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Difficulties in the Sonoluminescence Theory Based on Quantum Phenomenon of Vacuum Radiation

Pawel Tatrocki (Department of Physics, Pedagogical Academy, Cracow)

Published in physic.philica.com

Abstract
This study is aimed at discussion of some effects which could be
observed and are difficult to explain by the sonoluminescence theory
developed by C. Eberlein as based upon quantum phenomenon of vacuum radiation.

Article body

The sonoluminescence phenomenon consisting in light emmission by gas bubble placed in liquid in acoustic field had been first observed more than sixty years ago by Marinesco and Trillat [1], and since that time, many theories were laid down for explanation. However, for experimental difficulties in this observation and investigation as well as insufficient measurement accuracy, those theories could clarify only a slight portion of experimental results. Yet thanks to experiments by Gatain, Putterman, Barber, Löfstedt, Weninger, Hiller {[1] et al.}, it has been recently possible to structure theories of bigger perfection. One of them is the sonoluminescence theory proposed by Eberlein [2], [3]. This theory based upon quantum phenomenon of vacuum radiation consists briefly in that quantum fluctuations of electromagnetic field induce dipoles on the bubble surface which subsequently emit radiation while the bubble passes through its minimum radiation whereby radius velocity sense is changed and big accelerations are achived in this surface movements [2]. This study is intended to point out handicaps of this theory which have to be resolved for it to be recognised as complete quality— and quantity—wise in relation to the experimental material collected. This is the addition to the discussion made in [4] and in [5]. These are the problems:

1. The theory provides for Planck distribution to exist for radiation emitted by the bubble. The fact is supported by experiments of [6]. However, there are some experiment results [7] which prove the absence of Planck distribution in the light emitted.

2. The theory provides for rays emitted by the bubble as it obtains minimum ray when changing pulsation velocity sense. Experimental results obtained during work of [8] show that the emission occurs but in the range of 5 ns — 10 ns until the bubble obtains the minimum radius. In the time range of 1 ns, the bubble radius would increase while the acceleration and velocity of its surface are lower than when passing through the minimum. On the other hand, if we were to relocate the moment of emission, then the flash should occur also when the bubble passes through the minimum of its

$R_{c}$

because of real emission moments and minimum possibly being probable to be approximated very well by seamlessly gluing square function with straight line as well as two square functions [8, insert in Fig. 4B]. It results in a fact that fourth derivatives of radius velocity changes over time and products of its time derivatives of lower orders including products of time derivatives of a higher order or the one equal two as being responsible for emission should only slightly differ at those two places. Moreover, the relation of the minimum radius to that during which the emission occurs does not usually exceeds three (for

$R_{0} \geq 2\mu m$.,

wherein

$R_{0}$

is equilibrium radius of the bubble) which is of importance as the contribution to the radiation intensity is proportional to

$R^{2}R^{(4)}(t)R(t)$

(the point shall mean radius derivative over time) and sum of products of lower time derivatives. These conditions result in radiation intensity in

$R_{c}$

which should arrive at measurable values, i.e. radiation decrease in

$R_{c}$

should not be higher than 200.000 times (assuming radiation background at 1 photon/s [10]). But this point, similarly as next points of 3 and 4 require additional studies and publications more detailed and measurements more sizeable.

3. Similarly, sonoluminescence intensity drops more than 200 times as the ambient temperature increases [9]. Considering the light refraction coefficient change over temperature being too low, drop that big cannot be explained by this (differences of 273.16 K to 308.16 K are of some hundredths [16]) unless we include value jump of this coefficient during collapse so as is provided for in [11]. Again, if such jump proves immposible, this effect will be only explainable by means of bubble collapse velocity change as it passes through the real emission place. The question whether the bubble dynamics allows such rapid radiation drop is just justified since, according to experimental data obtained in work of [9], bubble equilibrium radius of

$R_{0}$

incerases as the temperature does, which causes also a slight increase of the bubble radius obtainable during emission (because of modulating pressure drop), so the accessible surface grows for photon couple emissions and the bubble dynamics close to collapse remains practically the same. Taking into account discussion in Point 2, one may come to the conclusion that small changes in bubble pulsations will have no influence on dramatic drop of radiation intensity.

4. How is it possible for sonoluminescence rate to change

$10^{4} - 10^{6}$

times [9], [12] during 50 ps to 1 ns while the relation curve of radius over time seems well approximated by seamlessly stitching together square and linear functions, and for bubble radius to change only slightly over radiation emission time (discussion in Points 2 and 3)?

5. Seeing that bubble surface is responsible only for radiation emission, so how to explain dynamically that the bubble suddenly decelerates to 5 ns —- 10 ns before collapse and light is emitted right then and not during collapse?

6. Furthermore [9], [10], the absence of light emission by the bubble was observed, too. If we explain it by the value jump of the refraction coefficient by abt. 0.3, then it should be proven that such jump is possible by such value as well as demonstrated that the light emission does not accompany it [2], [11].

7. That the theory provides for strong radial component of the bubble radiation towards the biggest active section for emission irrespective of the way it oscillates is not in accordance with experiments [4] wherein not only longitudal but also spherically symmetric radiation distribution is observed. In addition [4], no dependence of flash intensity on the angle between the given sense and any other sense distinguished in the space was found out, but only correlation dependent on the mutual angle between the detectors. Those observations contradict therefore the existence of the direction distinguished by the theory which foresees longitudal radiation distribution even for purely radial oscillations.

8. The

$\gamma$

parameter to define time scale SL is 100 fs to 10 ps [2] in this theory whereas really measured times of SL are to the tune of 50 ps to 1 ns [12], so in extreme case their time scale is over 100 times longer. Can these facts be reconciled with the theory?

9. If the gas is to rule only the bubble dynamics, so is it only this to be applied to explain the Gauss—like pulse shape over time and the existence of very momentary jitter [12]? The very momentary existence of the jitter could be explained by the bubble passing through the minimum, however, this situation does not happen. Should we on the other hand relocate the emission moment to the real place, that is for 5 ns —- 10 ns before reaching minimum [8], then the only places on the curve where the jitter could be generated would be curve bends [8, insert in Fig. 4B](because of zeroing of first radius derivatives over time in its local extremities which represent the every bends), which are, however, too remote from each other over time in relation to the jitter lenght observed. You cannot take the single bend as place for jitter origin for the time—related radius derivatives differ too much on its both sides. As it is not in accordance with the SL impulse course character over time, there remains only a possibility that the dependence line of radius over time [8] is marked with little accuracy and may be "uneven" which could explain the jitter existence.

10. There are some experiments [7] in which isotope effect was observed. To explain it as part of this theory is difficult as the heavier mass of

$He^{4}$

under identical conditions should make bubbles more inert than

$He^{3}$

which would result in the lower speed of bubble subsidence, thus, in consequence, in lower radiation intensity. During experiment, reverse effect is observed when comparing radiation distributions of those gases at 273.16 K and 276.16 K.

11. In the study of [14], Planck distribution was observed for the hydrogen oscillation and rotation spectrum. With the distribution established, a big (2 to 4 times) change value in radiation rate distribution between extreme frequencies and those lying between them, cannot be explained by continuous change of light refraction coefficient over wave length as this change is too small (similarly as in Point 3, it is of the order of some hundredhts [16]). How to explain this phenomenon by a single value jump of this coefficient? It is rather impossible to explain such distribution by oscillation irradiality because of good concordance with theoretic expectations.

12. If we assume that the experiment noise observed [14] being at the noise level of the respective gas contained in the bubble does not originate from the apparatus, then how to explain its existence within this model?

13. In work of [15], two existing light—emitting areas called jets could be photographed against the background of the dark bubble surface (ascertainment of why dark surface and not interior will be discussed in Point 14). In order to explain this fact it would be necessary to prove within this theory that the light refraction coefficient jump is possible, e.g. along bubble circumference, which could explain this effect, and it would be necessary also to determine the conditions for such phenomenon to occur. To this end, equations describing light emission effect will probably have to be tied together with those describing bubble movement dynamics. Furthermore, change should be expalained in the light emission brightness visible on those pictures at the edges of light area as it moves further from the centre.

14. Ibidem [15], thanks to the very quick—shot technique, a picture was obtained to show the radiation moment of on a single coherent bubble surface. A camera was applied to this end with frame shift speed of 300.000 frames/s, so the bubble pulsating in a 7 kHz acoustic wave would have to shrink by about half its radius during

$\sim 3.3 \mu s$

(or duration of a single flash) to result in the effect caused by exposure time being too long in which the non—radiating ball surrounds the light sphere. Since the bubble had the primary radius of 2.6 mm, average collapsing velocity would have to be

$\sim 394 m/s$

in order to reach the required effect. In addition, the fact should be taken into account that for bubble velocity measurement a series of pictures were taken where the effect of the bubble continuously collapsing was obtained implying that the bubble, after having rapidly collapsed, had to return to the vicinity of the former location. This results in an average speed at least twice as higher or abt. 788 m/s. In other words, dramatic collapse and expansion of the bubble would have had to take place in this experiment. Such scenario is, however, little probable as the measured maximum speed of bubble collapsing as obtained from the pictures is abt. 120 m/s or over 6 times less and the bubble shape change is well in accordance with the theory describing this change over time. In order to better know the bubble light—emitting mechanism, one could repeat the experiment of Lauterborn and Bolle for steady state of the bubble. By illuminating it with a maximum 1 ps laser, the exact flash time could be established as against bubble shape changes and then take the picture thereof at the time light is emitted with maximum available speed. If to this end a bubble with large minimum radius

$R_{c} of 10 \mu m$

is chosen, then we will be able by measuring the diameter of the shining area as occured and by comparing it with the bubble radius at the location as established by the measurements to state what area is covered by the light—emitting core as compared to the bubble size. On the other hand, accurate measurements of the time relation of the bubble at the flash point will allow also to establish whether the flash is formed along the bends of this curve or on its slope [8, insert in Fig. 4B]. Should the flash be formed on the curve slope, then in comparison to its practical linearity over time, the fourth derivatives of radius velocity over time being responsible for the radiation would be equal zero as will also all the elements with mixed derivatives. So it would mean a serious blow for quantitative expectations of this theory which requires substantial accelerations to emit radiation [2]. There are many other experimental problems such as dependence of the power of the emitted light on the shape of the vessel in which is the bubble [10], the amplification of the light emitted by the bubble caused by illuminating the bubble by the laser[17], the dependence of the light emitted by the bubble on the temperature (there is the "unexpected" spike in the light distribution emitted by the bubble [6]), the gaussian distribution of the light in time [12], short and long time scale of the emitting light, unability to obtain the Planck's distribution of the light [14], the dependence of the intensity of the light emitted by bubble on the magnetic field [18], the reason of emitting of acoustic wave by the bubble [19] strongly correlated with the emission of the light by the bubble, which are rather immpossible to explain within Mrs. Eberlein's theory. All these problems can be explained by some hypothesis which will be published this year or at the beginnig of the next (if it is approved by the editor) and which couldn't be published earlier for different reasons. This paper and the hypothesis critics are eight years old, but they are still goldies because as one can see in the papers in this field stll the same equations has been using for years and the scientists have been turning roundthem like dog trying to bite his own tail. This paper is an construcyive atempt to break such a situation.

Technical comment: it was impossible for author to set the derivative signgs in the fourth from the top equation. The second and the third terms in this equation should be time derivatives.

References:

[1]N. Marinesco and J.J. Trillat, C. R. Acad. Sci. Paris 196, 858 (1933) , after D.Felipe Gaitan, Lawrence A. Crum, Charles C. Church, and Ronald A. Roy, J. Acoust. Soc. Am. 91, 3166 (1992).

[2]Claudia Eberlein, Phys. Rev. A 53, 2772 (1996).

[3]Claudia Eberlein, Phys. Rev. Lett. 76, 3842 (1996).

[4]C.S. Unnikrishnan and Shomeek Mukhopadhyay, Phys. Rev. Lett. 77, 4690 (1996). Claudia Eberlein, Phys. Rev. Lett. {\bf 77}, 4691 (1996).

[5]Keith Weninger, Seth J. Putterman, and Bradley P. Barber, Phys. Rev. E 54, R2205 (1996).

[6]Robert Hiller, Seth J. Putterman, and Bradley P. Barber, Phys. Rev. Lett. 69, 1182 (1992).

[7]Robert A. Hiller and Seth J. Putterman, Phys. Rev. Lett. 75, 3549 (1995).

[8]Bradley P. Barber and Seth J. Putterman, Phys. Rev. Lett. 69, 3839 (1992).

[9]Bradley P. Barber, C. C. Wu, Ritva Löfstedt, Paul H. Roberts and Seth J. Putterman, Phys. Rev. Lett. 72, 1380 (1994).

[10]D. Felipe Gaitan, Lawrence A. Crum, Charles C. Church, and Ronald A. Roy, J. Acoust. Soc. Am. 91, 3166 (1992).

[11]E. Yablonovitch, Phys. Rev. Lett. 62, 1742 (1989).

[12]Bradley P. Barber, Robert Hiller, Katsuchi Ariaska, Harold Fetterman, and Seth Putterman, J. Acoust. Soc. Am. 91, 3061 (1992).

[13]Ritva Löfstedt, Keith Weninger, Seth Putterman, and Bradley P. Barber, Phys. Rev. E 51, 4400 (1995).

[14]G. E. Caledonia and R. H. Krech, T. D. Wilkerson, R. L. Taylor, G. Birnbaum, Phys. Rev. A 43, 6010 (1991).

[15]W. Lauterborn and H. Bolle, J. Fluid. Mech. (GB) 72, 391 (1975).

[16]The Book of Physical and Chemical Tables, collective authors, 2nd ed. (WNT Warsaw 1977) (In Polish).

[17]A. J. Walton, G. T. Reynolds, Adv. Phys. 33, 595 (1984).

[18] J. B. Young, T. Schmiedel, Woowon Kang, Phys. Rev. Lett. 77, 4816 (1996).

[19]K. R. Weninger, B. P. Barber, J. S. Putterman, Phys. Rev. Lett. 78, 1799 (1997).

This Article was published on 22nd September, 2006 at 10:19:15 and has been viewed 8030 times.

1 Author comment added 24th September, 2006 at 09:08:55

Actually this paper has been given to publication nine years ago to the Physical Review Letters, but some else decided to rejeceted it despite the even weaker critics had passed. The series of papers expalining all the effects of the sonoluminecence had been given into consideration to IoP of the Jagiellonian University in Cracow in 1996 before the Putterman discovered the sound that accompanies the sonoluminescence flash. And this sound wave had been qualitatively predicted by the model half a year earlier before Putterman did his experiment. As you will be able to see almost all confernces dealing with sonoluminescence after 1996 trying to solve all the problems that are solved by this model - All. Thus, I am preparing the cycle of articles devoted to this phenomenon. It will be nice to get some intelligent response to this model by others. But many effects since that time have to be commented thus, it will take a bit of time to do so, but not too much.

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