Oscillations, Waves, and Interactions - GWDG

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164 W. Lauterborn et al. Figure 28. Images of bubble luminescence taken by a gated ICCD camera. Each pixel value represents an average over 5 recordings, the exposure time per recording being 2.28 ms corresponding to 100 oscillation cycles. Bubbles were shot by a femtosecond laser in a sound field (fa = 44 kHz) at conditions where stable SBSL is possible (partially degassed water, sound amplitude around 1.3 bar). The times after laser breakdown are given for each frame. The results clearly demonstrate how the laser-generated bubbles slowly turn into a stable SBSL bubble. This process is accompanied by a steady increase of the cavitation luminescence up to full SBSL intensity (measurements by T. Wilken).
The single bubble – a hot microlaboratory 165 At present we are not able to look into the interior of bubbles at collapse to measure pressures and temperatures there, notably at the center. However, numerical investigations can be done to get an impression of the phenomena to expect and to couple them to the observed outside effects. One speculation that has been around for quite a long time [28] is that converging microshocks are launched in a bubble collapsing at supersonic speed, which are held responsible for the extreme heating. After the discovery of SBSL these ideas have been reconsidered and elaborated upon. Initial fluid-dynamical calculations revealed astonishing peak temperatures at the bubble center (greater than 1 million Kelvin [29]). Such results are now considered obsolete, and more sophisticated models [30–32] have yielded an interior dynamics that features inward-travelling compression waves, mixture segregation, vapour trapping, chemical reactions and entropy effects, a part of which may actually prevent the formation of focussing shock waves and limit the peak temperatures. Notwithstanding theses successes the numerical modelling of the bubble medium remains a formidable problem. A host of physical and chemical mechnisms have to be taken into account, while the bubble medium undergoes extreme changes of its thermodynamic state. The equation of state, chemical reactions and transport phenomena within the medium and across the phase boundary (heat and mass diffusion, phase change) have to be captured. It is clear that detailed models become complicated and difficult to solve, much more difficult to validate. Concerning the question of shock formation, continuous hydrodynamic solvers have to be used that are able to handle the shock discontinuity. This may become problematic for converging shocks whose real thickness near the origin approaches the size of the region to be modelled. To circumvent this problem, molecular dynamics (MD) simulations of the bubble medium have been proposed [33,34] as an alternative numerical approach. In fact, micrometer-sized bubbles contain relatively few (i. e., on the order of 10 10 ) particles. With suitable coarse-graining, the number of particles (pseudo-molecules) that can be expected to give a faithful representation of reality can be reduced to about one million, a number that is tractable by present-day computers. In our MD model the gas and vapour molecules are treated as hard spheres that bounce around in the bubble. The hard-sphere system can be advanced in time very efficiently by an event-driven algorithm [35]. The bubble wall is prescribed as a spherical container whose radial dynamics is governed by a Rayleigh–Plesset-type differential equation. It is coupled to the MD model by the pressure exerted on the wall by particle impacts. The physics at the phase boundary is implemented by an appropriate set of wall collision rules [34]. The MD approach naturally includes linear and nonlinear diffusive processes as heat conduction or molecular species diffusion. Chemical reactions can be modelled relatively easily by introducing different particle species and modifying collision rules to reflect possible chemical reactions. Being inherently three-dimensional the general case of aspheric collapse can be simulated without redesign of the algorithm when the bubble wall dynamics is known or can be calculated. Figure 29(top) depicts the temperature in the interior of a typical sonoluminescing bubble of radius Rn = 4.5µm driven at 26.5 kHz and 130 kPa as obtained with a MD simulation with 10 7 particles. The bubble contains argon and water vapour. Water dissociation and corresponding chemical reactions have been included in the
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Thomas Kurz, Ulrich Parlitz, and Ud
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erschienen im Universitätsverlag G
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Bibliographische Information der De
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iv Contents Laser speckle metrology
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Oscillations, Waves and Interaction
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Applied physics at the “Dritte”
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noise component [GNE] 5 4 3 2 1 can
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3.4 Transfer to running speech Spee
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3.4.2 Analysis of running speech Sp
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Speech research 33 Area [Pixels] 60
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Speech research 35 [13] D. Michaeli
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Specific signal types in hearing re
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74 D. Ronneberger et al. Mechel fou
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76 D. Ronneberger et al. (flow velo
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78 D. Ronneberger et al. |t + acous
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80 D. Ronneberger et al. Figure 6.
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82 D. Ronneberger et al. Figure 8.
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84 D. Ronneberger et al. (flow velo
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86 D. Ronneberger et al. R / L ⋅
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88 D. Ronneberger et al. e. g. temp
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90 D. Ronneberger et al. 3.2 Qualit
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92 D. Ronneberger et al. As usual t
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94 D. Ronneberger et al. (wavenumbe
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96 D. Ronneberger et al. powers of
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98 D. Ronneberger et al. an increas
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100 D. Ronneberger et al. The term
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102 D. Ronneberger et al. Neverthel
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104 D. Ronneberger et al. [4] J. Br
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106 D. Ronneberger et al. strömung
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108 D. Guicking synchronised tuning
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110 D. Guicking primary noise micro
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112 D. Guicking primary sensor desi
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214 W. Eisenmenger and U. Kaatze 6
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216 W. Eisenmenger and U. Kaatze Pr
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218 A. Vogel, I. Apitz, V. Venugopa
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260 K. D. Hinsch Generally, any of
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262 K. D. Hinsch Figure 1. Monitori
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264 K. D. Hinsch Figure 3. ESPI stu
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266 K. D. Hinsch Figure 4. Deterior
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268 K. D. Hinsch Often, in-plane mo
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270 K. D. Hinsch Figure 7. Optical
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272 K. D. Hinsch Figure 9. Humidity
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274 K. D. Hinsch locations that tak
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276 K. D. Hinsch Figure 13. Map of
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278 K. D. Hinsch References [1] D.
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280 Schreiber not moving along with
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282 Schreiber These properties made
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284 Schreiber Figure 3. The G ring
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286 Schreiber Rotation Rate [rad/s]
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288 Schreiber and it is currently b
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290 Schreiber n1 D A B n Figure 8.
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292 Schreiber Beamwalk [µm] 80.0 7
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294 Schreiber ∆ Perimeter [*10e12
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296 Schreiber and the last term acc
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298 Schreiber Δf [µHz] 100 50 0 -
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300 Schreiber formation of a new wo
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302 Schreiber PSD [*10 16 (rad/s) 2
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304 Schreiber 7.2 The ring laser co
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306 Schreiber Demodulator Signal [V
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308 Schreiber Est. Phase Vel. (m/s)
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310 Schreiber [18] V. Frede and V.
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312 Martin Dressel tice is reduced
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314 Martin Dressel Metallic whisker
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316 Martin Dressel (a) (b) (c) CH 3
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318 Martin Dressel 3.1 Charge densi
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320 Martin Dressel Absorptivity σ
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322 Martin Dressel brought a confir
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324 Martin Dressel a charge disprop
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326 Martin Dressel Conductivity 70
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328 Martin Dressel Reflectivity Con
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330 Martin Dressel References [1] M
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332 Martin Dressel and L. Montgomer
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334 R. Pottel, J. Haller and U. Kaa
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368 U. Kaatze and R. Behrends with
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370 U. Kaatze and R. Behrends Figur
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386 U. Kaatze and R. Behrends of th
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398 U. Kaatze and R. Behrends [6] M
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400 U. Kaatze and R. Behrends [49]
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402 U. Kaatze and R. Behrends (2002
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404 U. Kaatze and R. Behrends Copyr
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406 U. Parlitz here chaos control m
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408 U. Parlitz Figure 2. Amplitude
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410 U. Parlitz 4 10 5 5 (a) (b) (c)
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412 U. Parlitz two-parameter studie
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414 U. Parlitz GN differential opti
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416 U. Parlitz P 1 P 2 P 3 S P 1 P
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418 U. Parlitz Figure 9. Correlatio
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420 U. Parlitz series” where for
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422 U. Parlitz current state future
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424 U. Parlitz tion [69] of two uni
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426 U. Parlitz LD1 LD2 M BS1 BS2 OD
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428 U. Parlitz with a clear tendenc
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430 U. Parlitz (a) y (c) y 40 20 È
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432 U. Parlitz [29] P. Grassberger,
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434 U. Parlitz [76] H. D. I. Abarba
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436 S. Lakämper and C. F. Schmidt
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462 Index basin of attraction, 144
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464 Index cone bubble structure, 19
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466 Index turbulent, 111, 126 fluct
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468 Index LPC, 29 luminescence of b
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470 Index peak factor, 38, 43 Peier
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472 Index laser-induced bubble, 152
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474 Index ultraharmonic resonance,
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