Acta Polytechnica DOI:10.14311/AP.2020.60.0268 Acta Polytechnica 60(3):268–278, 2020 © Czech Technical University in Prague, 2020 available online at https://ojs.cvut.cz/ojs/index.php/ap ON THE SECOND LIGHT FLASH EMITTED FROM A SPARK-GENERATED BUBBLE OSCILLATING IN WATER Karel Vokurka Technical University of Liberec, Physics Department, Studentská 2, 461 17 Liberec, Czech Republic correspondence: karel.vokurka@tul.cz Abstract. The light emitted from the spark-generated bubbles oscillating in water is studied experimentally. Attention is paid to the emission of light from bubbles in the final stages of their first contraction and in the early stages of their following expansion. In some experiments, two close flashes of light were observed. The first light flash has already been studied in earlier works. In the present work, attention is paid to the second light flash. The relations between the first and second flashes of light and the size of the bubbles are studied and discussed in detail. It is assumed that these two light flashes are caused by two different processes taking place in the bubbles. The possible nature of these two processes is briefly discussed. Keywords: Spark-generated bubbles, bubble oscillations, light emission. 1. Introduction The physical processes taking place in bubbles oscillat- ing in liquids are very complex. Although much effort has been devoted to clarifying these physical processes, many issues in this field are still not well understood. For example, a great deal of works has been devoted to clarifying the processes responsible for cavitation erosion (see, e.g., reference [1]). However, the spe- cific mechanism responsible for cavitation erosion has not yet been satisfactorily identified. The emission of light from oscillating bubbles, which will be studied in this work, represents another unexplained problem. Other studies of bubble oscillations have focused on improving contrast-enhancement in medical ultrasonic imaging [2–6], and even in this case, a better under- standing of the physical processes running in bubbles may be useful. Oscillating bubbles are generated in laboratory ex- periments by many techniques, such as by focussing a laser beam into liquid [7–13], spark discharge in liquid [14–19], irradiating liquid with intense ultra- sonic waves (acoustic cavitation) [20], or in a liquid flow (hydrodynamic cavitation) [21]. All these tech- niques are also used in studies of light emission from bubbles [8–13, 15–18, 20, 21]. Over the last three decades, the emission of light from a single bubble oscillating in acoustic resonators has also been intensively studied (see, e.g., a recent re- view [22], which summarises results from 163 works). An advantage of a method based on acoustic res- onators is that relatively small experimental set-ups can be used. However, a serious disadvantage of this technique is that only small bubbles are generated which have maximum radii of less than 100 µm. These small bubbles oscillate very quickly, and therefore all the physical processes that take place in them also run very fast, which makes their study difficult. Measur- ing light flashes from these small sources at relatively large distances requires averaging, during which many important features are lost. And measuring ultrasonic waves radiated by these bubbles is also a difficult task because spectral components of these waves are ranging up to several hundreds of MHz. In the present work, the emission of light from large spark-generated bubbles freely oscillating in water far from boundaries is studied. As mentioned in earlier works [23–25], the large spark-generated bubbles have many advantages that will also be exploited in this study. During the study of the light flashes radiated from these bubbles in the final stages of their first con- traction and early stages of the following expansion, we occasionally observed that the first flash of light was accompanied by a slightly delayed second flash of light. Whereas the first flashes have been studied in detail in [24, 25], in this work we want to concentrate on the second flashes. In Section 3, the time distance between the two flashes, the maximum values of these flashes, and the position of the two flashes relative to the position of the pressure pulse (and thus also with respect to an instant when the bubble is contracted to its first minimum volume) will be studied in de- tail. Multiple secondary light flashes have also been observed by Ohl [9], Sukovich et al. [12], Supponen et al. [13] and Moran and Sweider [26]. However, in these works, secondary light pulses have not been studied in detail and no concurrently emitted pressure pulses have been used to analyse the observed events in the time domain. 2. Experimental setup and nomenclature The data analysed and discussed in this work are a sub- set of the data already presented in the works [24, 25]. This means that the data were obtained using the same experimental setup. Therefore, only a brief de- 268 https://doi.org/10.14311/AP.2020.60.0268 https://ojs.cvut.cz/ojs/index.php/ap vol. 60 no. 3/2020 On the second light flash emitted from a spark-generated bubble. . . scription of the instruments, the measuring procedure, and the nomenclature will be given here. Further details can be found in [24, 25]. The freely oscillating bubbles were generated by spark discharges in a large laboratory water tank hav- ing dimensions 4 m (width), 6 m (length), and 5.5 m (depth). The sparker used in the experiments con- sisted of two thin tungsten electrodes having a diame- ter of 1 mm and a length of 50 mm. The electrode tips were facing each other and were separated by a narrow gap. Due to electrode burning the length of the gap in subsequent experiments gradually increased from about 0.2 mm to 3 mm. The tungsten electrodes were mounted in conical brass holders and were connected by cables to a condenser bank, whose capacitance could be varied in 10 steps from 16 uF to 160 uF. The capacitors were charged from a high voltage source of 4 kV, and an air-gap switch was used to trigger the dis- charge. After closing the air-gap switch, at a time t0 the liquid breakdown occurs and the discharge channel starts growing explosively. This explosive growth is accompanied by intensive light (optical) emission and pressure (acoustic) wave radiation from the bubble. The explosively growing almost spherical bubble attains its first maximum volume at time t1 and has a radius Rm1. Then the bubble starts contracting. At time tc1, the bubble contracts to its first minimum volume. Although very little is currently known about the shape of the contracted bubble, it will be assumed that it is a sphere having radius RM 1. Then the bubble starts expanding and at time t2 attains its second maximum volume and has a radius RM 2. Further bubble oscillations follow, but these are beyond the scope of this work. In the following, the interval (t0, t1) will be referred to as the initial growth phase, the interval (t1, tc1) as the first contraction phase, and the interval (tc1, t2) as the first expansion phase of the bubble. Prior to the measurements reported here, a limited number of high-speed camera films were taken with framing rates ranging from 2800 to 3000 frames/s. These records were used to check the shape of the generated bubbles. Besides, the photographs yielded useful visual information about the bubble content. Examples of images of spark-generated bubbles can be seen in earlier works [23, 27]. Both the spark discharge and the subsequent bubble oscillations are accompanied by an intensive emission of light and pressure waves. A relatively simple ar- rangement was used to record the optical waves. A fibre optic cable was fixed at the same depth in water as the sparker. The input surface of this cable was pointing perpendicularly to the electrodes and was positioned at a distance r = 0.2 m from the sparker gap. A photodiode was positioned at the other end of the fibre optic cable. The output voltage u(t) from the photodiode was amplified, digitized and stored in a computer. The record of the optical radiation u(t) can be divided into two pulses. First, it is the pulse u0(t) that was emitted during the interval (t0, t1), and second, it is the pulse u1(t) that was emitted during the interval (t1, t2). In this work, only the pulses u1(t) will be considered and the instant, at which the pulse u1(t) attains the maximum value uM 1 will be denoted as tu1. The pressure waves p(t) were recorded using a broad- band hydrophone, which was positioned at the same depth as the sparker at a distance rh = 0.2 m from the gap of the sparker. The hydrophone output volt- age was digitized and stored in a computer. Like the optical wave, the pressure wave p(t) can be divided into two pulses. First, it is the pressure pulse p0(t) that was radiated during the interval (t0, t1), and sec- ond, it is the pressure pulse p1(t) that was radiated during the interval (t1, t2). Only the pulse p1(t) will be considered in this work. The instant, at which the pressure pulse p1(t) attains the peak value pp1 , will be denoted as tp1. The sparker was submerged in water at a depth of h = 2.5 m (ie. at hydrostatic pressure p∞) far away from the tank walls. Generated bubbles can be described by two parameters. First, it is the bubble size RM 1, and second, it is the bubble os- cillation intensity pzp1 (this parameter is defined as pzp1 = (pp1 ·rh)/(p∞·RM 1)). Both RM 1 and pzp1 were determined in each experiment from the respective pressure record using an iterative procedure described in [23]. The sizes RM 1 of the bubbles studied in this work ranged from 21 mm to 56.5 mm, the bubble oscillation intensities pzp1 ranged from 92.4 to 152.8. The pressure wave propagates from the bubble wall to the hydrophone at the speed of sound in water. Therefore, the times t0, t1 and t2 in the pressure record are delayed by about 135 µs after the times t0, t1, and t2 in the optical record. However, as shown in [25], the instants of the liquid breakdown t0 can be determined in both records u(t) and p(t) with a precision 0.1 µs. The pressure record can thus be shifted along the time axis so that the times t0 in both records are identical. Examples of the whole records u(t) and p(t) were presented in [25]. In this work, only small portions of the pulses u1(t) and p1(t) extracted from the records in the vicinity of tu1 and tp1 will be displayed and discussed in the following text. And even if it has not been verified experimentally yet, in the following discussion, it will be assumed that the peak pressure in the pulse p1(t) is radiated at the same instant the bubble is contracted to the first minimum volume. In other words, in the following discussion it is assumed that in the shifted pressure record tp1 = tc1. In earlier studies of light emission in the interval (t1, t2) from the spark-generated bubbles, a total of 98 experiments were quantitatively evaluated [24, 25]. In a prevailing part of these experiments, a single light flash was observed. An example of a typical single pulse u1(t) is shown in Figure 1. In [24] the single optical pulses were analysed and characterized 269 Karel Vokurka Acta Polytechnica by three parameters: the maximum voltage uM 1 in the pulse, the time tu1 of occurrence of maximum voltage, and the pulse width ∆ at the half value of the maximum voltage (that is the pulse width at uM 1/2). All these parameters are displayed in Figure 1. In [25], it was further shown that the light flashes u1(t) are not radiated from the bubble synchronously with the pressure pulses p1(t), but the light flashes are radiated either a bit earlier or a bit later than the pressure pulses. The difference between times tu1 and tp1 was denoted as δ1 and was defined as δ1 = tu1 − tp1. In some experiments (exactly in 22 of 98 experi- ments), beside the first optical pulse u1(t), a second optical pulse u2(t), slightly delayed after the first pulse, was also observed. An example of a record, where both the first pulse u1(t) and the second pulse u2(t) can be seen, is given in Figure 2. The situation, when two pulses are present in the record, can be char- acterized by six parameters: the maximum voltages uM 1 and uM 2 in pulses, the times of occurrence of these maxima tu1 and tu2, the distance d12 between the times tu1 and tu2 (this parameter is defined as d12 = tu2 − tu1), and the pulse width ∆ introduced already earlier for a single pulse u1(t). It is evident that now pulse width ∆ describes two pulses, which are more or less melted together. However, there is currently no way to separate the two pulses from each other. In defining the mutual position of the second light pulse u2(t) and the pressure pulse p1(t) on the time axis we will proceed in the same way as in the case of the time difference δ1. The difference between times tu2 and tp1 will be denoted as δ2 and is defined as δ2 = tu2 − tp1. The parameters describing the po- sition of the two optical pulses u1(t) and u2(t) and the acoustic pulse p1(t) on the time axis are shown in Figure 3. 3. Results In the experiments analysed here, pulses p1(t), u1(t) and u2(t) were radiated from almost spherical bub- bles [24, 25]. The sizes of these bubbles are described by the first maximum radius RM 1 and the bubble oscil- lation intensities are described by the non-dimensional peak pressure in the first acoustic pulse pzp1. Thus, there are eight parameters available that can be used in the analysis: six parameters describing pulses u1(t) and u2(t) and their time position with respect to pulse p1(t) and two parameters describing the bubble itself. Using the data from 22 experiments, where second light pulses were observed, a correlation anal- ysis was done between these eight parameters, that is between d12, δ1, δ2, uM 1, uM 2, ∆, RM 1, and pzp1. In most of these analyses, it was noticed that the correlation between selected parameters is very weak. Such weak correlation can be seen, for example, in cases where the bubble oscillation intensity pzp1 was entered as one of the two parameters into the analysis. This weak correlation of optical radiation with the intensity of bubble oscillation was already observed in references [24, 25] and was used as a proof for the as- sertion concerning the relative autonomous behaviour of plasma in the bubble interior. Some other weak correlations have also been observed. As these weak correlations currently do not provide any new infor- mation, they will not be considered any further and only the dependences of the selected parameters will henceforth be discussed. These are variations of d12, δ2, uM 2, and uM 2/uM 1 with RM 1, d12 with ∆, and δ1 with d12. These variations are shown in Figures 4 - 9. In Figure 4, the variation of the time distance d12 between the two optical pulses u2(t) and u1(t) with the bubble size RM 1 is shown. The regression line for the mean value of d12 in dependence on RM 1 is < d12 >= 0.27RM 1 − 4.55 [µs, mm]. It can be seen that d12 is only very weakly correlated with RM 1 and that the dispersion of d12 increases with RM 1. The variation of d12 with RM 1 agrees with the correlation between d12 and ∆ shown later in Figure 8 (d12 grows with ∆) and with the correlation between ∆ and RM 1 shown in Figure 9 in [24] (∆ grows with the bubble size as ∼ R3.3M 1). However, now the quantities d12 and RM 1 are only weakly correlated. This is in contrast to the moderate correlation of d12 with ∆ shown in Figure 8, and ∆ with RM 1, shown in Figure 9 in [24]. In Figure 5, the variation of the time difference δ2 between the radiation of the second light pulse u2(t) and the pressure pulse p1(t) with the bubble size RM 1 is shown. The regression line for the mean value of δ2 in dependence on RM 1 is < δ2 >= 0.097RM 1−1.12 [µs, mm]. It can be seen that δ2 is correlated with RM 1 only weakly and that the dispersion of δ2 increases with RM 1. The time difference δ2 grows with the bubble size RM 1. This is also in an agreement with the variation of distance d12 with the pulse width ∆ given in Figure 8 (distance d12 is part of ∆ and equals d12 = δ2 − δ1). And it is also in an agreement with previous results concerning the variation of the pulse width ∆ with RM 1 (Figure 9 in [24]). It can be seen in Figure 5 that δ2 was positive in all experiments reported here, which means that the second light flashes were always (with the exception of a single experiment, in which δ2 = 0) radiated some µs after the time tc1 when the bubbles were contracted to minimum volumes. However, as can be seen in Figure 7 in [25], the time difference δ1 between the radiation of the first optical pulse u1(t) and the pressure pulse p1(t) was negative in the prevailing number of experiments. This means that the first light flashes u1(t) are usually radiated a few µs before the bubbles have been contracted to minimum volumes at tc1, which is in contrast to the second light flashes u2(t) that were radiated some µs after the bubbles have been contracted to minimum volumes. In Figure 6, the variation of the maximum voltage uM 2 in the optical pulse u2(t) with the bubble size RM 1 is shown. The regression quadratic polynomial for the mean value of uM 2 in dependence on RM 1 is 270 vol. 60 no. 3/2020 On the second light flash emitted from a spark-generated bubble. . . −40 −30 −20 −10 0 10 20 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 t [ µs ] u 1 (t ) [ m V ] u M1 t u1 ∆ Figure 1. Detailed view of pulse u1(t) at the output of the optical detector. The spark-generated bubble has a size of RM 1 = 49 mm, and oscillates with an intensity of pzp1 = 142.1. In this figure, the time axis origin is set at tu1 and from the pulse u1(t), only a small portion near tu1 is shown. The width of this pulse is ∆ = 9.4 µs and the difference between times tu1 and tp1 is δ1 = −2.6 µs. −60 −40 −20 0 20 40 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 t [ µs ] u (t ) [ m V ] u M1 t u2 d 12 u M2 ∆ u 1 (t) u 2 (t) t u1 Figure 2. Detailed view of pulses u1(t) and u2(t) at the output of the optical detector. The spark-generated bubble has a size of RM 1 = 53.6 mm, and oscillates with an intensity of pzp1 = 98.0. In this figure, the time axis origin is set at tu1 and from the two pulses, only a small portion near tu1 is shown. The width of the two partially merged pulses is ∆ = 83.6 µs and the difference between times tu1 and tp1 is δ1 = −11 µs. 271 Karel Vokurka Acta Polytechnica −40 −30 −20 −10 0 10 20 −1 0 1 2 3 4 5 6 t [ µs ] p 1 (t ) [ M P a ] u (t ) [ a .u . ] t u2 t p1 t u1 u 1 (t) p 1 (t) u 2 (t) δ 1 δ 2 Figure 3. Example of optical and pressure waves in the vicinity of the times tu1 and tp1 (to display both waves in comparable sizes, the wave u(t) is shown in [a.u.]).The bubble size is RM 1 = 56.5 mm, the intensity of bubble oscillation is pzp1 = 127.3. Time differences in the occurrence of maxima in both optical pulses with respect to the pressure pulse are δ1 = −7.0 µs and δ2 = 4.6 µs. In this figure, the time axis origin is set at tp1 and only small portions near tu1, tp1 and tu2 are shown from the optical record u(t) and acoustic record p(t). 20 25 30 35 40 45 50 55 60 0 2 4 6 8 10 12 14 16 18 20 R M1 [ mm ] d 1 2 [ µs ] Figure 4. Variation of the time distance between the first and second optical pulses d12 with bubble size RM 1. 272 vol. 60 no. 3/2020 On the second light flash emitted from a spark-generated bubble. . . 20 25 30 35 40 45 50 55 60 0 1 2 3 4 5 6 R M1 [ mm ] δ 2 [ µs ] Figure 5. Variation of the time difference between the occurrence of the second optical pulse and the acoustic pulse δ2 with bubble size RM 1. < uM 2 >= 2.3 × 10−4R2M 1 − 6.2 × 10 −3RM 1 + 3.9 × 10−2 [mV, mm]. It can be seen that uM 2 is weakly correlated with RM 1 and grows with the bubble size as ∼ R2M 1. In Figure 7, the variation of the ratio uM 2/uM 1 with the bubble size RM 1 is shown. The regression line for the mean value of the ratio uM 2/uM 1 in dependence on RM 1 is < uM 2/uM 1 >= −0.004RM 1 + 0.87 [ - , mm]. It can be seen that the ratio uM 2/uM 1 is correlated with RM 1 only very weakly and that, in most of the experiments, uM 1 > uM 2. The ratio uM 2/uM 1 is almost independent of the bubble size RM 1. This is in an agreement with the fact that uM 2 grows with RM 1 as ∼ R2M 1 (Figure 6) and uM 1 grows with RM 1 as ∼ R2.5M 1 [24]. The variation of the time distance d12 between optical pulses u2(t) and u1(t) with the pulse width ∆ is shown in Figure 8. The regression line for the mean value of d12 in dependence on ∆ is < d12 >= 0.15∆ + 1.62 [µs, µs]. It can be seen that d12 is moderately correlated with ∆. The moderate correlation between d12 and ∆ is what could be expected, viz. that the distance d12 is larger for broader pulses (larger ∆) and smaller for narrower pulses (smaller ∆). The variation of the time difference δ1 between the first light pulse u1(t) and the pressure pulse p1(t) with the time distance d12 between optical pulses u2(t) and u1(t) is shown in Figure 9. The regression line for the mean value of δ1 in dependence on d12 is < δ1 >= −0.79d12 + 1.65 [µs, µs]. It can be seen that δ1 is moderately correlated with d12. As can also be observed, the bubbles with larger time distance d12 between optical pulses u2(t) and u1(t) radiate the first optical pulse more early before the bubble is contracted to the minimum volume at tc1. This finding can be compared with Figure 7 in [25], where the variation of δ1 with RM 1 is given and where it is shown that for larger bubbles, δ1 is larger, too. And as shown in Figure 9 in [24], for larger bubbles, the widths ∆ are also larger. Finally, as shown in Figure 8, the distance d12 grows with the pulse width ∆, hence it can be expected that δ1, in absolute values, will grow with d12 as well, a fact that is confirmed in Figure 9. In conclusion, it may be said that the variances of the parameters discussed above are in an agreement with the results set forth in references [24, 25]. Un- fortunately, at the current state of knowledge of the processes taking place in oscillating bubbles, no deeper physical explanation of the observed correlations is possible. The processes that may be responsible for the observed phenomena are briefly discussed in the following Section. 4. Discussion Although the light emission from oscillating bubbles has been intensively studied in many laboratories for several decades (see, e.g., works [8–13, 15–18, 20, 21, 26], and the recent review by Borisenok [22]), only very limited quantitative experimental data are still available at present, and therefore understanding of the physical or chemical processes taking place in oscillating bubbles is currently very difficult. In a review paper [22], many theories trying to explain the light emission from oscillating bubbles are mentioned, but none of the theoretical models can explain the experimental data presented in this work and in refer- ences [24, 25, 27, 28]. For example, as can be seen in Figures 2, 3 and 5, the shape of the pulses u1(t) and u2(t) and their timing with respect to the bubble wall motion at first sight exclude the “hot spot” theory pre- ferred by most researchers [22]. And both the shape of the pulse p1(t) (single pulse) and its position relative to the pulses u1(t) and u2(t) exclude the explanation 273 Karel Vokurka Acta Polytechnica 20 25 30 35 40 45 50 55 60 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 R M1 [mm] u M 2 [m V ] Figure 6. Variation of the maximum voltage in the second optical pulse uM 2 with bubble size RM 1. 20 25 30 35 40 45 50 55 60 0 0.2 0.4 0.6 0.8 1 1.2 1.4 R M1 [ mm ] u M 2 /u M 1 [ − ] Figure 7. Variation of the ratio of maximum voltages in the first and second optical pulses uM 2/uM 1 with bubble size RM 1. of the two light flashes by the bubble splitting in the final stages of the contraction and early stages of the following expansion into two parts. And although the values of the parameters d12,δ1,δ2,uM 1,uM 2, and ∆ may vary in different experiments (see, Figs 4 - 9), the shapes of the pulses u1(t) and u2(t) were always similar to the shapes shown in Figs. 2 - 3. And this also contradicts to the possible explanation that the bubble was split into several parts, because such a splitting can be expected to be random. From the optical records on which both pulses u1(t) and u2(t) are simultaneously present, it is evident that there are two physical or chemical processes taking place in a bubble. The first process is responsible for the emission of the optical pulse u1(t). The sec- ond process is responsible for the emission of the optical pulse u2(t). Based on the experimental data published in references [24, 25, 27, 28], where the long- lasting and very autonomously behaving plasma in bubbles was described, the author of this work came to the conclusion that in the interior of spark-generated bubbles, during their first oscillation, plasmoids are present (and not the usual plasma) and that these plasmoids are responsible for the emission of light pulses u1(t) [25] (the presence of these plasmoids in the bubble interior is clearly seen, for example, in images presented in Figure 2 in [27]). As mentioned already in [25], similar nonstandard plasma generated by electric discharges in water has been studied, e.g., by Egorov et al. [29]. These authors talk about au- tonomous glowing plasma (or about plasmoids) and refer to the works of Shevkunov [30, 31], where the process of interaction between H2O molecules and H+ and OH− ions in air containing water vapour is mod- 274 vol. 60 no. 3/2020 On the second light flash emitted from a spark-generated bubble. . . 0 20 40 60 80 100 120 0 2 4 6 8 10 12 14 16 18 20 ∆ [ µs ] d 1 2 [ µ s ] Figure 8. Variation of the time distance between the first and second optical pulses d12 with optical pulse width ∆. Bubble sizes: ‘o’ RM 1 > 50 mm, ‘x’ 50 mm ≥ RM 1 > 40 mm, ‘+‘ 40 mm ≥ RM 1 > 30 mm, ‘*’ 30 mm ≥ RM 1 > 20 mm, ‘.’ 20 mm ≥ RM 1. 0 5 10 15 20 −15 −10 −5 0 5 d 12 [ µs ] δ 1 [ µs ] Figure 9. Variation of the time difference in the occurrence of the first optical pulse and the pressure pulse δ1 with time distance between the first and second optical pulse d12. Bubble sizes: ‘o’ RM 1 > 50 mm, ‘x’ 50 mm ≥ RM 1 > 40 mm, ‘+‘ 40 mm ≥ RM 1 > 30 mm, ‘*’ 30 mm ≥ RM 1 > 20 mm, ‘.’ 20 mm ≥ RM 1. 275 Karel Vokurka Acta Polytechnica elled to explain the phenomenon of long-lasting and glowing plasma. Independently of Egorov et al. [29], Golubnichy et al. [15] also studied nonstandard plasma in bubbles generated by electric discharges in water and in this case, the authors call this form of plasma as “long-living luminous objects” (LLLO). It may also be interesting to note that, while the pulse u1(t) was observed independently on the bub- ble oscillation intensity pzp1 in all experiments, the pulse u2(t) was only observed when studying bubbles oscillating with an intensity of pzp1 > 92. However, as mentioned in Section 3, only very weak correlation of the studied parameters d12,δ1,δ2,uM 1,uM 2, and ∆ with intensity of bubble oscillations pzp1 was observed, and therefore no scatter plots of these parameters were presented. In the present paper, the shapes of the second light pulses u2(t) and their position on the time axis rela- tive to the position of the pressure pulses (and thus implicitly also relative to the instantaneous motion of the bubble wall) were studied in a greater detail. From Figures 2, 3, and 7, it is evident that to explain the existence of the second light pulses, a new physical or chemical process taking place in spark-generated bubbles must be considered. It is highly probable that the process responsible for the emission of the light pulses u2(t) is always present in the bubble, but the light emitted by this process is very often overlapped by the light emitted from the contracted (and thus heated) plasmoid. Therefore, only a single flash of light is visible in most experiments. The process re- sponsible for u2(t) lasts only several µs and emits light of comparable intensity as the contracted plasmoid (see Figures 2, 3, and 7). To explain the origin of this second light, a physical (or chemical) reaction of the plasmoid components H, H2, O, O2, OH, H2O can be assumed (in reference [15], the authors talk about unusual power-consuming compounds of oxygen and hydrogen present in the plasmoid). At present, however, it is still unclear what kind of physical (or chemical) reaction it should be. All that can be said is that, most probably, this reaction usually starts after the plasmoid is contracted sufficiently to a small volume and thus a very high pressure and temper- ature in the plasmoid is achieved. As can be seen in Figures 4 - 7, parameters d12, δ2, and uM 2 grow almost linearly with the bubble size RM 1 (parameter ∆ also grows with RM 1, but steeper than linearly, see Figure 9 in [24]). Thus, the amount of substances en- tering into the chemical reaction will be proportional to the bubble size RM 1. However, nothing else can be deduced from the available experimental data at the present time. And no other quantitative data are available in the literature [9, 12, 13, 26]. After a careful observation of the shapes and widths of the light pulses u2(t) and after closer examination of the data given in Figure 7, we came to a conclusion that under certain circumstances, such as those occur- ring in laser-generated bubbles and in bubbles that are oscillating in acoustic resonators, the emission of light caused by the second process can be significantly increased compared to the emission caused by the first process. In that case, the value of uM 2 may be much higher than the value of uM 1. If this assumption proves to be correct, then the light pulses observed in works [9, 12, 13, 26] are identical with the light pulses u2(t) observed in the present study. Finally, it may be useful to compare different types of oscillating bubbles from the point of view of light emission. As mentioned in the Introduction, beside the spark-generated bubbles studied here, other types of bubbles were also intensively used to investigate light emission. Most extensive data on light pulses were obtained when studying laser-generated bub- bles [8–10, 12, 13], and in the case of bubbles oscil- lating in acoustic resonators [22]. When comparing the experimental data on light emission from spark- generated bubbles with data measured with other types of bubbles, certain similarities and certain dif- ferences can be observed. The similarities can be seen, for example, in the values of the maximum surface tem- peratures of the emitting plasma. For different types of bubbles, these temperatures range from 4300 K to 8700 K [10, 18, 27, 28] (only bubbles oscillating in water under ordinary laboratory conditions are com- pared here). Authors of works [9, 12, 13] also mention the great scatter of the optical pulse maximum values, of the pulse widths, and of the pulse shapes. In the case of laser-generated bubbles [9, 12, 13], the multiple peaks in light flashes were also observed. And Moran and Sweider [26], who were studying bubbles in an acoustic resonator, also reported the occurrence of the first light pulse followed by a small second pulse, which they called “afterpulse”. Finally, to close the discussion of the similarities, let us mention that even in the article of Baghdassarian et al. [8], the light emission during the whole first bubble oscillation To1 can be seen in the published Figure 1. However, there are also differences between the light flashes emitted from spark-generated bubbles and other types of bubbles. These differences can be seen, for example, in the shape of the light pulses and in the variation of the light pulse widths ∆ with the bubble size RM 1. The shapes of the light pulses observed in the case of laser-generated bubbles and bubbles oscillating in acoustic resonators [8–10, 12, 26] are “Gaussian” and pulse widths increase almost lin- early with the bubble size RM 1 [8–10]. Unlike these observations, the shape of the light pulses u1(t) ob- served in our experiments is not “Gaussian” (see, e.g. Figures 1, 2, and 3) and pulse widths increase with the bubble size as ∼ R3,3M 1 [24]. In some experiments, the number of observed pulses was also greater than two. For example, Ohl [9] observed up to three local maxima before the main maximum and denoted these local maxima as precursors. As an explanation for these local maxima, he suggested that “the precursors originate from different hot spots; either a strongly 276 vol. 60 no. 3/2020 On the second light flash emitted from a spark-generated bubble. . . inhomogeneous bubble interior, or a splitting of the bubble into parts”. Sukovich et al. [12] also observed that “many events were shown to have multiple peaks in the emission curve for a single event”. And as an ex- planation of this, they said that “this likely suggests nonuniformities in either pressure or bubble distri- bution in the collapse region or that the conditions requisite for emissions are probabilistic in nature and so may occur at any point in space or time in the region so long as conditions are above some threshold value”. Finally, Supponen et al. [13] reported that “the number of peaks in the photodetector signals varies between one and four, suggesting multiple events yield- ing light emission”. The last-mentioned authors did not suggest any closer explanation for the origin of the events. Unfortunately, due to the lack of suitable ex- perimental data, the causes of the differences between the spark-generated and laser-generated bubbles can- not be explained in greater detail at present. 5. Conclusion In this work, the second light flashes emitted from the spark-generated bubbles in the final stages of the first bubble contraction and early stages of the following expansion were studied in detail. To obtain the neces- sary time information, optical waves u(t) and acoustic waves p(t) had to be simultaneously recorded. The large size of the generated bubbles also proved advan- tageous. To explain the existence of the observed two light flashes, two independent processes taking place in bubbles are assumed. The first process is responsi- ble for the light emission during the whole first bubble oscillation, and it is believed that the nature of this process is similar to the process running in plasmoids. The second process, which is responsible for the second light flashes, is assumed to be a physical (or chemical) reaction of the plasmoid components. Experimental investigation of these processes taking place in bub- bles under very high pressures and temperatures in a very limited space and lasting an extremely short time will require the development of new experimen- tal techniques. Also, the very low reproducibility of spark-generated bubbles must be overcome. And the new technique should avoid averaging, unfortunately so common in studies of light emission from bubbles. Acknowledgements This work was partly supported by the Ministry of Educa- tion of the Czech Republic as a research project MSM 245 100 304. The experimental part of this work was carried out during the author’s stay at the Underwater Acoustics Laboratory of the Italian Acoustics Institute, CNR, Rome, Italy. The author wishes to thank Dr. Silvano Buogo of the CNR-INSEAN Marine Technology Research Institute, Rome, Italy, for his very valuable help in preparing the experiments. References [1] G. L. Chahine, A. Gnanaskandan, A. Mansouri, et al. 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