Who knows the number of cavitation bubbles that can be generated in one second when applying ultrasound. Is there exact data? or order?
Measuring the number of bubbles generated in a cavitation cloud (where both inertial and non-inertial cavitation is occurring) is more challenging that using lower-amplitude acoustic fields to measure the number of long-lived bubbles {and in [1], below).
However it is possible. In 2003 we estimated (from experimental observations) the void fraction of gas present in a strongly cavitating field from the sound speed (see [2], below) to be around 3-4 x 10^(-3) %.
Of course there are many assumptions in this, for example:
-- (i) that this is the spatially averaged value over a sonochemical cell where clearly from the luminescence observations the bubble population is not homogeneous;
-- (ii) that the Mallock-Wood's equation holds (when clearly not all bubbles will be much smaller than resonance, and linearly oscillating, both of which would be the condition for Mallock-Wood's equation - this could be improved upon by iterative improving this starting value by nonlinear calculations of the sound speed, as shown in [3,4] )
-- (iii) that the boundary condition follows the simplified version described in the Appendix of reference [2].
Given the estimate of a void fraction, one can estimate the number of bubbles present (e.g. by assuming they are each around 80-100% of resonance size). It is a little ambiguous to ask 'how many are generated' because of course one must ask 'where does a cavitation bubble come from, and to where does it go?' which brings in questions of nucleation, fragmentation, and coalescence (which can produce large bubbles that do not undergo inertial cavitation and do not affect the sound speed in the same way [3,4]. However if one wishes to say that a cavitation bubble 'lasts' for 1-3 acoustic cycles; see references [5-8]) then from the above void fraction one can estimate the number of inertial cavitation events happening in the cell of a given size recorded in paper [2]. One could combine this with sonoluminescence photon counts from multibubble cavitation fields of this type to estimate the number of photos emitted per cavitation event, indeed combine any of the above estimates with an independent measurement of the number of photons produced per cavitation event, to get which unknown you don't have. The same could be done for biological cell death and sonochemical yield measurements: you can combine the most reliable estimates from this set to estimate the missing data. Of course it is vital that you ensure you are comparing like-with-like in terms of the cavitation field (as Apfel said, "know thy sound field, know thy liquid (and all its contents), know when something happens"): if one took some numbers from an SBSL event, some from the tip of an ultrasonic horn, and some from a spatially extensive sonochemical bioreactor (where my void fraction estimates come from), then you are mixing up different scenarios, which is less reliable than comparing like with like. As an example of the mixing that might occur, in the above example the photon count can be expressed in a variety of different ways, for example coming from a physiotherapeutic ultrasonic device used in vitro [9], flow over a hydrofoil [10] (which is not at all similar to the circumstances under which the void fraction was estimated), or a tank which [11] (whilst at first sight might look similar to the conditions under which the void fraction was measured, actually is undertaken at a much lower ultrasonic frequency than the void fraction measurements]).
Therefore, in closing, estimates can be made, but caution is needed in considering (i) what question is actually being asked; (ii) what are the assumptions in the theory and what are the implications of mismatches between these and the conditions of the experiment; and (iii) if data is used from different experiments, what are the experimental conditions which all the data used are taken.
REFERENCES
[1] Leighton, T.G. (2004) From seas to surgeries, from babbling brooks to baby scans: The acoustics of gas bubbles in liquids, International Journal of Modern Physics B, 18(25), 3267-3314 (doi: 10.1142/S0217979204026494)
[2] Birkin, P.R., Leighton, T.G., Power, J.F., Simpson, M.D., Vincotte, A.M.L. and Joseph, P. (2003) Experimental and theoretical characterisation of sonochemical cells. Part 1. Cylindrical reactors and their use to calculate the speed of sound in aqueous solutions, Journal of Physical Chemistry A, 107, 306-320
[3] Leighton, T.G., Meers, S.D. and White, P.R. (2004) Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics, Proceedings of the Royal Society of London A, 460(2049), 2521-2550 (doi:10.1098/rspa.2004.1298)
[4] Leighton, T.G. (2007) What is ultrasound? Progress in Biophysics and Molecular Biology, 93(1-3), 3-83 [doi:10.1016/j.pbiomolbio.2006.07.026].
[5] Leighton, T.G. (1994) The Acoustic Bubble, Academic Press, 640pages (ISBN 0124419208) figure 4.8 page 310
[6] Birkin, P.R., Offin, D.G. and Leighton, T.G. (2005) Experimental and theoretical characterisation of sonochemical cells. Part 2: Cell disruptors (ultrasonic horn) and cavity cluster collapse, Physical Chemistry Chemical Physics, 7, 530-537
[7] Birkin, P.R., Offin, D.G., Vian, C.J.B. and Leighton, T.G. (2011) Multiple observations of cavitation cluster dynamics to an ultrasonic horn tip, Journal of the Acoustical Society of America, 130(5), 3379-3388 (doi: 10.1121/1.3650536)
[8] Vian, C.J.B., Birkin, P.R. and Leighton, T.G. (2010) Cluster collapse in a cylindrical cell: Correlating multibubble sonoluminescence, acoustic pressure and erosion, The Journal of Physical Chemistry C, 114(39), 16416-16425 (doi: : 10.1021/jp1027977)
[9] Pickworth, M.J.W., Dendy, P.P., Leighton, T.G. and Walton, A.J. (1988) Studies of the cavitational effects of clinical ultrasound by sonoluminescence: 2 Thresholds for sonoluminescence from a therapeutic ultrasound beam and the effect of temperature and duty cycle, Physics in Medicine and Biology, 33(11), 1249-1260
[10] Leighton, T.G., Farhat, M., Field, J.E. and Avellan, F. (2003) Cavitation luminescence from flow over a hydrofoil in a cavitation tunnel, Journal of Fluid Mechanics, 480, 43-60
[11] Leighton, T.G., Birkin, P.R., Hodnett, M., Zeqiri, B., Power, J.F., Price, G.J., Mason, T., Plattes, M., Dezhkunov, N. and Coleman, A.J. (2005) Characterisation of measures of reference acoustic cavitation (COMORAC): An experimental feasibility trial. In A.A. Doinikov, ed. Bubble and Particle Dynamics in Acoustic Fields: Modern Trends and Applications, Research Signpost, Kerala, Research Signpost, 37-94,
Cite
Syed Amir Gilani
Green International University
Acoustic cavitation—the formation and implosive collapse of bubbles—occurs when a liquid is exposed to intense sound. Cavitation can produce white noise, sonochemical reactions, erosion of hard materials, rupture of living cells and the emission of light, or sonoluminescence1, 2. The concentration of energy during the collapse is enormous: the energy of an emitted photon can exceed the energy density of the sound field by about twelve orders of magnitude3, and it has long been predicted that the interior bubble temperature reaches thousands of degrees Kelvin during collapse. But experimental measurements4, 5 of conditions inside cavitating bubbles are scarce, and there have been no studies of interior temperature as a function of experimental parameters. Here we use multi-bubble sonoluminescence from excited states of metal atoms as a spectroscopic probe of temperatures inside cavitating bubbles. The intense atomic emission allows us to change the properties of the gas–vapour mixture within the bubble, and thus vary the effective emission temperature for multi-bubble sonoluminescence from 5,100 to 2,300 K. We observe emission temperatures that are in accord with those expected from compressional heating during cavitation.
Cite
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