*{Acknowledgments}

The authors gratefully acknowledge the support provided by their
respective laboratories. Considerable appreciation shall be expressed
to Professor J. Fr\"{o}hlich, Director of the institute and Head of the
chair of fluid mechanics and Dr. F. R\"{u}diger, Head of the group of
experimental fluid mechanics, who provided the opportunity for
experimental research on cavitating multiphase flows at the institute
of fluid mechanics of the TU Dresden. FA,
from the Laboratoire des Ecoulements G\'{e}ophysiques \& Industriels,
expresses his sincerest appreciation to Dr. L. Perrin, Dr. D. Colombet,
Dr. D. Podbevsek and Dr. G. Ledoux for the useful help and effective
collaborations that have led to the success of sophisticated
experiments devoted to hydrodynamic cavitation on a chip.

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