# Spontaneous chemical reactions between hydrogen and oxygen in nanobubbles

V. B. Svetovoy<EMAIL_ADDRESS><EMAIL_ADDRESS>A. N. Frumkin
Institute of Physical Chemistry and Electrochemistry, Russian Academy of
Sciencies, Leninsky prospect 31 bld. 4, 119071 Moscow, Russia

###### Abstract

Bulk nanobubbles (NBs) generated electrochemically by short voltage pulses of
alternating polarity behave differently from those produced by regular
methods. Only bubbles smaller than $200\;$nm are formed in the process and
their concentration is very high. Moreover, the bubbles containing both H2 and
O2 gases disappear quickly via the combustion reaction, although the reaction
in such a small volume cannot happen according to the classical combustion
theory. Experimental facts about these unusual NBs are reviewed and current
understanding of the observed phenomena is provided. Visualisation methods of
a cloud of NBs above the electrodes are briefly discussed. Experimental
signatures demonstrating the reaction between the gases in NBs are considered.
A surface-assisted mechanism proposed for the combustion reactions in
restricted volumes with a high surface-to-volume ratio is discussed. It it
explained how the same mechanism may describe the audible explosion of
microbubbles, that is observed in certain circumstances.

##  I Introduction

Nanobubbles have attracted significant attention in the last 20 years [1, 2,
3]. This attention is driven by a fundamental problem: NBs live much too long
in comparison with the prediction given by the diffusion dissolution theory
[4, 5]. On the other hand, exciting applications of NBs in environment [6, 7],
agriculture [8], flotation [9, 10], healthcare [11, 12], and chemistry [13]
have emerged to name only a few.

In contrast with surface NBs, which exist on the solid-liquid interface, bulk
NBs fill the volume of liquid. These NBs are generated by mostly mechanical
injection of different gases [9] or by ultrasonic cavitation [10], but
hydrogen and oxygen NBs where also generated by DC electrolysis [14, 15].
Later these methods will be called the regular methods. The size distribution
of the NBs was characterized by the dynamic light scattering and individual
bubbles were observed by electron microscopy from freeze fracture replicas
[16], by phase microscopy and polarimetric scatterometry [17].

Unexpectedly, NBs containing oxygen are able to produce reactive oxygen
species which can oxidize pollutants and pathogens in water [18, 19, 20],
while separate oxygen molecules have no effect on organics. Generation of OH
radicals from shrinking air microbubbles (MBs) without external dynamical
stimuli such as ultrasound or high pressure differential was observed by
Takahashi et al. [21] with the electron spin-resonance spectroscopy. This
finding was confirmed through reactivity with probe molecules by other
researches and it was established that only OH radicals can be produced from
air, O2, or O3 nanobubbles [19]. Observation of free radicals is a puzzling
phenomenon since radical formation is a high energy event, which is not
possible without external energy supply. Similar to the long lifetime of NBs
the controversy on the radical production by NBs persists.

One more puzzling phenomenon that can proceed only in a high energy
environment was observed in NBs containing mixture of H2 and O2 gases [22,
23]. To ignite a series of combustion reactions between these gases in a fixed
volume one has to produce a certain number of free radicals. Moreover, the
reactions will not be self-supported if the volume is too small. This is
because the heat produced by the exothermic reaction escapes too fast via the
volume boundaries and the temperature inside of the volume will be too low to
support the reaction. Nanobubbles seem especially unfavorable to support the
combustion reactions but in spite of this the combustion of the gases proceeds
in NBs spontaneously (without ignition).

Nanobubbles containing hydrogen, oxygen, but also a mixture of the gases were
generated in a so-called alternating polarity (AP) electrochemical water
decomposition process [22] when the polarity of the electrodes is changed with
a frequency of the order of $100\>$kHz or higher. In contrast with the DC
electrolysis [14, 15], in this process only NBs are formed, which do not
scatter the visible light but change the refractive index of liquid at a level
that can be easily observed optically.

In this paper we describe briefly formation and observation of NBs in the AP
process, but the main attention is directed to combustion of hydrogen and
oxygen in NBs. The latest progress in the observation and understanding of the
combustion reactions in NBs and closely related phenomenon observed in MBs is
discussed.

##  II Signatures of the reaction between H2 and O2 gases in NBs

### Generation of NBs in the AP process

Water electrolysis performed by short AP voltage pulses demonstrated very
unusual properties in comparison with the DC electrolysis [22]. If one applies
such pulses to the electrodes, for which the polarity of the working electrode
changes with a frequency of the orders of $100\;$kHz and the opposite
electrode is grounded, visible production of gas suddenly disappears [22]. The
transition occurs at frequencies above $20\;$kHz but the current through the
electrode only increases gradually with the frequency increase. For Pt
electrodes one can separate the Faraday component in the current [24], which
shows that the gas has to be produced with the increasing rate for higher
frequencies. It was concluded [22] that in the AP process only NBs with a size
smaller than $200\;$nm are formed. Since such bubbles practically do not
scatter the visible light, they become invisible in optical microscope.

This conclusion was confirmed with different optical methods in later works.
Although it is not possible to see the separate bubbles optically, it was
rather straightforward to observe collective effects produced by NBs. To
localise generation of NBs, concentric planar electrodes with the external
diameter $500\;\mu$m deposited on the oxidized Si substrate have been used. A
few different methods demonstrated the presence of a dense cloud of NBs above
the electrodes. Figure 1(a) shows the differential interference contrast [25]
of two mutually coherent orthogonally polarized beams, which are slightly
displaced spatially at the sample plane. The interference of the beams depends
on the optical path difference in the direction of the displacement. The
method is appropriate for visualisation of the gas distribution in dynamics.
One can see that the cloud of NBs covers the electrode and the gradient of the
refractive index becomes larger with the increase of the pulses amplitude.
This method gives, however, only a qualitative picture.

Figure 1: Cloud of NBs. (a) Differential interference contrast in dynamics.
The AP pulses at $f=400\;$kHz are modulated by triangle with a period of
$5\;$s and with the maximum amplitude $U_{max}=8\;$V. Images for the beams of
different polarization are shifted for $30\;\mu$m. (b) Schlieren contrast of
the cloud in dynamics (side view) at $f=200\;$kHz and $U_{max}=11\;$V. (c)
Interpretation of the contrast along the red dashed line in (b) in terms of
the refraction index $n$. (d) Amplitude of the pulses as a function of time.

Direct observation of optical distortion of the electrodes allows one to
estimate the gas concentration in the liquid. Analysis performed in [25] gave
the reduction of the refractive index of about 0.18. Any impurity in the
solution or Joule heating provided by the current cannot explain such a large
value. The only reasonable explanation is the gas in the liquid with the
concentration $n_{g}\approx 3.5\times 10^{26}\;$m-3. This gas cannot stay in
the dissolved state since its concentration is hundreds of times larger than
the saturated value for both gases. Therefore, the gas has to be collected in
NBs, which are able to accept large number of gas molecules due to a high
Laplace pressure. For this $n_{g}$ the concentration of NBs with a radius of
$40\;$nm is estimated as $n_{NB}\approx 1.5\times 10^{21}\;$m-3. This value
corresponds to an average distance between the bubbles of $90\;$nm that is
only $10\;$nm larger the minimum distance between the centers of two bubbles.
It means that the state of matter in the cloud can be considered as a
nanofoam.

The vertical structure of the cloud was analysed with a modified schlieren
method [26] that is sensitive to the gradient of the refractive index. The AP
pulses modulated by a triangle (see Fig. 1(d)) were applied to the electrodes.
A series of corresponding schlieren images is shown in Fig. 1(b). The stripe
(c) shows distribution of the refractive index along the red dashed line in
the image (b) at $t=2.0\;$s. It corresponds to the highest concentration of
NBs above the central electrode, which gradually decreases with the increase
of the distance from this electrode. The total size of the dense part of the
cloud is estimated as $1\;$mm. Schlieren contrast can also be generated by
liquid heating. A special heater that mimics the shape of electrodes and
dissipates the same power has been fabricated. The contrast from this heater
has completely different character and different dynamics that is determined
by internal convection rather than the amplitude of the current.

The size of NBs in the cloud was determined by the dynamic light scattering
method. The signal is related to the presence of the AP pulses. At frequency
$f=150\;$kHz particles with a size of $80\pm 10\;$nm have been found. At
higher frequency $f=325\;$kHz the size was $60\pm 10\;$nm, however, it was not
possible to make a convincing conclusion about frequency dependence.
Theoretically it is expected that for higher frequencies the bubbles have to
be smaller.

### Evidence of combustion of gases in NBs

The electrochemical decomposition of water by DC current is used to drive
different microfluidic devices [27], but these devices are known to be slow
due to long recombination time of the gases. This time is still within minutes
even if Pt coated metal foam is used as a catalyst of the reaction between H2
and O2 gases [28]. Slow recombination of the gases is due to the fact that
under normal conditions a spontaneous reaction between hydrogen and oxygen
does not occur because of a high energy barrier [29, 30, 31]. On the other
hand, the reaction in MBs cannot be ignited because the heat produced by this
exothermic reaction escapes too fast via the volume boundary to support the
combustion [32, 33]. Experimentally the minimum bubble, where it was possible
to ignite the reaction between oxygen and acetylene, was $2\;$mm in diameter
[34].

#### Gas balance

Nevertheless, it was found that the reaction can be ignited spontaneously in
very small bubbles (nanobubbles) [22]. As was already mentioned, generation of
the gas by the AP pulses (see Fig. 2(a)) is proven by the Faraday current and
reduction of the refractive index nearby the electrodes. If the durations of
the positive and negative pulses coincide (duty cycle $D=0.5$) stoichiometric
mixture of gases is produced above the same electrode. Since MBs are not
observed, this gas forms NBs containing H2, O2, or mixture of both gases. If
the average potential is shifted to the positive ($D=0.2$) or negative
($D=0.8$) side, one of the gases prevails and MBs appear in the system.
Additionally, it was noted that for $D=0.5$ the refraction index oscillates
with the period equal to that of the driving pulses. It was interpreted as
spontaneous reaction between H2 and O2 gases in NBs.

Figure 2: (a) Scheme of the experiment in the open chamber (top). Images of
the electrodes driven by the AP pulses with the amplitude $U=4.5\;$V and
frequency $f=100\;$kHz at the moment $t=200\;\mu$s (middle). Scheme of the
voltage applied to the working electrode for different duty cycles $D$
(bottom). (b) Scheme of the NBs nucleated above the electrode in the AP
process (top). Image of a microfluidic chip with the closed chamber (middle).
The inset shows the cross section of the chamber. Measured pressure in the
chamber as a function of time (bottom). The process is driven by the AP pulses
at $U=10\;$V and frequency $f=50\;$kHz during $t=600\;\mu$s. (c) The Faraday
current as a function of time for the AP pulses at $U=9\;$V and for different
frequencies (top). The same for SP pulses at $U=8\;$V (bottom).

This information was confirmed and refined further in the subsequent works. To
exclude the gas escape to atmosphere, the process was performed in a closed
chamber just $5\;\mu$m high [23] (see Fig. 2(b)). Platinum electrodes were
deposited on a thin ($150\;$nm) silicon nitride membrane that deflected
proportionally to the pressure in the chamber. The pressure increased linearly
with the process time and then reached a saturation state. As one can see the
pressure in this state oscillates with the frequency equal to that for the
driving pulses. When the pulses are switched off the pressure decreases very
fast in comparison with what one would expect if no reaction between gases
proceeds. It has to be stressed that at any stage of the process the MBs are
not formed in the chamber.

At the top of Fig. 2(b) the processes happening near the surface of the
electrode are shown schematically. The diffusion layer above the electrode
with the thickness $l_{D}\sim\sqrt{tD}\sim 100\;$nm is highly supersaturated
with both gases, where the diffusion coefficient for the gas in liquid is
$D\sim 10^{-9}\;$m2/s and the timescale $t=1/f\sim 10\;\mu$s. Simple estimates
show [23] that the relative supersaturation in this layer can exceed 1000. In
this case the bubbles in the diffusion layer can be nucleated homogeneously or
near homogeneously (with a low barrier) instead of growing at specific points
on the electrode. Three types of the bubbles can be formed: those containing
H2, O2, or mixture of the gases. The latter are formed and disappear each
driving period that is reflected in the pressure oscillations with the
frequency $f$. Moreover, the amplitude of oscillation of the refractive index
above the electrodes is considerably larger than that between the electrodes.
It means that most of the bubbles with the mixture of gases are created and
terminated in the diffusion layer above the electrodes. The bubbles containing
only H2 or O2 gas cannot grow larger than $l_{D}$ and they are pushed out to
the bulk of the liquid by new bubbles nucleated in the layer. In such a way
the volume of the chamber is filled with H2 and O2 nanobubbles, which produce
pressure resulting in the deflection of the membrane. Occasionally the bubbles
with different gases merge and disappear in the reaction. When saturation
state is reached in the chamber, the number of bubbles produced by the current
and the number of bubbles disappearing in the reaction are equal.

It is interesting to see the gas balance in the process demonstrated by the
graph in Fig. 2(b). The total number of gas molecules produced by the AP
process during $600\;\mu$s was estimated [23] from the Faraday current as
$N\approx 2.5\times 10^{13}$. On the other hand, the number of gas molecules
in the steady state $N_{ss}$ can be estimated from the relation

$(P_{a}+\Delta P+P_{L})\Delta V=N_{ss}kT$ (1)

that is the gas law for the gas in NBs. Here $P_{a}$ is the atmospheric
pressure, the overpressure in the chamber is $\Delta P=3.6\;$bar,
$P_{L}=36\;$bar is the Laplace pressure in a bubble with the radius
$r=40\;$nm, and $kT$ is the temperature in energy units. The increase in the
volume of the chamber due to the overpressure $\Delta V\approx 0.7\times
10^{4}\;\mu$m3 is taken from the collected data. This volume is equal to the
total volume of NBs. From this equation one finds $N_{ss}\approx 6.9\times
10^{12}$. It means that only 28% of the produced gas molecules left in the
steady state but the rest 72% are consumed by the reaction. The gas
concentration in the steady state is estimated as $n_{ss}=N_{ss}/(V_{0}+\Delta
V)\approx 1.2\times 10^{26}\;$m-3 and the concentration of NBs is
$n_{NB}=(3\Delta V/4\pi r^{3})/(V_{0}+\Delta V)\approx 0.5\times
10^{21}\;$m-3, where $V_{0}=5\times 10^{4}\;\mu$m3 is the volume of the
chamber. The last concentration can be compared with that for NBs produced by
the regular methods $n_{NB}\sim 10^{15}\;$m-3 [10].

#### Heat produced by the reaction

The overall reaction between hydrogen and oxygen produces significant amount
of heat ($242\;$kJ/mol) that can be directly sensed. It is very important to
separate the heat produced by the reaction from that generated by the current
flowing through the electrolyte (Joule heat). For open systems as in Fig. 2(a)
the effect of heating is observable but weak [22]. It is because the heat
produced by the reaction near the microelectrodes dissipates efficiently in
the substrate and thick layer of liquid. Nevertheless, the effect was measured
with a resistive sensor. More detailed information on the heat flux produced
by the reaction was collected with the use of a specially designed chip [35].
In addition to the electrodes the chip contained a built-in resistive heat
sensor insulated from the electrolyte by a thin SiN layer and a built-in
heater used to relate the signal from the sensor with the heat flux going
through the sensor. The integrated structure of the chip allowed accurate
measurement of the heat flux. It was confirmed independently from [22] and
[23] that the heat is produced by the AP process at frequency of the pulses
higher than $15\;$kHz and increases with frequency up to a tested maximum of
$500\;$kHz; the heat flux is reduced if the duty cycle $D$ of the pulses
deviates from 0.5 in any direction. For the electrodes used in [35] it was
found for the heat flux $J=8\times 10^{4}\;$W/m2 while the theoretical value
expected for the stoichiometric mixture of H2 and O2 gases is $1\times
10^{5}\;$W/m2. It is a good agreement for such a delicate experiment.

Although for the closed chamber it was not possible to measure the heat flux,
the thermal effect of the reaction was demonstrated very clearly [23]. The
membrane and a thin layer of liquid have a very small thermal mass in
comparison with that for the bulk materials and the temperature rise due to
the reaction is more pronounced. It was noted that one can use the thermal
dependence of the Faraday current for the temperature sensing in the same way
as for the resistive sensors. Since mobility of ions increases with
temperature, the Faraday current in the electrolyte depends on the temperature
as

$I_{F}=I_{0F}\left(1+\alpha\Delta T\right),\ \ \ \Delta T=T-T_{0},$ (2)

where $I_{0F}$ is the current at $T=T_{0}$. For $1\;$M solution of Na2SO4 in
water it was found that $\alpha=0.024\;$K-1. Figure 2(c) shows the Faraday
current as a function of the process time for the AP pulses (upper panel) and
for single polarity (SP) pulses (lower panel). The process driven by the SP
pulses generates only one gas above each electrode and demonstrates decrease
of the current with the time increase. It is explained by partial coverage of
the electrodes with MBs and shows that the Joule heating is less significant
than the effect of coverage. No frequency dependence is observed for the SP
pulses. In contrast, the AP process generating the heat due to combustion
reactions demonstrates the increase of the current with time and its
subsequent saturation. The temperature increase depends on the frequency and
can be as high as $40^{\circ}\;$C. With the increase of the driving frequency
the diffusion layer becomes more homogeneous and smaller number of H2 and O2
bubbles leave this layer. On the other hand more bubbles with mixture of the
gases are formed producing more heat.

Let us summarize the signatures of the reaction between hydrogen and oxygen in
NBs. (i) Periodic reduction of the refractive index of liquid and pressure (in
closed chamber) with the period equal to the driving period. (ii) Steady state
for the pressure in the closed chamber demonstrating the balance between
produced and reacted gas. (iii) Fast relaxation of the pressure in the chamber
after switching off the driving pulses. (iv) Heat produced by the reaction and
observed by different methods.

##  III Mechanism of the reaction

#### Domination of the interface

Due to a very large surface-to-volume ratio for NBs, the heat escapes too fast
from such bubbles. The time for heat dissipation from a bubble with the radius
$r$ is $t\sim(r^{2}/\chi_{l})(C_{pg}/C_{pl})^{2}\sim 10^{-13}\>$s, where
$\chi_{l}\sim 10^{-7}\;$m2/s is the heat diffusion coefficient in water and
$C_{pg}/C_{pl}\sim 10^{-3}$ is the ratio of the heat capacities in gas and
liquid states. This time is actually shorter than the reaction time $t_{r}\sim
10\;$ns (see below). Therefore, the temperature in the bubble cannot be high.
It is also supported by the observations [22] where no hot spots have been
found with a high sensitivity camera. In this case, the interface between the
gas and the liquid has to play a special role in the reaction mechanism.

Bubbles in water [36, 37] and similar oil drops in water [38, 39] carry a
negative charge. The $\zeta$-potential of both increases with pH from zero at
$\textrm{pH}=2-4$ up to $\zeta=-120\;$mV at $\textrm{pH}=10$. The surface
density of charges measured for oil drops at neutral pH is $n_{s}=(3-4)\times
10^{13}\;$cm-2 and a similar value is expected for the bubbles [40]. The
$\zeta$-potential of the bubbles and drops is associated with hydroxyl ions
adsorbed on the interface. Not all authors support this point of view [41],
but the presence of the negative charges is not disputed.

A mechanism of the surface-assisted combustion was proposed [42], although it
is able to explain the puzzle only partially. Generation of OH radicals by
shrinking microbubbles observed in [21, 43] was used as a hint. If these
radicals can be generated in NBs with a sufficiently large surface-to-volume
ratio, then one could expect generation of other radicals on the gas-liquid
interface. The surface charges can assist in the formation of radicals, but
the exact mechanism of this assistance is still unknown. It was postulated
[42] that the collision of an H2 or O2 molecule with the charged interface
with some probability can generate H or O radicals (see Fig. 3(a)). The
surface reactions seem to be the only way to explain spontaneous combustion in
a small volume at room temperature.

The reaction constant at the surface explicitly depends on the surface-to-
volume ratio $S/V$ [31]

$K_{i}=(\varepsilon_{i}/4)\bar{v}_{i}(S/V)$ (3)

where $\bar{v}_{i}$ is the average thermal velocity for the $i$-species. The
parameter $\varepsilon_{i}$ can be considered as the probability of the
surface reaction. This probability can be presented as
$\varepsilon_{i}=\sigma_{i}n_{s}$, where $\sigma_{i}$ is the cross-section for
$i$-th radical formation on the surface and $n_{s}$ is the concentration of
the active centers on the bubble wall. Taking $n_{s}\sim 10^{13}\;$cm-2 and a
typical cross-section $\sigma\sim 1\;$Å2 one finds the expected probability of
the surface reactions as $\varepsilon\sim 10^{-3}$.

#### Path of the reaction

In the classical combustion process the chemical branching reactions
$\textrm{H}+\textrm{O}_{2}\rightarrow\textrm{O}+\textrm{OH}$ and
$\textrm{O}+\textrm{H}_{2}\rightarrow\textrm{H}+\textrm{OH}$ play a key role
[29]. These reactions are characterized by high energy barriers and they will
be strongly suppressed if the temperature in the bubble is not high enough.
Therefore, the classical combustion in NBs is not possible since the heat
escapes too fast from small bubbles. On the other hand, according to (3) the
role of the surface reactions increases with the increase of the ratio $S/V$.
The radicals formed on the surface trigger a chain of the low-energy reactions
transforming H2 and O2 gases into H2O. The equations of chemical kinetics for
four radicals H, O, OH, HO2 and four molecules H2, O2, H2O, H2O2 have been
solved [42]. In general 19 low-energy reactions in the bulk (with the reaction
constant $>1\;\mu$s-1) were included in the analysis and their reaction
constants were collected from different sources.

Figure 3: (a) Scheme of the spontaneous ignition of the combustion in a NB
with charged interface. It is assumed that molecules approaching the reaction
center at the interface are able to produce radicals. (b) Solution of the
equations of chemical kinetics for long-lived species in the process of
surface-assisted (cold) combustion. (c) The same for short-lived radicals. All
concentrations are shown with respect to the initial gas concentration.

The most important conclusion is that there exists a chain of low-energy bulk
reactions that transforms mixtures of H2 and O2 gases with the assistance of
the surface processes into water. For the probability of hydrogen radical
generation at the surface $\varepsilon_{H}=0.003$ the time evolution of
different species is shown in Fig. 3(b),(c) starting from the stoichiometric
mixture of H2 and O2 gases. The characteristic process time $t_{r}\sim 10\;$ns
is defined by the reaction constants. In contrast with the standard combustion
there is in excess of hydrogen peroxide in the final state. Some amount of H2
and H radicals in the final state is because the slow reactions (for example,
decomposition of H2O2) were not included in the analysis. Generation of H
radicals on the surface is principal for the surface-assisted combustion, but
generation of O radicals does not play a key role although it can influence on
the amount of hydrogen peroxide in the final state. Among the bulk reactions
the principal role belong to the trimolecular reaction
$\textrm{H}+\textrm{O}_{2}+\textrm{M}\rightarrow\textrm{H}\textrm{O}_{2}+\textrm{M}$
where M is any third species taking part in the process. The surface-assisted
combustion becomes impossible if this reaction is excluded. A significant
amount of hydrogen peroxide in the final state is related to the reaction
$\textrm{H}\textrm{O}_{2}+\textrm{H}\textrm{O}_{2}\rightarrow\textrm{H}_{2}\textrm{O}_{2}+\textrm{O}_{2}$.
The data in Fig. 3 are presented for a bubble radius of $50\;$nm. If the
radius of the NB decreases, the amount of H2O2 in the final state increases.

#### Molecular dynamics simulation

Independently the surface-assisted combustion has been analysed [44] using the
reactive molecular dynamics simulation. To simplify the calculations a cubic
volume filled with the gases was considered instead of a sphere, but the extra
pressure in this volume was introduced to account for the Laplace pressure.
The method used avoids the restrictions of continuous media approach; it does
not need such parameters as heat diffusion rates, bi and tri-molecular
reaction rates, and pressure in the bubble which are not always known.
Generation of radicals on the walls was modeled inserting a certain number of
radicals near the walls or inserting the radicals periodically. The main
conclusions of Ref. [42] were confirmed qualitatively. The quantitative
agreement cannot be expected since the chemical kinetics describes the system
on a relatively long timescale up to $1\;\mu$s while the molecular dynamics
can describe the system on a timescale shorter than $0.1\;$ns.

It was confirmed by the direct simulation that the temperature in the bubble
cannot reach the value of $700^{\circ}\;$C needed for standard combustion but
it can be as high as $100^{\circ}\;$C. It does not contradict to the statement
[42] that temperature in NBs is close to room temperature. The temperature in
the bubble is equalized during $t\sim r^{2}/\chi_{g}\sim 1\;$ns where
$\chi_{g}\sim 10^{-6}\;$m2/s is the heat diffusion coefficient in gas. This
time cannot be reached by the molecular dynamics. It was confirmed also that
the final products contain a significant amount of hydrogen peroxide. It was
stressed that for the surface-assisted combustion the main intermediate
product is HO2 while for the normal combustion the most important intermediate
product is OH radicals. Important role of HO2 can also be seen in Fig. 3(c).

Summarizing the current understanding of the mechanism of the reactions in NBs
we can separate the following important points. (i) Combustion in NBs is the
low-temperature process closely related to a high surface-to-volume ratio for
NBs. (ii) If H radicals can be generated at the gas-liquid interface, then
there is a chain of elementary reactions that transforms stoichiometric
mixture of H2 and O2 gases into water and hydrogen peroxide. (iii) Generation
of H radicals is assumed to be related to the charges at the gas-liquid
interface but the precise mechanism is still unknown.

##  IV Combustion in microbubbles

The main conclusion from the previous section is that the surface-assisted
combustion can be realised only for a high surface-to-volume ratio. All the
more surprising that the combustion was observed in MBs produced at special
conditions by the AP process [45]. To investigate this phenomenon in detail
the concentric electrodes shown in Fig. 4(a) were used [46]. For such
electrodes the NBs are well concentrated between the electrodes.

Figure 4: Explosion of a microbubble. (a) The sample fixed in small Petri dish
filled with Na2SO4 solution and zoomed view of Ti concentric electrodes. (b)
Electrodes just before the explosion. The cloud of NBs is so dense that it
scatters slightly the visible light. Right side shows the sound amplitude that
demonstrates two sources of the sound. (c) Current between the electrodes
drops synchronously with the growing MB. The AP process is at $U=14\;$V and
$f=500\;$kHz. Black circles show positions of the frames in the fast video.
(d) The MB in its maximum size observed from the top. (e) The same as (d) but
viewed from the side.

#### Experimental facts

With the increase of the amplitude of the pulses more and more NBs are
generated in the AP process. When the concentration of NBs reaches a critical
value, a very interesting phenomenon occurs. The cloud of NBs visible in the
left side of Fig. 4(b) suddenly is transformed into a MB that explodes with a
clearly audible ’click’ sound. The clicks are repeated with a frequency of
$12\;$Hz. The sound consists of two sources separated by a time interval of
$300\;\mu$s as one can see in the right side of (b). Synchronously with the
sound the current in the system decreases in just $20\;\mu$s (c) and stays low
during $300\;\mu$s. Absence of a sharp increase in the current together with
insufficient electrical field demonstrate that the phenomenon cannot be
related to the electrical breakdown. Observation of the process with a fast
camera demonstrates that synchronously with the current decrease a MB with an
initial size of $150\;\mu$m appears above the electrodes, grows to a maximum
size of $1200\;\mu$m in $200\;\mu$s, than shrinks fast, and disappears. The MB
in its maximum is shown in Fig. 4(d) and (e) from the top and from the side
respectively. Reduction of the current is explained by the growing bubble,
which overlaps the electrodes in $20\;\mu$s.

For understanding of the phenomenon it is important that there are two sources
of the sound accompanying the process. The first sound appears together with
the decrease of the current and when the current starts to restore the second
more powerful sound emerges. The second sound appears in the moment when the
bubble reaches its minimum value and can be explained by the cavitation
effect. From the fast video one can find the time dependence of the bubble
radius as shown in Fig. 5 (right). In this dependence one can resolve the
second bump that is a characteristic feature of cavitation. Moreover, after
many clicks the silicon sample with the deposited Ti electrodes is destroyed
locally very similar to that produced by cavitating bubbles (Figure S1 in
[46]).

Figure 5: (Left) Scheme explaining formation of the MB and chemical reaction
happening in the bubble. (Right) Evolution of the final MB observed with the
fast camera with an interval between the frames of $13.7\;\mu$s.

The first sound one can relate to the explosion in the initial bubble. It
starts synchronously with the current decrease and obviously is related to the
expanding MB. The expansion rate estimated from the fast video is about
$8\;$m/s. This rate is in agreement with a typical velocity of the burning
front for normal combustion. However, the observed process cannot be induced
by normal combustion because the heat escapes from the bubble with a radius of
$75\;\mu$m too fast ($t\sim 10\;$ns) to support normal combustion. A special
experiment was performed to check the possibility of spontaneous combustion of
H2 and O2 mixture in MBs. The stoichiometric mixture of gases was pumped into
the gas channel of a microfludic bubble generator. The MBs with a diameter of
$10\;\mu$m moving in water one by one was observed in the output channel. No
spontaneous combustion in these bubbles was observed [45]. It seems that the
surface-assisted combustion also cannot explain the phenomenon of expanding MB
because the $S/V$ ratio in Eq. (3) is three orders of magnitude smaller than
that for NBs.

#### Role of nanodrops

Nevertheless, the process has been interpreted [46] as the surface-assisted
combustion in MBs. The main steps of this process are shown schematically in
Fig. 5. As was already mentioned, when the amplitude of the pulses increases,
the NBs approach very close to each other and the density of the cloud
approaches the critical value. This value corresponds to the close packing of
spheres and is equal $n_{NB}\approx 2\times 10^{21}\;$m-3 for $r=40\;$nm.

The cloud consists of H2 and O2 NBs. When two similar bubbles are close to
each other, there is no significant diffusion of gases since the concentration
gradient is low. However, when two bubbles with different gases meet, fast
exchange by the gases occurs. The minimum distance between the bubbles is
defined by the disjoining pressure in the separating membrane with the
thickness $d\sim 1\;$nm. Then the exchange time by the gases is estimated as
$t\sim d^{2}/D_{l}\sim 1\;$ns, where $D_{l}\sim 10^{-9}\;$m2/s is the
diffusion coefficient of gas in liquid. It means that the cloud of NBs with
the critical density will be transformed to a MB containing mixture of H2 and
O2 gases. However, the volume filled with the close-packed NBs has the volume
fraction of gas $f_{0}=0.74$ and the rest is liquid. After merging of NBs this
liquid will be collected in nanodrops with the radius
$r^{\prime}=r[(1-f_{0})/f_{0}]^{1/3}$.

The MB formed by merging of many NBs (initial MB) is filled with the
stoichiometric mixture of gases, but 24% of its volume is occupied by the
nanodrops. The surface-to-volume ratio in this MB is $S/V=3/r^{\prime}\sim
1/r$. This ratio is nearly as high as that for the NBs and for this reason it
is able to support the surface-assisted reactions. These reactions can proceed
in the same way as it was described in Sec. III. On a timescale of $10\;$ns
hydrogen and oxygen in the MB will turn into water vapor (final MB). In spite
of a large size of the MB the thermal equilibrium in the final MB is
established on the same timescale as for NBs $t\sim 1\;$ns because of the
presence of nanodrops separated by the average distance
$l=r(4\pi/9f_{0})^{1/3}\sim r$. Therefore, the final MB has well-defined
pressure and temperature, which determine the following evolution of the
bubble directly observed in the experiment. This evolution is much more slow
(the time scale $t>1\;\mu$s) and, in principle, can be described by the
Rayleigh–Plesset equation [47] with the accurate inclusion of the heat
exchange effects between the MB and surrounding liquid. Therefore, the final
MB is in the state, in which the bubble has not yet expanded, but the chemical
reaction is already over and the steam–liquid equilibrium is established.

#### State in the exploding MB

Owing to the thermal equilibrium it is possible to find the pressure $P_{f}$
and temperature $T_{f}$ in the final MB using only the energy balance equation
[46]. The internal energy of the initial MB plus the energy produced by the
reaction are spent on the energies of the gas phase, liquid phase, and partial
vaporization of nanodrops in the final MB. The effect of surface tension in
the balance is insignificant. Since the gas and liquid phases in the final MB
are in equilibrium, the pressure in the bubble is defined by the temperature
$P_{f}=P_{eq}(T_{f})$, where the function $P_{eq}(T)$ and other thermodynamic
values were taken from the vapor-liquid equilibrium tables [48]. The resulting
value depends on the size of merging NBs. For $r=30\;$nm it was found that
$T_{f}=220.8^{\circ}\;$C and $P_{f}=23.5\;$bar but for $r=40\;$nm these
parameters are $T_{f}=185.5^{\circ}\;$C and $P_{f}=11.4\;$bar.

The pressure in the final MB is much higher than that in the surrounding
liquid $P_{f}\gg P_{a}$ and this pressure jump is the source of the first
sound shown in Fig. 4(b). The temperature in the final MB is higher than that
found for NBs [44], but it is still not enough for the spontaneous ignition of
the normal combustion.

Summarizing combustion in MBs one can stress the following. (i) The process is
observed only for MBs formed from a cloud of NBs produced in the AP process;
no reactions happen in the MBs filled with H2 and O2 gases taken from external
sources. (ii) Explosion of the initial MB is accompanied by the sound of
explosion and after a delay of $300\;\mu$s by the sound of cavitation. (iii)
Nanodrops that left in the MB after merging of many NBs provide the surface-
to-volume ratio as high as in a separate NB and ensure conditions for the
surface-assisted combustion. (iv) The final MB immediately after the chemical
reaction is characterized by the pressure $P_{f}=10-20\;$bar and the
temperature $T_{f}\approx 200^{\circ}\>$C; high pressure in the final MB is
the source of the first sound.

##  V Open problems

We still do not know if the NBs generated in the AP process are the same as
those produced by the regular methods. Short lifetime of the bubbles generated
in the AP process is explained by the interaction between H2 and O2 NBs.
However, if we menage to separate hydrogen and oxygen NBs, for example by
diluting the solution, would they live much longer? A recent paper [49]
relates stability of the regular NBs to their origin. It is assumed that long-
lived NBs appear only from shrinking MBs and their stability is related to the
increasing concentration of the surface charges. The answer to the above
question will be a critical test for this hypothesis because only NBs are
produced in the AP process.

It is not clear why only NBs are generated by the AP pulses. We know that very
high supersaturation supports homogeneous nucleation of NBs, but for some
reason these bubbles do not grow or merge easily. It is expected that such
processes are controlled by the surface charges and opposite charges
distributed in the electrolyte. However, these effects have never been
analysed in depth.

Although the surface-assisted combustion is able to give a basic explanation
of the reactions in NBs and in MBs, generation of radicals on the gas-liquid
interface is the most important open question. Direct evidence for the
presence of the radicals is still lacking. It could be obtained using the
electron spin resonance spectroscopy or using different radical scavengers in
the solution. It is also possible that generation of OH radicals in the
regular NBs and H (O) radicals in NBs produced by the AP process are related
effects. In this respect it is interesting to consider a reaction path for
’cold’ combustion via OH radicals generated on the surface instead of H or O
radicals as in [42].

Dynamics of exploding MB was determined experimentally. On the other hand, the
evolution of exploding NB also has a special interest. Recently it was
demonstrated [50] that a flux of H2 and O2 NBs directed to a Pt plate is able
to produce Pt nanoparticles that is a high energy process. Understanding of
the dynamics of exploding NBs can shed light on the observed phenomena.

##  VI Conclusions

In this paper we presented the current status and understanding of the
phenomena observed during generation of NBs by short alternating polarity
voltage pulses. In contrast with the regular methods no bubbles larger than
$200\;$nm are produced by the AP method. The concentration of NBs is so high
that one can easily observe collective optical effects produced by these NBs.
Since high supersaturation with both H2 and O2 gases is generated above the
same electrode, three types of NBs can be produced: those containing H2, O2,
and mixture of the gases.

The most important difference from the regular NBs is that inside of one NB
hydrogen and oxygen are able to react with each other in spite of the
expectations from the classical combustion theory. It is clear demonstrated by
a series of experimental facts such as pressure oscillation in a closed volume
with the frequency of the driving pulses, fast relaxation of the pressure
after switching off the pulses, heat produced by the reactions, and others.

A possible mechanism of the combustion reactions in a small volume relies on a
very high surface-to-volume ratio characterizing NBs. It assumes generation of
free radicals on the gas-solid interface presumably due to the charges known
to be adsorbed on the interface. With this assumption the chain of ’cold’
reactions exists, which is able to transform mixture of hydrogen and oxygen
into water without necessity of high temperature. However, the exact mechanism
of the radical formation at the interface is still unknown.

At special conditions combustion of the gases is observed in MBs that is
accompanied by audible clicks, by significant expansion of the bubble followed
by the cavitation. It seems that the combustion in MB cannot be described by
the surface-assisted mechanism because MBs are characterized much smaller
surface-to-volume ratio. However, as described in the paper a MB formed by
merging of many NBs contains nanodrops so that the total surface-to-volume
ratio is of the same order as for NBs. Theoretical estimates of the pressure
and temperature in the MB immediately after the reaction show that the sound
and expansion are produced by a pressure jump of $10-20\;$bar but the gas
temperature stays relatively low of about $200^{\circ}\>$C.

Finally we discuss different problems that need deeper understanding. The most
important problem is the mechanism of radical formation at the interface.

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