Waves of Acoustically Induced Transparency in Bubbly Liquids: Theoretical Prediction and Experimental Validation

Transcription

1 Waves of Acoustically Induced Transparency in Bubbly Liquids: Theoretical Prediction and Experimental Validation Nail A. Gumerov University of Maryland, USA Iskander S. Akhatov North Dakota State University, USA Claus-Dieter Ohl Nanyang Technology University, Singapore Sergei P. Sametov, Maxim V. Khazimullin, and Galia I. Gilmanova Bashkir State University, Russia Center for Micro- and Nanoscale Dynamics of Dispersed Systems, Ufa, Russia This study is supported by the Grant of Ministry of Education and Science of the Russian Federation Presented on ASME 2013 International Mechanical Engineering Congress Exposition, IMECE2013 November 18, 2013, San Diego, CA, USA

2 Outline Introduction Experiments Theory Computations Discussion Conclusion

3 Introduction Many practical problems are related to bubbles in acoustic fields Surface cleaning Sonochemistry Enhancement of boiling in microgravity Some micro- and nanotechnologies More General scientific interest, as the problem has very rich physics and new applications can be found as a result of discovery

4 Introduction One-way interactions Acoustic field strongly affects bubbles (single bubble dynamics) Bubbles strongly affect acoustic fields (sound in bubbly liquids) Theory and experiments are available (from the mid of the 20th century) Two-way interaction Self-organization Theory and computations (Kobelev & Ostrovsky, Lauterborn, Akhatov, Gumerov, Mettin, Ohl, and more) Very few experiments (mostly observations of acoustic cavitation) Present study New experiments and experimental observation of a selforganization phenomenon (transparency wave) predicted theoretically Simplified model describing the phenomenon Comparisons, insight, discussion

5 Experimental Setup

6 Effect (movie)

7 Effect (frames) 89 khz 10 ms 160 ms 310 ms 459 ms khz 10 ms 52 ms 92 ms ms

8 Bubble size distribution and void fraction Void fractions: % 1) Imaging; 2) Image filtering 3) Counting; 4) Average neighborhood estimation

9 Theory (assumptions) Acoustic amplitude in the region of bubbly liquid is small Mass diffusion is neglected Collisions are negligible Bubbles are spherical Time harmonic acoustic field

10 Theory (linear bubble response) Bubble response function: resonance radius Dissipation: viscous radiation thermal Polytropic exponent:

11 Theory (linear acoustic field) Helmholtz equation with space-dependent wavenumber Multiple scattering theory (point sources, k l a << 1, valid even for a few bubbles) Continuum theory (justified for a large amount of bubbles) Finite void fraction correction

12 Nonlinearity provides two-way interaction (closed system of self-organization) buoyancy added mass Bjerknes viscous drag + boundary conditions for the Helmholtz equation and initial conditions for bubbles Bjerknes force here includes both the primary and the secondary forces!

13 Computations Particle-in-cell (PIC) method to get local wavenumber and void fraction Second order finite difference solver for the Helmholtz equation Time marching: explicit scheme (the 4 th order Adams-Bashforth) Three-dimensional model One-dimensional model used for comparisons

14 z y x Experimental Box Computational domain Model of Experimental Setup Details (y and z projections) z Air Water Acrylic Transducer 0 x y z x -20 y All sizes in mm x

15 Typical run Frequency 89 khz Void fraction: 0.4% Bubble size distribution from experiments Total number of bubbles in the system: 2,971,256 FD grid 41 x 41 x 28 (1 x 1 x 1 mm boxes) X and Y-symmetries applied to accelerate time steps Total computational time: a few hours (4 core PC)

16 Computational results (1)

17 Computational results (2) Good qualitative agreement with experiments

18 Comparison with experiments (void fraction wavefront position) experiment t = 160 ms simulation What is needed for comparison: Initial void fraction and bubble size distribution Frequency and amplitude of the acoustic field in pure liquid

19 Discussion Why the wave of transparency exist (bubbles move away from the acoustic source)? (It is known that the Bjerknes force in a standing wave has a different sign for subresonance and superresonance bubbles). Why the weakly nonlinear theory for bubble oscillations agrees well with experiments for strong acoustic fields?

20 Why the wave of acoustically induced transparency exist? In bubbly liquid: The wave exists because of attenuation! Most important mechanism of attenuation for subresonance bubbles is usually THERMAL DISSIPATION, e.g. properties of gas in bubbles.

21 Why the weakly nonlinear theory agrees with strong acoustic field experiments? Due to small compressibility of the liquid in the region of pure liquid (or with a few bubbles) linear theory for acoustic field is applicable to high enough amplitudes (one-way interaction); In the bulk of bubbly liquid the field attenuate very strongly (within several interbubble distances). So small amplitude theory works well;

22 Conclusion Existence of waves of self-induced acoustic transparency is confirmed experimentally; There is a satisfactory qualitative and quantitative agreement of 3D/1D simulations and experiments, while neglecting 3D effects can decrease the velocity of the waves several times and some effects, like 2D clustering of bubbles on the wave front observed in experiments, cannot be modeled within the 1D approach, while they are clearly present in 3D simulations; The present theory relates the waves of self-induced transparency with attenuation of acoustic waves in bubbly liquids, in which case the Bjerknes force drives bubbles away from the acoustic source independently on their size; More studies are needed, to reveal the role of various mechanisms for bubbles near the wavefront, including strong nonlinearity of oscillations, and collisions. Parametric studies should be conducted.

23 THANK YOU!