Acta Polytechnica doi:10.14311/AP.2018.58.0323 Acta Polytechnica 58(5):323–333, 2018 © Czech Technical University in Prague, 2018 available online at http://ojs.cvut.cz/ojs/index.php/ap THE TIME DIFFERENCE IN EMISSION OF LIGHT AND PRESSURE PULSES FROM OSCILLATING BUBBLES Karel Vokurka Physics Department, Technical University of Liberec, Studentská 2, 461 17 Liberec, Czech Republic correspondence: karel.vokurka@tul.cz Abstract. Oscillations of spark-generated bubbles are studied experimentally. In this work, an attention is paid to the time difference in the radiation of light flashes and pressure pulses from a bubble at the final stages of the first bubble contraction and the early stages of the first bubble expansion. It is found that light and pressure pulses are not radiated synchronously. In some experiments, the light flashes are radiated before the pressure pulses by a few µs and in other experiments, the light flashes are radiated later than the pressure pulses by a few µs. The time difference in the radiation of the two pulses is examined in detail in relation with the bubble size, bubble oscillation intensity, maximum value of the light flash and the width of the light flash. It is shown that the magnitude of the time differences is very weakly correlated with the bubble size, intensity of oscillation and intensity of the light flashes and that the magnitude of the time differences is only moderately correlated with the light flashes widths. Keywords: spark-generated bubbles; light emission; bubble oscillations. 1. Introduction Bubble oscillations have long been an important topic in fluid dynamics. While they have traditionally been studied in connection with erosion damage [1], re- cent efforts have been aimed at medical applications such as contrast-enhancing in ultrasonic imaging [2– 7]. Physical processes in oscillating bubbles are very complex and so far many points in this field have not yet been clarified. One of these points that is not well understood is the emission of light from bubbles. And this phenomenon will be discussed in this work. In experiments, oscillating bubbles are generated using a wide variety of techniques. These techniques encompass, e.g. laser beam focusing in the liquid [8– 10], spark discharge in liquid [11–15], multiple bub- bles oscillating in ultrasonic fields [16], hydrodynamic cavitation in the liquid flow [17, 18], and shock in- duced bubble oscillations [19]. All these techniques are also used in studies of the light emission from bubbles [9, 11, 13–19]. During the last thirty years, the light emission from oscillating bubbles has also been intensively studied in a number of laboratories using acoustic resonators. A recent review of papers published in this area [20] mentions 309 references. Although this review concen- trates on the light emission from bubbles oscillating in acoustic resonators, it also includes papers deal- ing with the light emission from bubbles generated during acoustic cavitation. Papers dealing with the light emission from bubbles generated during hydrody- namic cavitation and from laser- and spark-generated bubbles are not included in this review. In this work, the emission of light from large spark- generated bubbles freely oscillating in water far from boundaries is studied. An obvious advantage of large bubbles is that the optical and acoustic radiation from them can be recorded more easily than in the case of smaller bubbles. This is because, in large oscillating bubbles, physical processes are taking place more slowly. The light emitted by large bubbles is also sufficiently intensive so that averaging on light pulses from different experiments, which is always accompanied by a loss of natural variety (e.g., in pulse shape), is not necessary. The technique of low voltage spark discharges makes it also possible to generate bubbles of different sizes and oscillating with different intensities [21], which further enhances the data analysis. In this work, the time difference in radiation of the optical and acoustic pulses at the first bubble con- traction and at the following first bubble expansion is studied. It will be shown that the instants, when the maxima in the optical pulses and pressure pulses are radiated, may differ by a few µs. In some ex- periments, the maxima in optical pulses are radiated earlier than the peaks in the pressure pulses, and in some experiments, the maxima of the optical pulses are radiated later than the pressure peaks. This phe- nomenon has also been observed by Golubnichiy et al. [11], Huang et al. [13] and Zhang et al. [14]. Re- sults discussed here have been presented in a brief form at conferences [22, 23]. 2. Experimental setup The experimental setup used in this work is schemat- ically shown in Figure 1. Freely oscillating bubbles were generated by discharging a capacitor bank via a sparker submerged in a laboratory water tank hav- ing dimensions of 6 m (length)×4 m (width)×5.5 m 323 http://dx.doi.org/10.14311/AP.2018.58.0323 http://ojs.cvut.cz/ojs/index.php/ap Karel Vokurka Acta Polytechnica Figure 1. Experimental setup used to generate oscillating bubbles and to record the optical and acoustic radiation from them (abbreviations in the figure: DAQ – data acquisition board, hv – additional high voltage used to trigger the air gap). (depth). The experiments were performed in tap wa- ter at a constant hydrostatic pressure p∞ = 125 kPa, at a room temperature Θ∞ = 292 K, and far from any boundaries. The capacitance of the capacitor bank could be varied in steps by connecting 1 to 10 capacitors in parallel. Each of these capacitors had a capacitance of 16 µF. The capacitors were charged from a high voltage source of 4 kV. An air-gap switch was used to trigger the discharge through the sparker. Earlier measurements [24] have shown that the current flowing through the discharge circuit has the form of a highly damped sinusoid and depending on the total bank capacity, it drops to zero in 0.3–0.7 ms after the liquid breakdown. A more detailed description of the experimental setup is given in an earlier work [24]. Both the spark discharge and the subsequent bubble oscillations were accompanied by an intensive optical radiation and acoustic radiation. The optical radia- tion was monitored by a detector, which consisted of a fiber optic cable, a photodiode, an amplifier, and an A/D converter. The input surface of the fiber optic cable was positioned in water at the same level as the sparker at a distance r = 0.2 m aside, pointing perpendicularly to the sparker gap and the electrodes. At the output surface of the fiber optic cable, a Ham- mamatsu photodiode type S2386-18L was positioned. The usable spectral range of the photodiode is 320 nm to 1100 nm. An analysis of the optical spectra given in the literature showed that the maximum tempera- tures in spark-generated and laser-generated bubbles range from 5800 K to 8150 K [9, 14]. Then, using the Wien and Planck law, it can be verified that the spectral maxima of the optic radiation are within the photodiode band-pass and that the prevailing part of the radiation is received by the detector. The load resistance of the photodiode was 75 Ω, so the rise time of the measured pulses is about 50 ns. A broadband amplifier (0–10 MHz) was connected to the photo- diode output terminals. The output voltage from the amplifier was recorded using a data acquisition board (National Instruments PCI 6115, 12 bit A/D converter) with a sampling frequency of 10 MHz. The presented optical data are referring to the photodiode output. The acoustic radiation was monitored using a Re- son broadband hydrophone type TC 4034. The hy- drophone was positioned with the sensitive element at the same depth as the sparker. The distance between the hydrophone acoustic centre and the sparker gap was rh = 0.2 m. The output of the hydrophone was connected via a divider 10:1 to the second channel of the A/D converter. In the experiments, a large number of almost spher- ical bubbles freely oscillating in a large expanse of liquid were successively generated. The sizes of these bubbles, as described by the first maximum radius RM1, ranged from 18.5 mm to 56.5 mm, and the bub- ble oscillation intensity, as described by the non- dimensional peak pressure in the first acoustic pulse pzp1 = (pp1rh)/(p∞RM1) ranged from 24 to 153 [21]. Here, pp1 is the peak pressure in the first acoustic pulse p1(t). The non-dimensional quantity pzp1 can be best interpreted by multiplying it by the hydrostatic pres- sure p∞. Then it represents the peak acoustic pressure pp1 in the first acoustic pulse p1(t) measured at a dis- tance rh = RM1. Both RM1 and pzp1 were determined 324 vol. 58 no. 5/2018 The Time Difference in Emission of Light and Pressure Pulses in each experiment from the respective pressure record using an iterative procedure described in detail in [21]. This iterative procedure is an extension of the well- known Rayleigh’s formula for the “collapse time” of a bubble having a size RM1. The Rayleigh formula is commonly used in studies of spark and laser gen- erated bubbles (see, e.g. [1, 9]). It has been verified experimentally many times that for bubbles oscillat- ing sufficiently intensively, it gives satisfactory results. However, for bubbles oscillating with lower intensity, it gives less precise values. The iterative procedure is thus extending this approach to any oscillation inten- sity. Prior to the measurements reported here, a limited number of high-speed camera records were taken with framing rates ranging from 2800 to 3000 frames/s. These records were used to check the shape of the gen- erated bubbles and the photographs yielded also useful visual information on the bubble content. Examples of the photographs of the spark-generated bubbles taken by the high-speed camera at different instants of their life and the experimentally determined variations of the bubble radius R with time t were given in earlier works [21, 25]. 3. Results Let us assume that at a time t0, the liquid breakdown initiates a spark-discharge. Thus at the instant t0, the bubble starts growing explosively and radiating light (optical) and pressure (acoustic) waves inten- sively. The instant t0 thus represents the beginning of all the physical processes considered here. The bubble wall motion is oscillatory. At a time t1, the explosively growing spherical bubble attains its first maximum volume (a sphere of radius RM1). Then the bubble starts contracting and at a time tc1, it attains its first minimum volume (a sphere of radius Rm1). Then the bubble starts expanding again and at a time t2, it attains its second maximum volume (a sphere of ra- dius RM2). After time t2, the bubble performs several further oscillations. However, these are already out of scope of the present work. The interval (t0, t1) repre- sents the growth phase, the interval (t1, tc1) the first contraction phase and the interval (tc1, t2) the first expansion phase. The interval (t0, tc1) represents the time of the first bubble oscillation To1. In this work, we shall concentrate on the processes taking place in a very short interval encompassing the final stages of the bubble contraction and the early stages of the bubble expansion. To abbreviate the description of this interval, a term “subinterval in the vicinity of the minimum bubble volume” (shortly “subinterval MBV”) will be used in the following. This subinterval is centred on the instant tc1, when the bubble is com- pressed to its first minimum volume and the extent of this subinterval is about 0.5 % of the time of the first bubble oscillation To1. As already said in Section 2, both the spark dis- charge and the subsequent bubble oscillations are accompanied by an intensive optical radiation and acoustic radiation. An example of an optical record, represented by the voltage u(t) at the output of the optical detector, is given in Figure 2. As can be seen, the voltage u(t) consists of two pulses. First, it is a pulse u0(t) that corresponds to the optical radia- tion from the bubble during the growth phase (t0, t1). Second, it is a pulse u1(t) that represents the optical radiation from the bubble during the first contraction phase and the first expansion phase that is in the interval (t1, t2). In this work, only the pulse u1(t) will be considered, and therefore the pulse u0(t) is shown clipped in Figure 2. The maximum value of the pulse u1(t) is denoted as uM1 and the time of its occurrence is denoted as tu1. An example of an acoustic record p(t) is given in Figure 3. The pressure wave has been measured at a distance from the bubble center rh = 0.2 m and recalculated to the nominal distance rn = 1 m. As can be seen, the pressure wave also consists of several pulses. First, it is a pressure pulse p0(t) radiated by the bubble during the growth phase (t0, t1). Second, it is a pressure pulse p1(t) radiated by the bubble during the first contraction phase and the first expansion phase that is in the interval (t1, t2). The peak value of the pulse p1(t) is denoted as pp1 and the time of its occurrence is denoted as tp1. Further pressure pulse p2(t) can also be seen in Figure 3. However, this pulse will not be considered in this work. The pressure wave propagates from the bubble wall to the hydrophone at a distance rh = 0.2 m at the speed of sound in water c = 1482 m/s and thus the instants t0, t1, tp1, and t2 in the pressure record are delayed by about 135 µs after the instants t0, t1, tc1, and t2 defined above for the bubble wall motion. How- ever, to simplify the discussion the propagation time of the pressure wave in water is not considered here and it will be assumed that the instants t0 defined above for the beginning of the bubble wall motion, optical radiation, and acoustic radiation are identical, even if the hydrophone is at the distance rh. From the above discussion, it is evident that an accurate determination of the instants t0 in the optical and acoustic records is crucial in this work. The instants t0 are defined as the points in the records at which the pulses u0(t) and p0(t) start rising steeply from an undisturbed level. Small portions of the optical and acoustic pulses u0(t) and p0(t) extracted from the records at the vicinity of t0 are displayed together in Figure 4. It can be seen that the instant t0 can be determined relatively accurately. The precision of the determination of t0 is given by the sampling interval dt = 1/fs = 0.1 µs. The instants t0 have been defined as the starting points of the recorded waves u(t) and p(t). In the fol- lowing, the instants t0 in both waves will be assumed to be identical, that is, the propagation time of the pressure wave will be ignored, or, which is the same, it will be assumed that the pressure wave propagates 325 Karel Vokurka Acta Polytechnica 0 2 4 6 8 10 12 −1 −0.5 0 0.5 1 1.5 2 2.5 3 t [ ms ] u (t ) [ m V ] u 0 (t) u 1 (t) t u1 t 1 t 0 t 2 u M1 Figure 2. An example of a radiated optical wave u(t). The bubble size is RM1 = 49 mm, the intensity of bubble oscillation is pzp1 = 142.1. with the speed of light. Then, both waveforms can be displayed together in one figure with an identical starting point t0 on the time axis. And in this way, both waveforms can easily be mutually compared (see also Figure 4). Because in this work, we are interested in comparison of the optical and acoustic radiations from the bubble at the subinterval MBV, only small portions of the pulses u1(t) and p1(t) extracted from the records in the vicinity of the instants tu1 and tp1 will be considered in the following discussion. Examples of the pulses u1(t) and p1(t) recorded in two different experiments are shown in Figures 5 and 6. In these figures, the time origins have been set at the instants tp1 and the sizes of the waveforms u1(t) have been adjusted by using arbitrary units so that the shapes of both waveforms can be compared easily. And as said above, the instants t0 of both waves are identical on the time axis. It can be seen in Figures 5 and 6 that the shapes of the pulses u1(t) and p1(t) differ, and that the times tu1 and tp1 are not identical. The difference in shapes of the pulses u1(t) and p1(t) is evidently connected with the autonomous behaviour of plasma in the bubble interior, already discussed in [25–27]. The difference in times tu1 and tp1 has not been discussed yet and the existence of this time difference is a surprising fact because a “reasonable” assumption is that the maxima in optical and acoustic radiations will oc- cur at the same instant tc1, when the bubble is con- tracted to the first minimum volume. Even if this has not yet been verified experimentally, it seems highly probable that the instants tc1 and tp1 are identical. However, this assumption then means that the max- imum in the optical radiation is not firmly tied to the instant of the bubble maximum contraction tc1, but can occur a bit earlier (Figure 5), or a bit later (Figure 6). In Figures 5 and 6 the time difference between the instants tp1 and tu1 has been denoted as δ1 and this quantity is defined by the relation δ1 = tu1 − tp1. As shown in Figures 5 and 6 the time difference δ1 can have both a positive and a negative value. As said in Section 2, the spark-generated bubble is described by two parameters, by its size RM1 and oscillation intensity pzp1. It is convenient to charac- terise the optical pulse u1(t) by two parameters as well [26]. First, it is the maximum value of the pulse uM1. Second, it is the pulse width ∆ at one-half of the maximum value (that is at uM1/2). Thus defined pulse widths ∆ are shown in Figures 5 and 6. In the following, the dependence of the time differences δ1 on these four parameters, that is on RM1, pzp1, uM1 and ∆, will be shown and discussed. The variation of the time difference δ1 with the bubble size RM1 determined on a larger set of exper- imental data is shown in Figure 7. The regression line for the mean value of the time difference δ1 in dependence on RM1 is 〈δ1〉 = −0.2RM1 + 5.9 [µs, mm]. It can be seen in Figure 7 that the time difference δ1 is correlated with the bubble size RM1 only very weakly and that the dispersion of the time differences δ1 grows with the bubble size RM1. 326 vol. 58 no. 5/2018 The Time Difference in Emission of Light and Pressure Pulses 0 2 4 6 8 10 12 −200 0 200 400 600 800 1000 1200 t [ ms ] p (t ) @ r n = 1 m [ k P a ] t 1 p 0 (t) t p1 p p1 t 0 p 1 (t) p 2 (t) t 2 Figure 3. An example of a radiated pressure wave p(t). The bubble size is RM1 = 49 mm, the intensity of bubble oscillation is pzp1 = 142.1. −4 −3 −2 −1 0 1 2 −4 −2 0 2 4 6 8 10 12 14 t [ μs ] p 0 (t ) [ a .u . ], u 0 (t ) [ a .u . ] u 0 (t) t 0 p 0 (t) Figure 4. An example of voltage and pressure pulses u0(t) and p0(t) in the vicinity of the instant t0. The bubble size is RM1 = 49 mm, the intensity of bubble oscillation is pzp1 = 142.1. 327 Karel Vokurka Acta Polytechnica −100 −80 −60 −40 −20 0 20 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 t [ µs ] p 1 (t ) [ M P a ] , u 1( t) [ a .u . ] ∆ p 1 (t) u 1 (t) t p1 t u1 δ 1 Figure 5. An example of optical and pressure waves in the vicinity of instants tu1 and tp1. The bubble size is RM1 = 38.1 mm, the intensity of bubble oscillation is pzp1 = 107, the hydrophone was at a distance rh = 0.2 m, the optical pulse width is ∆ = 57.9 µs, and the time difference in occurrence of the maxima in both pulses is δ1 = −12.7 µs. −100 −80 −60 −40 −20 0 20 0 1 2 3 4 5 t [ µs ] p 1 (t ) [ M P a ] , u 1( t) [ a .u . ] t p1 t u1 u 1 (t) p 1 (t) δ 1 ∆ Figure 6. An example of optical and pressure waves in the vicinity of instants tu1 and tp1. The bubble size is RM1 = 49 mm, the intensity of bubble oscillation is pzp1 = 142.1, the hydrophone was at a distance rh = 0.2 m, the optical pulse width is ∆ = 9.4 µs, and the time difference in occurrence of the maxima in both pulses is δ1 = 2.6 µs. The waveforms displayed in Figures 2, 3, 4 and 6 were recorded in the same experiment. If the records shown in Figures 2 and 3 are aligned as it is done in Figure 4, the overlapping records shown in Figure 6 are obtained. 328 vol. 58 no. 5/2018 The Time Difference in Emission of Light and Pressure Pulses 10 20 30 40 50 60 −15 −10 −5 0 5 R M1 [ mm ] δ 1 [ µ s ] Figure 7. The variation of the time difference δ1 with the bubble size RM1. 40 60 80 100 120 140 160 −15 −10 −5 0 5 p zp1 [ − ] δ 1 [ µ s ] Figure 8. The variation of the time difference δ1 with the bubble oscillation intensity pzp1. 329 Karel Vokurka Acta Polytechnica 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 −15 −10 −5 0 5 u M1 [ mV ] δ 1 [ µ s ] Figure 9. The variation of the time difference δ1 with the maximum voltage uM1. Bubble sizes: (◦) RM1 > 50 mm, (×) 50 mm ≥ RM1 > 40 mm, (+) 40 mm ≥ RM1 > 30 mm, (∗) 30 mm ≥ RM1 > 20 mm, (·) 20 mm ≥ RM1. 0 20 40 60 80 100 120 −15 −10 −5 0 5 ∆ [ µs ] δ 1 [ µ s ] Figure 10. The variation of the time difference δ1 with the pulse width ∆. Bubble sizes: (◦) RM1 > 50 mm, (×) 50 mm ≥ RM1 > 40 mm, (+) 40 mm ≥ RM1 > 30 mm, (∗) 30 mm ≥ RM1 > 20 mm, (·) 20 mm ≥ RM1. 330 vol. 58 no. 5/2018 The Time Difference in Emission of Light and Pressure Pulses The variation of the time difference δ1 with the bub- ble oscillation intensity pzp1 is shown in Figure 8. The regression line for the mean value of the time difference δ1 in dependence on pzp1 is 〈δ1〉 = 0.07pzp1−10.3 [µs, – ]. It can be seen that the time difference δ1 is very weakly correlated with the bubble oscillation inten- sity pzp1 and that is another proof of the autonomous behaviour of plasma in the bubble interior that has already been observed earlier in works [25–27]. As discussed in [25–27], this autonomous behaviour man- ifests itself in the relatively large independence of the light radiation from the plasma surface on the pressure at the bubble wall. The variation of the time difference δ1 with the maximum voltage in the optical pulse uM1 (and thus with the maximum intensity of the light radiated by the bubble) is shown in Figure 9. The regression line for the mean value of the time difference δ1 in dependence on uM1 is 〈δ1〉 = −5.9uM1 −1.03 [µs, mV]. It can be seen again that the time difference δ1 is weakly correlated with the maximum voltage in the optical pulse uM1. However, the dependence of the time difference δ1 on the bubble size RM1, already observed in Figure 7, can also be seen in Figure 9. The variation of the time difference δ1 with the pulse width ∆ is shown in Figure 10. The regression line for the mean value of the time difference δ1 in dependence on ∆ is 〈δ1〉 = −0.17∆ + 1.3 [µs, µs]. It can be seen that now, the time difference δ1 is moderately correlated with the optical pulse width ∆. For broader optical pulses u1(t) (that is for light flashes with larger widths ∆), the time difference δ1 is negative, which means that the light flashes are radiated before the pressure pulses p1(t) (and thus also before the bubble contraction to Rm1). However, for narrower optical pulses u1(t) (that is, for light flashes with smaller widths ∆), the time difference δ1 is positive, which means that the optical pulses are radiated later than the pressure pulses p1(t) (and thus are also radiated after the instant tc1, when the bubble volume is contracted to Rm1). The dependence of δ1 on the bubble size RM1 can also be observed. For larger bubbles, the time difference δ1 is predominantly negative, for smaller bubbles, the time difference δ1 can be both positive and negative (cf. also Figure 7). 4. Discussion When comparing the instants of occurrence of the max- ima in the first optical pulse and in the first acoustic pulse, it can be seen that the times tu1 and tp1 may differ by a few µs, in some experiments, the maxima of the optical radiation are radiated earlier than the peaks in the pressure pulses (an example of this case is given in Figure 5) and in some experiments, the maxima in optical radiation are radiated later than the peaks in pressure pulses (an example of this case is given in Figure 6). As can be seen in Figures 7–10, the occurrence of the optical maxima before the pres- sure maxima is prevailing. However, occurrence of the optical maxima after the pressure maxima can also be seen, but it is not so frequent and occurs predom- inantly for smaller bubbles and for more intensively oscillating bubbles. The time differences δ1 between these maxima are very small when compared with the times of the first bubble oscillations To1, the ratio δ1/To1 is of the order 10−3 typically. Due to this small magnitude, it is difficult to observe the time differences δ1 when studying smaller bubbles such as those oscillating in acoustic resonators. At present, there is no explanation for the existence of the time differences δ1. But their presence further confirms the earlier findings concerning the autonomous plasma behaviour in bubbles [25, 26]. As shown in Figures 7– 10, the time difference δ1 may be of both positive and negative values and these values are only very weakly correlated with the bubble size RM1, intensity of bub- ble oscillation pzp1, and maximum values of the optical radiation uM1. The time difference δ1 is moderately correlated only with the optical pulse widths ∆. As can be seen in Figure 10, it grows with ∆. For large bubbles and for large ∆, the time differences δ1 are of negative values, and thus the maxima uM1 always occur before the peaks pp1. The time difference δ1 can be of positive values, and thus the maxima uM1 can be delayed behind the peaks pp1, only for small bubbles and small optical pulse widths ∆. The time difference between tu1 and tp1 has also been observed by Golubnichiy et al. [11], Huang et al. [13] and Zhang et al. [14]. In these experiments, the time difference δ1 was negative (that is, the optical pulse occurred earlier than the pressure pulse). Varia- tion of the time difference δ1 with bubble parameters and optical pulse parameters has not been studied in [11, 13, 14]. For the analysis carried out in this and in previous works [25, 26], the measurement of pressure waves radiated by oscillating bubbles is essential. However, in the review paper by Crum [20], there are only 2 papers mentioned in which pressure waves radiated by oscillating bubbles were recorded [20, Section VIII, Subsection L]). And even in these 2 papers, the pres- sure waves were not used for a more detailed analysis. Therefore, it is not surprising that in the works in- cluded in the above review, no findings similar to those presented here and in our earlier works [25, 26] were mentioned. In the review [20], altogether 40 various theoretical models trying to clarify the ori- gins of the light emission from bubbles are also sum- marized [20, Section VI, Subsections A, B, C, and Section VIII, Subsection E]). An interested reader may find the full bibliographical data of these pa- pers and short summaries of the main results given in these works in the review. The presented theories include the hot spot model, electro-hydrodynamic hy- pothesis, re-entrant jet impacting the opposite bubble wall, electron-neutral atom-Bremsstrahlung, proton- tunnelling radiation, Becquerel effect and quantum vacuum radiation, just to name some of the hypothesis 331 Karel Vokurka Acta Polytechnica given in the review. However, the conclusion that can be made from the review is that none of these theo- retical models has been verified experimentally and none has been accepted by the research community as a definitive valid clarification of the processes taking place in bubbles that are leading to the light emis- sion. And, unfortunately, none of these theoretical models can also explain the facts observed when study- ing the light radiation from spark-generated bubbles, that is, none can explain the persisting light emission during the whole first bubble oscillation, relatively autonomous behaviour of the plasma in the bubble interior and the differences in instants of the radiation of light and pressure pulses. In view of the fact that at present, there is no suit- able theoretical explanation for the observed phenom- ena, at the end of this Section, we would like to draw an attention to the results published by researchers studying plasmoids generated by electrical discharges in wet air [28–33]. The aim of those works is to sim- ulate the ball lightning, also known as fireballs. The electrical discharges in wet air are performed with volt- ages and capacitor banks roughly similar to those used in this work, i.e. the voltages are about 5 kV and the capacitor banks have a capacitance about 1 mF. The generated plasmoids usually have an almost spherical form and live for about 0.5–1 s. The main conclusions of these works can be summarized as follows [33]: the plasmoid consists of a hot core surrounded by cool shell, possessing a translational temperature of about 600–1300 K, an electron temperature of 2000–5000 K and a rotational temperature of about 15000 K and is displacing air with a warm, partially ionized water- aerosol produced by the discharge. And, according to authors of work [33], this conclusion is consistent with the ball-lightning models proposed by Shevkunov [34– 36], where a cation – anion recombination is inhibited by many orders of magnitude by the clustering of water around ion atomic and molecular ion cores. We believe that the strange behaviour of plasma in the spark-generated bubbles can be best compared with these results. Of course, the plasmoids that are stud- ied in [28–33] are generated under other conditions than is the case of plasma in spark-generated bubbles. However, the research of plasmoids most likely shows the way that should be followed in studies of the light emission from spark-generated bubbles. 5. Conclusions When analysing the experimental data, it was found that there is no exact coincidence in the radiation of the light flashes and pressure pulses from the spark- generated bubbles at the final stages of their first contraction and early stages of their first expansion (that is, in the subinterval MBV). The time difference between the maxima of the two pulses is only a few µs and is, therefore, about three orders smaller than the time of the first bubble oscillation. Thus it is not easy to detect it in the case of smaller bubbles. This time difference is a further evidence of the relatively autonomous plasma behaviour that has already been observed earlier in connection with other physical processes taking place in oscillating bubbles [25–27]. Unfortunately, at the present state of knowledge of the bubble oscillations, there is no clear explanation for this phenomenon. The only physical processes that may be considered to be similar can be observed in plasmoids generated in wet air [28–33]. Acknowledgements This work was supported by the Ministry of Education Youth and Sports of the Czech Republic as the research project MSM 245100304. The experimental part of this work was carried out during the author’s stay at the Un- derwater Acoustics Laboratory of the Italian Acoustics In- stitute, CNR, Rome, Italy. The author wishes to thank Dr. Silvano Buogo from the CNR-INSEAN Marine Technology Research Institute, Rome, Italy, for his very valuable help in preparing the experiments. References [1] A. Jayaprakash, C.-T. 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High Energy Chem. 43, 341-349, 2009. doi:10.1134/S0018143909050026 333 http://dx.doi.org/10.1063/1.3003068 http://dx.doi.org/10.1063/1.4935206 http://dx.doi.org/10.1063/1.4974452 http://dx.doi.org/10.1016/j.expthermflusci.2014.09.017 http://dx.doi.org/10.1098/rspa.2010.0134 http://dx.doi.org/10.1098/rsta.1999.0328 http://dx.doi.org/10.1016/j.jsv.2010.04.030 http://dx.doi.org/10.3813/AAA.918126 http://dx.doi.org/10.14311/AP.2017.57.0149 http://dx.doi.org/10.1051/epjap/2017170332 http://dx.doi.org/10.1016/j.expthermflusci.2013.07.004 http://dx.doi.org/10.1134/1.1529952 http://dx.doi.org/10.1070/PU2004v047n01ABEH001691 http://dx.doi.org/10.1585/pfr.1.039 http://dx.doi.org/10.1134/S1063784208060029 http://dx.doi.org/10.1088/0963-0252/17/024014 http://dx.doi.org/10.1021/jp400001y http://dx.doi.org/10.1134/1.1390398 http://dx.doi.org/10.1134/1.1364740 http://dx.doi.org/10.1134/S0018143909050026 Acta Polytechnica 58(5):323–333, 2018 1 Introduction 2 Experimental setup 3 Results 4 Discussion 5 Conclusions Acknowledgements References