Spontaneous chemical reactions between hydrogen and oxygen in nanobubbles
SSpontaneous chemical reactions between hydrogen and oxygen in nanobubbles
V. B. Svetovoy ∗ A. N. Frumkin Institute of Physical Chemistry and Electrochemistry,Russian Academy of Sciencies, Leninsky prospect 31 bld. 4, 119071 Moscow, Russia
Bulk nanobubbles (NBs) generated electrochemically by short voltage pulses of alternating polar-ity behave differently from those produced by regular methods. Only bubbles smaller than 200 nmare formed in the process and their concentration is very high. Moreover, the bubbles contain-ing both H and O gases disappear quickly via the combustion reaction, although the reaction insuch a small volume cannot happen according to the classical combustion theory. Experimentalfacts about these unusual NBs are reviewed and current understanding of the observed phenomenais 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. Asurface-assisted mechanism proposed for the combustion reactions in restricted volumes with a highsurface-to-volume ratio is discussed. It it explained how the same mechanism may describe theaudible explosion of microbubbles, that is observed in certain circumstances. I. INTRODUCTION
Nanobubbles have attracted significant attention in thelast 20 years [1–3]. This attention is driven by a funda-mental problem: NBs live much too long in compari-son with the prediction given by the diffusion dissolu-tion theory [4, 5]. On the other hand, exciting applica-tions of NBs in environment [6, 7], agriculture [8], flota-tion [9, 10], healthcare [11, 12], and chemistry [13] haveemerged to name only a few.In contrast with surface NBs, which exist on the solid-liquid interface, bulk NBs fill the volume of liquid. TheseNBs are generated by mostly mechanical injection of dif-ferent gases [9] or by ultrasonic cavitation [10], but hy-drogen and oxygen NBs where also generated by DCelectrolysis [14, 15]. Later these methods will be calledthe regular methods. The size distribution of the NBswas characterized by the dynamic light scattering andindividual bubbles were observed by electron microscopyfrom freeze fracture replicas [16], by phase microscopyand polarimetric scatterometry [17].Unexpectedly, NBs containing oxygen are able to pro-duce reactive oxygen species which can oxidize pollu-tants and pathogens in water [18–20], while separate oxy-gen molecules have no effect on organics. Generationof OH radicals from shrinking air microbubbles (MBs)without external dynamical stimuli such as ultrasoundor high pressure differential was observed by Takahashi et al. [21] with the electron spin-resonance spectroscopy.This finding was confirmed through reactivity with probemolecules by other researches and it was established thatonly OH radicals can be produced from air, O , or O nanobubbles [19]. Observation of free radicals is a puz-zling phenomenon since radical formation is a high energyevent, which is not possible without external energy sup-ply. Similar to the long lifetime of NBs the controversyon the radical production by NBs persists. ∗ Corresponding author: [email protected]; [email protected]
One more puzzling phenomenon that can proceed onlyin a high energy environment was observed in NBs con-taining mixture of H and O gases [22, 23]. To ignitea series of combustion reactions between these gases ina fixed volume one has to produce a certain number offree radicals. Moreover, the reactions will not be self-supported if the volume is too small. This is because theheat produced by the exothermic reaction escapes toofast via the volume boundaries and the temperature in-side of the volume will be too low to support the reaction.Nanobubbles seem especially unfavorable to support thecombustion reactions but in spite of this the combustionof the gases proceeds in NBs spontaneously (without ig-nition).Nanobubbles containing hydrogen, oxygen, but also amixture of the gases were generated in a so-called al-ternating polarity (AP) electrochemical water decompo-sition process [22] when the polarity of the electrodesis changed with a frequency of the order of 100 kHz orhigher. In contrast with the DC electrolysis [14, 15], inthis process only NBs are formed, which do not scatterthe visible light but change the refractive index of liquidat a level that can be easily observed optically.In this paper we describe briefly formation and obser-vation of NBs in the AP process, but the main attentionis directed to combustion of hydrogen and oxygen in NBs.The latest progress in the observation and understandingof the combustion reactions in NBs and closely relatedphenomenon observed in MBs is discussed. II. SIGNATURES OF THE REACTIONBETWEEN H AND O GASES IN NBSGeneration of NBs in the AP process
Water electrolysis performed by short AP voltagepulses demonstrated very unusual properties in compar-ison with the DC electrolysis [22]. If one applies suchpulses to the electrodes, for which the polarity of theworking electrode changes with a frequency of the orders a r X i v : . [ c ond - m a t . s o f t ] F e b of 100 kHz and the opposite electrode is grounded, visibleproduction of gas suddenly disappears [22]. The transi-tion occurs at frequencies above 20 kHz but the currentthrough the electrode only increases gradually with thefrequency increase. For Pt electrodes one can separatethe Faraday component in the current [24], which showsthat the gas has to be produced with the increasing ratefor higher frequencies. It was concluded [22] that in theAP process only NBs with a size smaller than 200 nm areformed. Since such bubbles practically do not scatter thevisible light, they become invisible in optical microscope.This conclusion was confirmed with different opticalmethods in later works. Although it is not possible tosee the separate bubbles optically, it was rather straight-forward to observe collective effects produced by NBs. Tolocalise generation of NBs, concentric planar electrodeswith the external diameter 500 µ m deposited on the oxi-dized Si substrate have been used. A few different meth-ods demonstrated the presence of a dense cloud of NBsabove the electrodes. Figure 1(a) shows the differentialinterference contrast [25] of two mutually coherent or-thogonally polarized beams, which are slightly displacedspatially at the sample plane. The interference of thebeams depends on the optical path difference in the di-rection of the displacement. The method is appropriatefor visualisation of the gas distribution in dynamics. Onecan see that the cloud of NBs covers the electrode andthe gradient of the refractive index becomes larger withthe increase of the pulses amplitude. This method gives,however, only a qualitative picture.Direct observation of optical distortion of the elec-trodes allows one to estimate the gas concentration inthe liquid. Analysis performed in [25] gave the reduc-tion of the refractive index of about 0.18. Any impurityin the solution or Joule heating provided by the currentcannot explain such a large value. The only reasonableexplanation is the gas in the liquid with the concentration n g ≈ . × m − . This gas cannot stay in the dis-solved state since its concentration is hundreds of timeslarger than the saturated value for both gases. Therefore,the gas has to be collected in NBs, which are able to ac-cept large number of gas molecules due to a high Laplacepressure. For this n g the concentration of NBs with aradius of 40 nm is estimated as n NB ≈ . × m − .This value corresponds to an average distance betweenthe bubbles of 90 nm that is only 10 nm larger the min-imum distance between the centers of two bubbles. Itmeans that the state of matter in the cloud can be con-sidered as a nanofoam.The vertical structure of the cloud was analysed witha modified schlieren method [26] that is sensitive to thegradient of the refractive index. The AP pulses modu-lated by a triangle (see Fig. 1(d)) were applied to theelectrodes. A series of corresponding schlieren images isshown in Fig. 1(b). The stripe (c) shows distributionof the refractive index along the red dashed line in theimage (b) at t = 2 . FIG. 1. Cloud of NBs. (a) Differential interference contrast indynamics. The AP pulses at f = 400 kHz are modulated bytriangle with a period of 5 s and with the maximum amplitude U max = 8 V. Images for the beams of different polarizationare shifted for 30 µ m. (b) Schlieren contrast of the cloud indynamics (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 pulsesas a function of time. gradually decreases with the increase of the distance fromthis electrode. The total size of the dense part of thecloud is estimated as 1 mm. Schlieren contrast can alsobe generated by liquid heating. A special heater thatmimics the shape of electrodes and dissipates the samepower has been fabricated. The contrast from this heaterhas completely different character and different dynam-ics that is determined by internal convection rather thanthe amplitude of the current.The size of NBs in the cloud was determined by thedynamic light scattering method. The signal is relatedto the presence of the AP pulses. At frequency f =150 kHz particles with a size of 80 ±
10 nm have beenfound. At higher frequency f = 325 kHz the size was 60 ±
10 nm, however, it was not possible to make a convincingconclusion about frequency dependence. Theoretically itis expected that for higher frequencies the bubbles haveto be smaller.
Evidence of combustion of gases in NBs
The electrochemical decomposition of water by DCcurrent is used to drive different microfluidic devices [27],but these devices are known to be slow due to long re-combination time of the gases. This time is still withinminutes even if Pt coated metal foam is used as a cata-lyst of the reaction between H and O gases [28]. Slowrecombination of the gases is due to the fact that un-der normal conditions a spontaneous reaction betweenhydrogen and oxygen does not occur because of a highenergy barrier [29–31]. On the other hand, the reactionin MBs cannot be ignited because the heat produced bythis exothermic reaction escapes too fast via the volumeboundary to support the combustion [32, 33]. Experi-mentally the minimum bubble, where it was possible toignite the reaction between oxygen and acetylene, was2 mm in diameter [34]. a. Gas balance Nevertheless, it was found that thereaction can be ignited spontaneously in very small bub-bles (nanobubbles) [22]. As was already mentioned, gen-eration of the gas by the AP pulses (see Fig. 2(a)) isproven by the Faraday current and reduction of the re-fractive index nearby the electrodes. If the durationsof the positive and negative pulses coincide (duty cycle D = 0 .
5) stoichiometric mixture of gases is producedabove the same electrode. Since MBs are not observed,this gas forms NBs containing H , O , or mixture of bothgases. If the average potential is shifted to the positive( D = 0 .
2) or negative ( D = 0 .
8) side, one of the gasesprevails and MBs appear in the system. Additionally, itwas noted that for D = 0 . and O gases in NBs.This information was confirmed and refined further inthe subsequent works. To exclude the gas escape to at-mosphere, the process was performed in a closed chamberjust 5 µ m high [23] (see Fig. 2(b)). Platinum electrodeswere deposited on a thin (150 nm) silicon nitride mem-brane that deflected proportionally to the pressure in thechamber. The pressure increased linearly with the pro-cess time and then reached a saturation state. As one cansee the pressure in this state oscillates with the frequencyequal to that for the driving pulses. When the pulses areswitched off the pressure decreases very fast in compar-ison with what one would expect if no reaction betweengases proceeds. It has to be stressed that at any stage ofthe process the MBs are not formed in the chamber.At the top of Fig. 2(b) the processes happening nearthe surface of the electrode are shown schematically. Thediffusion layer above the electrode with the thickness l D ∼ √ tD ∼
100 nm is highly supersaturated with bothgases, where the diffusion coefficient for the gas in liquidis D ∼ − m /s and the timescale t = 1 /f ∼ µ s.Simple estimates show [23] that the relative supersatura-tion in this layer can exceed 1000. In this case the bubblesin the diffusion layer can be nucleated homogeneously or near homogeneously (with a low barrier) instead of grow-ing at specific points on the electrode. Three types of thebubbles can be formed: those containing H , O , or mix-ture of the gases. The latter are formed and disappeareach driving period that is reflected in the pressure oscil-lations with the frequency f . Moreover, the amplitude ofoscillation of the refractive index above the electrodes isconsiderably larger than that between the electrodes. Itmeans that most of the bubbles with the mixture of gasesare created and terminated in the diffusion layer abovethe electrodes. The bubbles containing only H or O gas cannot grow larger than l D and they are pushed outto the bulk of the liquid by new bubbles nucleated in thelayer. In such a way the volume of the chamber is filledwith H and O nanobubbles, which produce pressureresulting in the deflection of the membrane. Occasion-ally the bubbles with different gases merge and disappearin the reaction. When saturation state is reached in thechamber, the number of bubbles produced by the currentand the number of bubbles disappearing in the reactionare equal.It is interesting to see the gas balance in the processdemonstrated by the graph in Fig. 2(b). The total num-ber of gas molecules produced by the AP process during600 µ s was estimated [23] from the Faraday current as N ≈ . × . On the other hand, the number of gasmolecules in the steady state N ss can be estimated fromthe relation ( P a + ∆ P + P L )∆ V = N ss kT (1)that is the gas law for the gas in NBs. Here P a is theatmospheric pressure, the overpressure in the chamber is∆ P = 3 . P L = 36 bar is the Laplace pressure in abubble with the radius r = 40 nm, and kT is the temper-ature in energy units. The increase in the volume of thechamber due to the overpressure ∆ V ≈ . × µ m is taken from the collected data. This volume is equalto the total volume of NBs. From this equation onefinds N ss ≈ . × . It means that only 28% ofthe produced gas molecules left in the steady state butthe rest 72% are consumed by the reaction. The gasconcentration in the steady state is estimated as n ss = N ss / ( V +∆ V ) ≈ . × m − and the concentration ofNBs is n NB = (3∆ V / πr ) / ( V + ∆ V ) ≈ . × m − ,where V = 5 × µ m is the volume of the chamber.The last concentration can be compared with that forNBs produced by the regular methods n NB ∼ m − [10]. b. Heat produced by the reaction The overall reac-tion between hydrogen and oxygen produces significantamount of heat (242 kJ/mol) that can be directly sensed.It is very important to separate the heat produced bythe reaction from that generated by the current flowingthrough the electrolyte (Joule heat). For open systemsas in Fig. 2(a) the effect of heating is observable butweak [22]. It is because the heat produced by the reac-tion near the microelectrodes dissipates efficiently in thesubstrate and thick layer of liquid. Nevertheless, the ef-
FIG. 2. (a) Scheme of the experiment in the open chamber (top). Images of the electrodes driven by the AP pulses withthe amplitude U = 4 . f = 100 kHz at the moment t = 200 µ s (middle). Scheme of the voltage applied tothe working electrode for different duty cycles D (bottom). (b) Scheme of the NBs nucleated above the electrode in the APprocess (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 andfrequency f = 50 kHz during t = 600 µ s. (c) The Faraday current as a function of time for the AP pulses at U = 9 V and fordifferent frequencies (top). The same for SP pulses at U = 8 V (bottom). fect was measured with a resistive sensor. More detailedinformation on the heat flux produced by the reactionwas collected with the use of a specially designed chip[35]. In addition to the electrodes the chip containeda built-in resistive heat sensor insulated from the elec-trolyte by a thin SiN layer and a built-in heater used torelate the signal from the sensor with the heat flux goingthrough the sensor. The integrated structure of the chipallowed accurate measurement of the heat flux. It wasconfirmed independently from [22] and [23] that the heatis produced by the AP process at frequency of the pulseshigher than 15 kHz and increases with frequency up to atested maximum of 500 kHz; the heat flux is reduced ifthe duty cycle D of the pulses deviates from 0.5 in anydirection. For the electrodes used in [35] it was found forthe heat flux J = 8 × W/m while the theoreticalvalue expected for the stoichiometric mixture of H andO gases is 1 × W/m . It is a good agreement forsuch a delicate experiment.Although for the closed chamber it was not possible tomeasure the heat flux, the thermal effect of the reactionwas demonstrated very clearly [23]. The membrane anda thin layer of liquid have a very small thermal massin comparison with that for the bulk materials and thetemperature 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 thesame way as for the resistive sensors. Since mobility ofions increases with temperature, the Faraday current inthe electrolyte depends on the temperature as I F = I F (1 + α ∆ T ) , ∆ T = T − T , (2)where I F is the current at T = T . For 1 M solution ofNa SO in water it was found that α = 0 .
024 K − . Fig-ure 2(c) shows the Faraday current as a function of theprocess time for the AP pulses (upper panel) and for sin-gle polarity (SP) pulses (lower panel). The process drivenby the SP pulses generates only one gas above each elec-trode and demonstrates decrease of the current with thetime increase. It is explained by partial coverage of theelectrodes with MBs and shows that the Joule heating isless significant than the effect of coverage. No frequencydependence is observed for the SP pulses. In contrast,the AP process generating the heat due to combustionreactions demonstrates the increase of the current withtime and its subsequent saturation. The temperature in-crease depends on the frequency and can be as high as40 ◦ C. With the increase of the driving frequency thediffusion layer becomes more homogeneous and smallernumber of H and O bubbles leave this layer. On theother hand more bubbles with mixture of the gases areformed producing more heat.Let us summarize the signatures of the reaction be-tween hydrogen and oxygen in NBs. (i) Periodic reduc-tion of the refractive index of liquid and pressure (inclosed chamber) with the period equal to the drivingperiod. (ii) Steady state for the pressure in the closedchamber demonstrating the balance between producedand reacted gas. (iii) Fast relaxation of the pressure inthe chamber after switching off the driving pulses. (iv)Heat produced by the reaction and observed by differentmethods. III. MECHANISM OF THE REACTION a. Domination of the interface
Due to a very largesurface-to-volume ratio for NBs, the heat escapes too fastfrom such bubbles. The time for heat dissipation froma bubble with the radius r is t ∼ ( r /χ l )( C pg /C pl ) ∼ − s, where χ l ∼ − m /s is the heat diffusion co-efficient in water and C pg /C pl ∼ − is the ratio of theheat capacities in gas and liquid states. This time isactually shorter than the reaction time t r ∼
10 ns (seebelow). Therefore, the temperature in the bubble can-not be high. It is also supported by the observations [22]where no hot spots have been found with a high sensi-tivity camera. In this case, the interface between the gasand the liquid has to play a special role in the reactionmechanism.Bubbles in water [36, 37] and similar oil drops in wa-ter [38, 39] carry a negative charge. The ζ -potentialof both increases with pH from zero at pH = 2 − ζ = −
120 mV at pH = 10. The surface den-sity of charges measured for oil drops at neutral pH is n s = (3 − × cm − and a similar value is expectedfor the bubbles [40]. The ζ -potential of the bubbles anddrops is associated with hydroxyl ions adsorbed on theinterface. 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 wasproposed [42], although it is able to explain the puzzleonly partially. Generation of OH radicals by shrinkingmicrobubbles observed in [21, 43] was used as a hint. Ifthese radicals can be generated in NBs with a sufficientlylarge surface-to-volume ratio, then one could expect gen-eration of other radicals on the gas-liquid interface. Thesurface charges can assist in the formation of radicals,but the exact mechanism of this assistance is still un-known. It was postulated [42] that the collision of anH or O molecule with the charged interface with someprobability can generate H or O radicals (see Fig. 3(a)).The surface reactions seem to be the only way to explainspontaneous combustion in a small volume at room tem-perature.The reaction constant at the surface explicitly dependson the surface-to-volume ratio S/V [31] K i = ( ε i / v i ( S/V ) (3)where ¯ v i is the average thermal velocity for the i -species. The parameter ε i can be considered as the probability ofthe surface reaction. This probability can be presentedas ε i = σ i n s , where σ i is the cross-section for i -th rad-ical formation on the surface and n s is the concentra-tion of the active centers on the bubble wall. Taking n s ∼ cm − and a typical cross-section σ ∼ onefinds the expected probability of the surface reactions as ε ∼ − . b. Path of the reaction In the classical combustionprocess the chemical branching reactions H + O → O + OH and O + H → H + OH play a key role [29].These reactions are characterized by high energy barriersand they will be strongly suppressed if the temperaturein the bubble is not high enough. Therefore, the classicalcombustion in NBs is not possible since the heat escapestoo fast from small bubbles. On the other hand, accord-ing to (3) the role of the surface reactions increases withthe increase of the ratio
S/V . The radicals formed onthe surface trigger a chain of the low-energy reactionstransforming H and O gases into H O. The equationsof chemical kinetics for four radicals H, O, OH, HO andfour molecules H , O , H O, H O have been solved [42].In general 19 low-energy reactions in the bulk (with thereaction constant > µ s − ) were included in the analysisand their reaction constants were collected from differentsources.The most important conclusion is that there exists achain of low-energy bulk reactions that transforms mix-tures of H and O gases with the assistance of the surfaceprocesses into water. For the probability of hydrogen rad-ical generation at the surface ε H = 0 .
003 the time evolu-tion of different species is shown in Fig. 3(b),(c) startingfrom the stoichiometric mixture of H and O gases. Thecharacteristic process time t r ∼
10 ns is defined by thereaction constants. In contrast with the standard com-bustion there is in excess of hydrogen peroxide in thefinal state. Some amount of H and H radicals in thefinal state is because the slow reactions (for example,decomposition of H O ) were not included in the analy-sis. Generation of H radicals on the surface is principalfor the surface-assisted combustion, but generation of Oradicals does not play a key role although it can influ-ence on the amount of hydrogen peroxide in the finalstate. Among the bulk reactions the principal role be-long to the trimolecular reaction H + O + M → HO + Mwhere M is any third species taking part in the process.The surface-assisted combustion becomes impossible ifthis reaction is excluded. A significant amount of hydro-gen peroxide in the final state is related to the reactionHO + HO → H O + O . The data in Fig. 3 are pre-sented for a bubble radius of 50 nm. If the radius ofthe NB decreases, the amount of H O in the final stateincreases. c. Molecular dynamics simulation Independentlythe surface-assisted combustion has been analysed [44]using the reactive molecular dynamics simulation. Tosimplify the calculations a cubic volume filled with thegases was considered instead of a sphere, but the ex-
FIG. 3. (a) Scheme of the spontaneous ignition of the com-bustion in a NB with charged interface. It is assumed thatmolecules approaching the reaction center at the interfaceare able to produce radicals. (b) Solution of the equationsof chemical kinetics for long-lived species in the process ofsurface-assisted (cold) combustion. (c) The same for short-lived radicals. All concentrations are shown with respect tothe initial gas concentration. tra pressure in this volume was introduced to accountfor the Laplace pressure. The method used avoids therestrictions of continuous media approach; it does notneed such parameters as heat diffusion rates, bi andtri-molecular reaction rates, and pressure in the bubblewhich are not always known. Generation of radicals onthe walls was modeled inserting a certain number of rad-icals near the walls or inserting the radicals periodically.The main conclusions of Ref. [42] were confirmed quali-tatively. The quantitative agreement cannot be expectedsince the chemical kinetics describes the system on a rel-atively long timescale up to 1 µ s while the moleculardynamics can describe the system on a timescale shorterthan 0 . ◦ C needed for standard combustion but it can be ashigh as 100 ◦ C. It does not contradict to the statement[42] that temperature in NBs is close to room tempera-ture. The temperature in the bubble is equalized during t ∼ r /χ g ∼ χ g ∼ − m /s is the heatdiffusion coefficient in gas. This time cannot be reachedby the molecular dynamics. It was confirmed also thatthe final products contain a significant amount of hydro-gen peroxide. It was stressed that for the surface-assistedcombustion the main intermediate product is HO whilefor the normal combustion the most important interme-diate product is OH radicals. Important role of HO canalso be seen in Fig. 3(c).Summarizing the current understanding of the mecha-nism of the reactions in NBs we can separate the follow-ing 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 generatedat the gas-liquid interface, then there is a chain of elemen-tary reactions that transforms stoichiometric mixture ofH and O gases into water and hydrogen peroxide. (iii)Generation of H radicals is assumed to be related to thecharges at the gas-liquid interface but the precise mech-anism is still unknown. IV. COMBUSTION IN MICROBUBBLES
The main conclusion from the previous section is thatthe surface-assisted combustion can be realised only fora high surface-to-volume ratio. All the more surprisingthat the combustion was observed in MBs produced atspecial conditions by the AP process [45]. To investi-gate this phenomenon in detail the concentric electrodesshown in Fig. 4(a) were used [46]. For such electrodesthe NBs are well concentrated between the electrodes. a. Experimental facts
With the increase of the am-plitude of the pulses more and more NBs are generated inthe AP process. When the concentration of NBs reachesa 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 witha clearly audible ’click’ sound. The clicks are repeatedwith a frequency of 12 Hz. The sound consists of twosources separated by a time interval of 300 µ s as onecan see in the right side of (b). Synchronously with thesound the current in the system decreases in just 20 µ s(c) and stays low during 300 µ s. Absence of a sharp in-crease in the current together with insufficient electricalfield demonstrate that the phenomenon cannot be relatedto the electrical breakdown. Observation of the processwith a fast camera demonstrates that synchronously withthe current decrease a MB with an initial size of 150 µ mappears above the electrodes, grows to a maximum sizeof 1200 µ m in 200 µ 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. Reductionof the current is explained by the growing bubble, whichoverlaps the electrodes in 20 µ s.For understanding of the phenomenon it is importantthat there are two sources of the sound accompanying FIG. 4. Explosion of a microbubble. (a) The sample fixedin small Petri dish filled with Na SO solution and zoomedview of Ti concentric electrodes. (b) Electrodes just beforethe explosion. The cloud of NBs is so dense that it scattersslightly the visible light. Right side shows the sound ampli-tude that demonstrates two sources of the sound. (c) Currentbetween the electrodes drops synchronously with the growingMB. The AP process is at U = 14 V and f = 500 kHz. Blackcircles show positions of the frames in the fast video. (d) TheMB in its maximum size observed from the top. (e) The sameas (d) but viewed from the side. the process. The first sound appears together with thedecrease of the current and when the current starts torestore the second more powerful sound emerges. Thesecond sound appears in the moment when the bubblereaches its minimum value and can be explained by thecavitation effect. From the fast video one can find thetime dependence of the bubble radius as shown in Fig. 5(right). In this dependence one can resolve the secondbump that is a characteristic feature of cavitation. More-over, after many clicks the silicon sample with the de-posited Ti electrodes is destroyed locally very similar tothat produced by cavitating bubbles (Figure S1 in [46]).The first sound one can relate to the explosion in the initial bubble. It starts synchronously with the currentdecrease and obviously is related to the expanding MB.The expansion rate estimated from the fast video is about8 m/s. This rate is in agreement with a typical velocityof the burning front for normal combustion. However,the observed process cannot be induced by normal com-bustion because the heat escapes from the bubble witha radius of 75 µ m too fast ( t ∼
10 ns) to support nor-mal combustion. A special experiment was performedto check the possibility of spontaneous combustion of H and O mixture in MBs. The stoichiometric mixture ofgases was pumped into the gas channel of a microfludicbubble generator. The MBs with a diameter of 10 µ mmoving in water one by one was observed in the out-put channel. No spontaneous combustion in these bub-bles was observed [45]. It seems that the surface-assistedcombustion also cannot explain the phenomenon of ex-panding MB because the S/V ratio in Eq. (3) is threeorders of magnitude smaller than that for NBs. b. Role of nanodrops
Nevertheless, the process hasbeen interpreted [46] as the surface-assisted combustionin MBs. The main steps of this process are shownschematically in Fig. 5. As was already mentioned, whenthe amplitude of the pulses increases, the NBs approachvery close to each other and the density of the cloud ap-proaches the critical value. This value corresponds to theclose packing of spheres and is equal n NB ≈ × m − for r = 40 nm.The cloud consists of H and O NBs. When two simi-lar bubbles are close to each other, there is no significantdiffusion of gases since the concentration gradient is low.However, when two bubbles with different gases meet,fast exchange by the gases occurs. The minimum dis-tance between the bubbles is defined by the disjoiningpressure in the separating membrane with the thickness d ∼ t ∼ d /D l ∼ D l ∼ − m /s isthe diffusion coefficient of gas in liquid. It means thatthe cloud of NBs with the critical density will be trans-formed to a MB containing mixture of H and O gases.However, the volume filled with the close-packed NBs hasthe volume fraction of gas f = 0 .
74 and the rest is liq-uid. After merging of NBs this liquid will be collected innanodrops with the radius r (cid:48) = r [(1 − f ) /f ] / .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 (cid:48) ∼ /r . Thisratio is nearly as high as that for the NBs and for thisreason it is able to support the surface-assisted reactions.These reactions can proceed in the same way as it was de-scribed in Sec. III. On a timescale of 10 ns hydrogen andoxygen in the MB will turn into water vapor (final MB).In spite of a large size of the MB the thermal equilibriumin the final MB is established on the same timescale asfor NBs t ∼ l = r (4 π/ f ) / ∼ r .Therefore, the final MB has well-defined pressure and FIG. 5. (Left) Scheme explaining formation of the MB and chemical reaction happening in the bubble. (Right) Evolution ofthe final MB observed with the fast camera with an interval between the frames of 13 . µ s. temperature, which determine the following evolution ofthe bubble directly observed in the experiment. This evo-lution is much more slow (the time scale t > µ s) and,in principle, can be described by the Rayleigh–Plessetequation [47] with the accurate inclusion of the heat ex-change effects between the MB and surrounding liquid.Therefore, the final MB is in the state, in which the bub-ble has not yet expanded, but the chemical reaction isalready over and the steam–liquid equilibrium is estab-lished. c. State in the exploding MB Owing to the thermalequilibrium it is possible to find the pressure P f and tem-perature T f in the final MB using only the energy bal-ance equation [46]. The internal energy of the initial MBplus the energy produced by the reaction are spent onthe energies of the gas phase, liquid phase, and partialvaporization of nanodrops in the final MB. The effect ofsurface tension in the balance is insignificant. Since thegas and liquid phases in the final MB are in equilibrium,the pressure in the bubble is defined by the tempera-ture P f = P eq ( T f ), where the function P eq ( T ) and otherthermodynamic values were taken from the vapor-liquidequilibrium tables [48]. The resulting value depends onthe size of merging NBs. For r = 30 nm it was foundthat T f = 220 . ◦ C and P f = 23 . r = 40 nmthese parameters are T f = 185 . ◦ C and P f = 11 . P f (cid:29) P a and this pressure jumpis the source of the first sound shown in Fig. 4(b). Thetemperature in the final MB is higher than that found forNBs [44], but it is still not enough for the spontaneousignition of the normal combustion.Summarizing combustion in MBs one can stress the fol-lowing. (i) The process is observed only for MBs formedfrom a cloud of NBs produced in the AP process; no re- actions happen in the MBs filled with H and O gasestaken from external sources. (ii) Explosion of the ini-tial MB is accompanied by the sound of explosion andafter a delay of 300 µ s by the sound of cavitation. (iii)Nanodrops that left in the MB after merging of manyNBs provide the surface-to-volume ratio as high as ina separate NB and ensure conditions for the surface-assisted combustion. (iv) The final MB immediately af-ter the chemical reaction is characterized by the pressure P f = 10 −
20 bar and the temperature T f ≈ ◦ C; highpressure 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 APprocess are the same as those produced by the regularmethods. Short lifetime of the bubbles generated in theAP process is explained by the interaction between H and O NBs. However, if we menage to separate hydro-gen and oxygen NBs, for example by diluting the solu-tion, would they live much longer? A recent paper [49]relates stability of the regular NBs to their origin. It isassumed that long-lived NBs appear only from shrink-ing MBs and their stability is related to the increasingconcentration of the surface charges. The answer to theabove question will be a critical test for this hypothesisbecause only NBs are produced in the AP process.It is not clear why only NBs are generated by the APpulses. We know that very high supersaturation supportshomogeneous nucleation of NBs, but for some reasonthese bubbles do not grow or merge easily. It is expectedthat such processes are controlled by the surface chargesand opposite charges distributed in the electrolyte. How-ever, these effects have never been analysed in depth.Although the surface-assisted combustion is able togive a basic explanation of the reactions in NBs and inMBs, generation of radicals on the gas-liquid interface isthe most important open question. Direct evidence forthe presence of the radicals is still lacking. It could beobtained using the electron spin resonance spectroscopyor using different radical scavengers in the solution. It isalso possible that generation of OH radicals in the regu-lar NBs and H (O) radicals in NBs produced by the APprocess are related effects. In this respect it is interest-ing to consider a reaction path for ’cold’ combustion viaOH radicals generated on the surface instead of H or Oradicals as in [42].Dynamics of exploding MB was determined experimen-tally. On the other hand, the evolution of exploding NBalso has a special interest. Recently it was demonstrated[50] that a flux of H and O NBs directed to a Pt plateis able to produce Pt nanoparticles that is a high energyprocess. Understanding of the dynamics of explodingNBs can shed light on the observed phenomena.
VI. CONCLUSIONS
In this paper we presented the current status and un-derstanding of the phenomena observed during genera-tion of NBs by short alternating polarity voltage pulses.In contrast with the regular methods no bubbles largerthan 200 nm are produced by the AP method. The con-centration of NBs is so high that one can easily observecollective optical effects produced by these NBs. Sincehigh supersaturation with both H and O gases is gen-erated above the same electrode, three types of NBs canbe produced: those containing H , O , and mixture ofthe gases.The most important difference from the regular NBs is that inside of one NB hydrogen and oxygen are able toreact with each other in spite of the expectations fromthe classical combustion theory. It is clear demonstratedby a series of experimental facts such as pressure oscilla-tion in a closed volume with the frequency of the drivingpulses, fast relaxation of the pressure after switching offthe pulses, heat produced by the reactions, and others.A possible mechanism of the combustion reactions ina small volume relies on a very high surface-to-volumeratio characterizing NBs. It assumes generation of freeradicals on the gas-solid interface presumably due to thecharges known to be adsorbed on the interface. With thisassumption the chain of ’cold’ reactions exists, which isable to transform mixture of hydrogen and oxygen intowater without necessity of high temperature. However,the exact mechanism of the radical formation at the in-terface is still unknown.At special conditions combustion of the gases is ob-served in MBs that is accompanied by audible clicks,by significant expansion of the bubble followed by thecavitation. It seems that the combustion in MB cannotbe described by the surface-assisted mechanism becauseMBs are characterized much smaller surface-to-volumeratio. However, as described in the paper a MB formedby merging of many NBs contains nanodrops so that thetotal surface-to-volume ratio is of the same order as forNBs. Theoretical estimates of the pressure and temper-ature in the MB immediately after the reaction showthat the sound and expansion are produced by a pres-sure jump of 10 −
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