Predictions for Upscaling Sonoluminescence

Abstract

Only a small fraction of the high-dimensional parameter space that governs the occurrence of stable single-bubble sonoluminescence (SBSL) has been explored so far. We predict that decreasing the acoustic driving frequency f upscales SBSL. More specifically, at f 5 kHz we expect more than 100 times as many photons per flash as at f 20 kHz and a flash width of about 1000 ps. The application of lower frequencies has to be assisted by reducing the partial inert gas pressure of the dissolved gas (e.g., stronger degassing) to maintain diffusive stability of the bubbles.[ S0031-9007(98) Experimentally [2] it was found that an efficient way to achieve more intense light is to cool the water. Decreasing the water temperature from 33 to 2.5 ± C gives nearly 1000 times more photons per pulse. Following the hydrodynamical/chemical approach to SBSL [7][8][9][10], the water temperature dependence was quantitatively accounted for by considering the temperature dependence of the material constants of water [11].In this paper we focus on the upscaling of SBSL by reducing the driving frequency f, a procedure suggested by Apfel [12]. The effect of reducing the frequency is twofold: (i) In the SL regime the dynamics of the bubble radius R͑t͒ is characterized by a long and relatively slow expansion that occurs during the negative pressure phase of the driving, and by a subsequent violent collapse. Because a smaller frequency gives the bubble more time to expand, it leads to a larger expansion ratio R max ͞R 0 (maximum radius divided by ambient radius) and a stronger collapse. Indeed, the example of Fig. 1 shows that, in comparison to frequencies commonly used today in experiment (e.g., f ഠ 20 40 kHz), more violent collapses can be reached (at fixed R 0 ) with smaller f. (ii) For smaller f the threshold of shape instability which limits the SBSL regime [8] is shifted towards larger bubbles which potentially emit more sonoluminescence light. Indeed, experiments with smaller f by Barber and Putterman [13] and by Cordry [14] found brighter SL bubbles. But what is the maximum light intensity which can be expected, and how should one choose the forcing pressure P a and the gas concentration in the liquid to achieve an optimal photon yield? The present study will make quantitative predictions for answers to these questions.Our analysis of upscaled SBSL is based on the hydrodynamical approach to SBSL [7][8][9][10], augmented by an approximate description of the thermal bremsstrahlung of the partially ionized gas inside the bubble [15,16].The bubble is driven by the harmonic driving P͑t͒ 2P a cos 2pft; it responds according to the RayleighPlesset (RP) dynamics [2,8,17,18]. The pressure p͑ ͑ ͑R͑t͒͒ ͒ ͒ inside the bubble is approximated by a spatially homogeneous van der Waals pressure. This approximation is well 1͞f. While in all cases, R 0 4 mm and P a 1.2 atm are the same, the maximum radius R max reached for 5 kHz is almost 7 times larger than for 50 kHz, leading to a more violent collapse. This is demonstrated in the inset which shows ho...

Does Water Vapor Prevent Upscaling Sonoluminescence?

“…The volume of this resonator is approximately 6l corresponding to a resonance frequency of 7.1 kHz. As predicted in [5] degassing down to about 5% of the natural air saturation (monitored through the oxygen concentration) is necessary to achieve stable sonoluminescence. The gas concentration is expressed in terms of the relative argon saturation c Ar ͞c 0,Ar which is the relevant one for sonoluminescence [16,17] and which originates from the 1% argon contained in air.…”

“…Upscaling single-bubble sonoluminescence (SBSL) [1][2][3][4] is of prime importance both for possible application and for understanding the phenomenon. It has been suggested [5] that lowering the acoustical driving frequency from the standard f 20 35 kHz to f ഠ 5 kHz should yield a 100 to 1000 times higher gain of light, due to the larger ambient radius R 0 and the prolonged expansion phase. These numbers are based on the thermal bremsstrahlung model [6][7][8][9]; however, water vapor was not taken into consideration.…”

“…We then extend the theoretical model of Refs. [5,7,14,15] by taking the water vapor into consideration. In this way the flux of vapor and its influence on the temperature can be quantitatively described.…”

Sonoluminescence: how bubbles glow

“…Excellent quantitative agreement between theory and experiment was obtained, thus providing further evidence for the assumption of rare gas recti cation. Also based on the rare gas recti cation model, as another method for upscaling sonoluminescence and increasing the light emission, it was suggested to reduce the frequency of the driving pressure [79]. This would give the bubble more time to expand, thus achieving a larger expansion ratio and a more violent collapse.…”

Sonolumineszenz: Die Lichtblitze in schallgetriebenen Blasen sind thermische Strahlung eines nicht‐schwarzen Körpers

“…Tatsächlich gibt es bereits eine Beobachtung von (dann ja zu erwartenden) deutlich differierenden Pulslängen im Roten und im UV [13] bei besonders niedrigen Umgebungstemperaturen, die heftige Kollapse und also hohe Temperaturen in der Blase begünstigen [14]. Gleichermaßen sollte das so genannte "Hochskalieren" von SBSL zu höheren R 0 und/oder P a , das bei kleineren Antriebsfrequenzen [15] …”