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
Outline
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Introduction
Experiments
Theory
Computations
Discussion
Conclusion
Introduction
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Many practical problems are related to
bubbles in acoustic fields
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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
Introduction
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One-way interactions
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Two-way interaction
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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)
Self-organization
Theory and computations (Kobelev & Ostrovsky, Lauterborn,
Akhatov, Gumerov, Mettin, Ohl, and more)
Very few experiments (mostly observations of acoustic cavitation)
Present study
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New experiments and experimental observation of a selforganization phenomenon (transparency wave) predicted
theoretically
Simplified model describing the phenomenon
Comparisons, insight, discussion
Experimental Setup
Effect (movie)
Effect (frames)
89 kHz
10 ms 160 ms 310 ms 459 ms
209.2 kHz
10 ms 52 ms 92 ms
136.5 ms
Bubble size distribution and
void fraction
Void fractions: 0.3-0.5%
1)
2)
3)
4)
Imaging;
Image filtering
Counting;
Average neighborhood estimation
Theory (assumptions)
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Acoustic amplitude in the region of
bubbly liquid is small
Mass diffusion is neglected
Collisions are negligible
Bubbles are spherical
Time harmonic acoustic field
Theory (linear bubble response)
Bubble response function:
Dissipation:
viscous radiation
resonance radius
thermal
Polytropic exponent:
Theory (linear acoustic field)
Helmholtz equation with space-dependent wavenumber
Multiple scattering theory (point sources, kla << 1, valid even for a few bubbles)
Continuum theory (justified for a large amount of bubbles)
Finite void fraction correction
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!
Computations
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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 4th order
Adams-Bashforth)
Three-dimensional model
One-dimensional model used for comparisons
Model of Experimental Setup
Experimental Box
30 22
Details (y and z projections)
z
Air
Acrylic
Water
15
15
5
5
y
z
0
5
x
x
Transducer
y
Computational domain
z
22
14
0
x
y
20
14
-5
-20
-20
20
x
All sizes in mm
Typical run
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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
500-2500 time steps
Total computational time: a few hours (4 core
PC)
Computational results (1)
Computational results (2)
Good
qualitative
agreement
with
experiments
Comparison with experiments
(void fraction wavefront position)
experiment
t = 160 ms
simulation
What is needed for comparison:
9 Initial void fraction and bubble size distribution
9 Frequency and amplitude of the acoustic field in pure liquid
Discussion
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Why the wave of transparency exist (bubbles
move away from the acoustic source)?
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(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?
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.
Why the weakly nonlinear theory agrees
with strong acoustic field experiments?
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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;
Conclusion
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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.
THANK YOU!