first place is in which, the maximum compression of gas is ... control the initial volume of the bubble, the inert gas volume in the bubble, the host liquid ... Hundreds of chemical reactions can ... emission with their dynamical behavior considering some ... conical apex was sealed by a quartz window and was then used.
Temporal and spatial separation in conical bubble collapse: two sites of emission M. Navarrete Instituto de Ingeniería, UNAM J.R. Alvarado Instituto de Ingeniería, UNAM
C. Sanchez-Ake CCADET, UNAM
J.L. Naude Facultad de Ingeniería, UNAM
M. Villagrán CCADET, UNAM
F. A. Godínez Facultad de Ingeniería, UNAM
SUMMARY We describe a summary of experimental findings on the luminescence from conical bubble collapse, CBL, by means of a liquid piston. The Temporal, spatial, and impulsive forces features were analyzed concerning the collapse-expansion dynamics. High-speed video was utilized for observation this phenomenon in three conical ends: short (60º), large (22º), and stepped (32º). The results provide evidence of the two principal points of stagnation as the asymmetric collapse-expansion proceeds. The first of them is located near to cone apex and second one is generates by collision between a liquid/gas jet and bulk liquid piston. When the jet through the gas pocket hits and deforms the gas-liquid interface; sometimes forms a hump, sometimes perforate the interface. Consequently, the gas pocket and hump move in opposite directions producing the other stagnation point, between the two surfaces and within the liquid. These sites are favored as light emitting locations. The first place is in which, the maximum compression of gas is located (adiabatically heated gas, thermal mechanism), and the second one is formed by the liquid/gas-liquid interaction. The plasma in the breakdown channel in liquid is an electric mechanism to produce photons. The emission of this second mechanism is generally more intense and wide than the first. This process seems accentuated in the collapse using the short cone end. INTRODUCTION Luminescence from conical bubble collapse implies the emission of UV±VIS light generated by the violent collapse of a conical bubble driven by a liquid piston [1±6]. The advantages of the CBL procedure include that solid boundaries tend to stabilize the gas±liquid interface, the heat transferred between the system and its surroundings through the interface and/or solid boundaries, and that the centre of the collapse is well-defined [2]. Furthermore, CBL renders it possible to control the initial volume of the bubble, the inert gas volume in the bubble, the host liquid impurities, and the driving force. According to radial dynamical models, the collapse time in SBSL and MBSL ( 0.5 s) is shorter than in CBL ( 1 ms).
This produces a large difference in both, the pressure and temperature reached. Nevertheless, a longer collapse time implies a greater interaction among the inert gas and atomic and molecular components. Hundreds of chemical reactions can occur within the conical cavity during the timeline of the slow collapse, and the study of these reactions is more feasible in CBL. Most reactions could be chemiluminescent, which would explain the large and bright pulses from CBL compared with the flashes from SBSL and MBSL [7, 8]. In laboratory cavitation bubbles often produced by tension on liquids (acoustically or by changing the geometry of the pipeline). Other procedures deposit energy locally by light burst, spark discharge, or elementary particles through the liquid [9-11]. Under appropriate conditions, regardless of the method by which the rapid bubble compression is achieved, a light flash is emitted only if a small amount of noble gas is contained in the bubble [12]. In conical bubble collapse, one more light emission mechanisms activated depending on the details of collapse, i. e. the timeline during bubble gas-liquid piston interaction. The intensity and shape of the emitted light depend not only on the initial gas pressure and the driving pressure but also on the physicochemical properties of the host liquid and substances dissolved in it. As in other types, compression in CBL also is necessary understanding the fluid dynamics mechanisms responsible of the impulsive forces registered during the collapse. If we consider that in CBL, the gas pocket is completely confined by solid boundaries in its conical part (upper part and body) and the bottom base, the gas liquid interface coupled to bulk liquid piston forms a thick border that it may be considered as an elastic boundary. For the above, the same phenomena that occur in the cavitation bubble near a rigid wall are applied to CBL. At least three dynamical mechanisms identified the cavitation bubble near a rigid wall associated to the impulsive forces: shock wave, the impinging liquid jet, and the splashing effects [13-16]. In this papers claims that the mainly parameter that affects the impulse behavior is the proximity parameter, (the ratio between distance the center bubble from the boundary and maximum bubble radius).
Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) Edited by Claus-Dieter OHL, Evert KLASEBOER, Siew Wan OHL, Shi Wei GONG and Boo Cheong KHOO. c 2012 Research Publishing Services. All rights reserved. Copyright ISBN: 978-981-07-2826-7 :: doi:10.3850/978-981-07-2826-7 030
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Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) Experimental observations such as those of Tomita and Shima [17] and Lauterborn and Bolle [19] showed that a cavitation bubble almost inevitably fissions into many fragments after the first collapse. For a bubble collapsing very close to a solid boundary, a reentrant jet forms toward the boundary before the bubble reaches its minimum size. We present the experimental findings on conical bubble collapse, using three conical ends, to correlate the light emission with their dynamical behavior considering some concepts of the theory that describes the collapsing of a bubble near a rigid boundary.
Device response In this section, we illustrate the response of the device in a short outline, for more details see reference [8]. Figure 2 collects some experimental data from dynamic force sensor (16 mm in diameter, 75 kHz in resonant frequency and rise time of 100 s), which it provides the temporal impulsive forces induced by the bubble collapse. In a) under an empty bubble condition, and b) when the inert gas is injected to fill the tubular conical cavity. In this case, the force signals include features from initial compression until reaching the equilibrium. The top waveform of the Figure 2 corresponds to the signal from laser that registered the pressure history measured at the Arm 2 of the U tube.
EXPERIMENTAL SET UP A U-tube apparatus was assembled based on the conical device originally employed by other authors, e.g., Kosky [1] and Hawtin [2], for studying the collapse of water vapor cavities, Leighton et al. [3] for analyzing the dynamics of the collapse, Chen et al. [4, 5] that studied similar topics. Fig. 1a shows a schematic of the U-tube device with its measurement equipment and two figures of the data recorded during an experimental run. The conical ends were milled from PC (Polycarbonate) with a hexagonal external shape, and on the inside, a right conical hollow (60º, 22º and 32º stepped). The bore at the conical apex was sealed by a quartz window and was then used to record the spectra. Two or three photomultipliers (Hamamatsu, R5783-04 module, PMTs) were fixed around the apex cone to capture the luminescence. The signal from a dynamic force sensor (PCB Piezotronics, ICP 200B05, 75 kHz) on the top-plate provided data about the dynamic oscillating forces from a pressure pulse that was caused by the bubble collapse. All signals were captured with a Tektronix DPO7054 digital oscilloscope (500 MHz, 5GS/s). Compression, collapse, and rebound was observed with a Phantom v9.1 camera at a speed of 35,000 frames/s. Optical emissions from the bubble were collected on the vertical axis through a quartz window, by quartz optical fiber towards the entrance slit of a 50 cm focal length spectrometer (Princeton Ins. SpectraPro 500i) equipped with a 150 lines/mm grating. The dispersed light was analyzed by a gated intensified charge couple device (ICCD) camera (Princeton Instruments, PI-MAX2 1020x1024) equipped with a pulse/delay generator. The procedure to compress the gas pocket in the conical end was as follows. First, the U-tube partially filled with a degasified liquid (270 ± 10 ml) at ambient conditions. Subsequently, the free and dissolved air was removed from the system, until a vacuum pressure around 2500 Pa reached. Next, a small volume of inert gas was injected into arm 1, filling the free pipe volume, and displacing the liquid in arm 2. This pressure was measured as a differential height, h. At some arbitrary zero time, valve B was opened, thereby allowing air pressure into arm 2, after which the liquid started to move until the gas collapsed on the conical end. The displacement air± liquid interface blocked two laser lines that were separated by 50 mm. To calculate the velocity of the liquid in the cylindrical part was used these signals. The compression, collapse, rebounds, and re-expansion until the equilibrium reached was approximately in 100 ms, during which the remaining gas pocket and liquid were balanced by the external pressure. The liquid piston was 1,2-Propanediol to which added small quantities of H2SO4 and NaCl powder to increase the brightness of the light emission.
c)
Figure 1: a) Diagram of the apparatus to reproduce the luminescence from conical bubble collapse, CBL, b) the signals acquired by oscilloscope, and c) spectral features in the 280-250 nm wavelength range associated with OH transitions from two cases in a typical experimental run, more information about the spectroscopic features see reference [8].
Figure 2. Simultaneous record features from velocimetry (upper trace) and dynamical force transducer a) under an empty bubble condition, and b) in full experimental conditions.
Conical ends The geometric features of conical ends and video files associated for each cone are indicated in Table 1.
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Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) RESULTS Each experimental run described in this paper was under the same experimental conditions, however the amplitude, width, and shape of the light emission greatly varied, as described in references [3, 5-6, 8], this means that each collapse has its own dynamic behavior. CBL Diagram section indicates the nomenclature.
Table 1. Features of the conical ends Conical ends
Top [mm]
Bottom [mm]
Height [mm]
Volume [cm3]
File
60° Short 22° Large 32° Stepped
1.8
26.5
23
04.9±0.2
6.3
25.4
45
10.2±0.1
1
26.5
45
05.9±0.1
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Some typical photographs concerned with the luminescence from conical bubble collapse, CBL, by means of liquid piston, using three conical ends as shown in Figure 3a to 3d. In this figures, (a) corresponds to photographs of the short, large, and stepped conical ends, respectively, b) a selected frame of light emission obtained by ICCD camera with 8 ms of aperture, in dark room condition, c) light emission profiles detected by a PMT, and d) signals from a dynamic force sensor. As it observed, each cone shows its distinctive features as the light emission spots, light pulse profile, and the signal of the force transducer corresponding to the first phase compression. These first results, tell us that exist very different dynamic behavior for each one, even though the experimental run conditions are the same. As clearly seen in the frames, to explain the light spots is necessary to include the dynamics about shock waves, shock wave-bubble interaction, jet formation and its impact, circulation process, ring bubble formation, among others fluid dynamic processes. For instance, Short: temporal and spatial separation of light emissions, illustrating jet break-up; Large: compression and jet emerging, Stepped; formation of a vertical toroid bubble with multi-peak emissions. Short Large Stepped
Figure 4. Diagram and nomenclature used in CBL.
The experiments include two main parts: I) dynamic tracking of the conical bubble by measuring of the liquid displacement into conical part using fast video and detection of the impulsive force during the bubble collapse, and II) dynamic tracking of light HPLVVLRQ E\ PHDQV RI 307¶V DQG IDVW YLGHR LQ GDUN conditions. 1. Bulk liquid velocity and Impulsive forces The motion of compression and expansion of the conical bubble was evaluated following a selected point in the gasliquid interface through consecutive frames, acquired by a highspeed video camera (Phantom v9.1).
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Figure 4. Bulk liquid displacement into the conical ends showing the asymmetrical compression phase, (a), and asymmetrical rebounds. The light pulse onsets are indicate by arrows.
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Figure 5. Comparison among outputs of the dynamic force sensor for each conical end. The light pulse onsets are indicated by arrows. The fluid dynamical mechanisms thar are indicated, for these assumptions see references [14-23].
d)
The videos were taken with the cone fully illuminated for the correct visualization the liquid displacement. Obviously, the video frames are not displayed by space restrictions; the interval frame was 33.25 s. Displacement-time curves at different portions of bubble wall were obtained also, allowing a
Figure 3. Comparisons in CBL using different conical ends, data were taken simultaneously and under similar conditions. a) Photographs of the conical ends, b) selection frame for each cone, c) light emission profiles, d) impulsive forces profiles during the light emission.
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Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) reliable calculation of wall velocities (except at the actual instant of light emission). Impulse signals generated by collapse were registered by dynamic force sensor attached on a steel plate on the top of the cone tip. The experimental conditions were h= 60 mm, L=0.5m, P0= 2170 Pa, Pext= 230 kPa, liquid density= 1036 kg/m3 The Figures 4 and 5 show the bulk liquid displacement and the impulsive force behavior for each conical end, respectively. The light pulse onsets are indicated by arrows. In next three paragraphs we refer to both figures.
Stepped cone / 30075-22-06-11-06 In this case, the bulk liquid reaches the cone bottom at a velocity of 7.18 m/s, and keeps moving until it reaches 21 m/s, filling up the cone volume at 74%. The tip of this conical end is very slender, for this the liquid never reaches the frustum cone, a gas pocket forms a plug, when reaching the correct compression, this dense pocket emits light, as it is observed in selection frame of the Figure 3c. The geometry of cone, due to the stepped boundaries presents asymmetrical countercurrent flows, this generates several stagnation points. The displacement and the impulse forces generated during this experimental run are drawn with red paths in Figure 4 and 5. In general, as it expected, the impulsive forces generated by the CBL resemble a collapse of a cavitation bubble near a rigid wall, but in this case, the conical bubble is fully bordered,it has two main boundaries: one is near to the frustum diameter, which is different in each conical end, and second one is a dynamic rigid wall formed by flows in countercurrent in the interface gas-bulk liquid. Extrapolating the analysis on measurement impulsive forces which are generated by cavitation bubble collapse near a solid boundary carried out by authors in references [14-24], we presented are own assumption with respect to CBL:
Large cone / 30075-22-06-01 As the compression phase progress, the bulk liquid reaches the cone bottom at a velocity of 7.15 m/s, and keeps moving until it reaches about 17 m/s, filling up the cone volume at 85%. In the end of the compression phase, zone (a), Figure 4, the liquid piston has compressed the gas pocket in non-homogeneous form, has developed a density gradient, in the cone tip the gas is denser and puts resistence for further compressed, then a gas jet is emited from the top, crosses the gas pocket and perforates the gas-liquid interface forming a hump into the liquid piston, see frames 66-67 (Figure 6). Now, the gas pocket has decreased its energy and has two secctions. The hump continues to grow and the top gas pocket moves in opossite direcction produccing a stagnation point. In this case, the initial light emissión is generated in the hump inside of bulk liquid (frame 67). While the hump is expanding (frames 68-70), the liquid piston compresses the gas pocket, a portion of the bubble is continuing upwards while the hump is moved in the opposite direction caussing a rotation and separation (frames 71-80). Finally, in the botom of the frames 81to 89 is observed a vortex that expands, while the bubble cluster is separated. In this particular case; the maximum compression, the peak force and onset of light emission almost coincide. The impulse force and displacement behavior during this experimental run is shown in figs 4 and 5 with blue color. The fluid dynamic mechanisms that are specify on the force profiles were indicated by similarity with the impulsive signals adquired or calculated by authors who analyzed the behavior of the cavitation bubble collapse near a solid boundary (using focusing laser and high-voltage spark discharge), see references [14-23].
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a) the collapse is strongly asymmetric, as it is observed in the afterbounces, force shapes and light emission profiles. b) the collapse resembles of a bubble near a several solid boundaries, c) at least, two stagnation points may be formed, d) the maximun compression does not always coincide with the light emission, and e) two sources of light may be involved during the emission: i) thermal-chemical, and ii) plasma in the breakdown channel in liquid. II. Temporal force and light pulse vs video frames In this section, the light emission acquired E\PHDQVRI307¶V, the impulsive force and fast video in dark conditions are matched. Short cone / 20000-corto-2 In Figure 7 the impulsive forces on the transducer and the light pulse profiles are recorded and compared against the frames of emission shapes from video. The light pulse profiles were acquired frRP WZR 307¶V RQH QHDU WR WKH FRQH WLS DQG WKH other directed towards its middle. Both pulses coincide at their maximum, but are shifted with respect to the maximum force. The light emission onset in the cone tip and expands as a wake (see frame 2 to 4), in 5 a small bright spot appears to 8 mm below to the cone tip then, the two spots grow, see frame 7, in 8, the upper spot begins to disappear meanwhile the lower spot continues to increase its brightness and dark lines begin to appear. This dark lines are considered as lines of high density and marks the flow, following the radial flow outside the expanding bubble. Frame 5, corresponds when the second site of emission appears. After these forms also become extinct. Large cone / 30075-22-11-03 In the large cone, see Figure 8, everything seems to happen at the top, however the force and the emission profiles tell us another history as complicated as described in figure 6. Frames 3 to 6 shows a black spots which believed to be the density change due to liquid jet flow. In this case, only is present one location for light emission in the top.
69
75
89
Figure 6. Selection frames which the hump formation and light pulse emission is observed at the same time during the CBL in large conical end. Interval video frame 33.25 s.
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Proceedings of the Eighth International Symposium on Cavitation (CAV 2012)
Stepped cone / 30075-22-06-11-08 As shown in the frames below the graphs of Figure 9, the light pulse onset occurs to the middle of the cone and expands toward the top increasing its brightness (frames 1 to 6), in this process the gas pocket loses kinetic energy, and the liquid piston compress it, again and reaches the slender tip (frames 10 to 12).
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Figure 9. Variation of pressure and light pulse as a function of time during the collapse of conical bubble is matched to emission light photographs, in a stepped conical end.
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Figure 7. Variation of impulse force and light pulses as a function of time matched to light emission photographs using a short conical end.
The following frames (7 to 21) show a wake of light that fades until disapear. The dynamic force and light profiles (obtained from different position, see frame 1) describe the dynamical mechanism, under which the conical bubble was subjeted. This is observed in the plots, wherein the PMT, located in the middle of cone, capturing the light (blue line) firstly. The maximun peak force appear 100 s after. The double peak and distortions which displays the force profile is associated with the formation of a ring bubble that is attached to a vortex sheet, starting from the first collapse of the conical bubble, see references [14-24] about this topic.
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DISCUSSION The possibility to obtaining a light pulse from another source (that not be thermal or chemical), is to ensure that the system generates a liquid jet with sufficient energy to punch the interface and collides with the bulk liquid. The assumption is based on the well-known physical effect of double electric layer, which appears in liquid near to a liquid-gas boundary surface. Deformation of this layer under an asymmetric jet generates an electric field inside the bubble and electric breakdown might take place under certain conditions [24]. In accordance with the findings of numerous authors (see references within [8]), one or more light emission mechanisms can be activated depending on the details of the collapse. The intensity and shape of the emitted light depends on the initial gas pressure, driving pressure and physicochemical properties of the host liquid and the substances dissolved it, and now it
17
Figure 8. Variation of the pressure and light pulses as a function of time mached to light emission photographs using a large conical end.
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Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) [5] He, S.J., Ai, X.C., Dong, L. F., Chen, D.Y., Wang, O., Li, ;& =KDQ -3 :DQJ / ³&RQLFDO EXEEOH photoluminescence from rhodamine 6G in 1,2-propanediol,´ Chin. Phys., 15, 1615-1620. [6] Jing, H., He, S. J., Fang, W., Min, S. - ³&DYLWDWLRQ luminescence of argon-saturated alkali-metal solutions from a conical bubble,´ J. Phys. B: At. Mol. Opt. Phys., 41, 195402. [7] Xu, H., Eddingsaas, N. C., Suslick, K. S. 2009, ³Spatial separation of cavitation bubble populations: the nanodroplet injection model´ J. Am. Chem. Soc., 131, 6060-6061. [8] Godínez, F. A., Navarrete, M., Sánchez-Ake, C., Mejía, E.V., Villagrán, 0 ³6SHFWURVFRSLF DQG WKHrmodynamic features of conical bubble luminescence´ Ultrasonics Sonochemistry, 19, 668-681. [9] Ohl, C. D. 2002, ³Probing luminescence from nonspherical bubble collapse,´ Phys. Fluids, 14, 2700-2708. [10] Harvey, E. N. 1939 ³6RQROXPLQHVFHQFH DQG VRQLF chemiluminescence´, J. Am. Chem. Soc., 61, 2392±2398. [11] Khodorkovskii, M.A., Murashov, S.V., Artamonova, T.O, Rakcheeva, L. P. ³Excitation of water molecules by electron impact with formation of OHº radicals in the A2 + state´ J. Phys. B: At. Mol. Opt. Phys., 42, 215201-215206. [12] Rayleigh, L. ³The pressure developed in a liquid on the collapse of a spherical cavity´ Philos. Magn., 34, 94-98. [13] Brennen, C. E. 1995 ³Cavitation and Bubble Dynamics,´ Oxford University Press, New York, NY. [14] Tong, R.P., Schiffers, W. P., Shaw, S. J., Blake, J. R., Emmony, D.C. ³The UROHRIµVSODVKLQJ¶LQWKHFROODSVH of a laser-generated cavity near a rigid boundary´ J. Fluid Mech., 380, 339-361. [15] Takayama, S. K., Tomita, Y. 1983 ³Mechanism of impact pressure generation from spark-generated bubble collapse near a wall´ AIAA J, 21 (1), 55-59. [16] Lauterborn W. 1998 ³Cavitation erosion by single laser produced bubbles,´ J. Fluid Mech., 361, 75-116. [17] Tomita, Y., Shima, A. ³High-speed photographic observations of laser induced cavitation bubbles in water´ Acustica, 71,161-171. [18] Blake J. R., Tomita Y., and Tong R. P., 1998, ³The art, craft and science of modelling jet impact in a collapsing cavitation bubble´Applied Scientific Research, 58, 77-90. [19] Lauterborn W., Bolle H. ³Experimental investigations of cavitation bubble collapse in the neighborhood of a solid boundary,´ J. Fluid. Mech., 135, 373-387. [20] Wang, Yi-Chun, Chen, Yu-:UQ ³$SSOLFDWLRQV RI piezoelectric PVDF film to the measurement of impulsive forces generated by cavitation bubble collapse near a solid ERXQGDU\´ Experimental Thermal and Fluid Science, 32, 403-414. [21] Ohl, C. ',NLQN5³6KRFN-wave-induced jetting of micron-VL]H EXEEOHV´ Phys. Rev. Lett., 80, 214502-1214502-4. [22] Duncan, -+ =KDQJ 6 &KDKLQH * / ³7KH ILQDO stage of the collapse of a cavitation bubble near a rigid ZDOO´J. Fluid Mech., 257, 147-181. [23] 7RPLWD
