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

Nail A. GumerovUniversity of Maryland, USAIskander S. Akhatov

North Dakota State University, USAClaus-Dieter Ohl

Nanyang Technology University, SingaporeSergei P. Sametov, Maxim V. Khazimullin, and Galia I. Gilmanova

Bashkir State University, Russia

Center for Micro- and Nanoscale Dynamics of Dispersed Systems, Ufa, Russia

Presented on ASME 2013 International Mechanical Engineering Congress Exposition, IMECE2013November 18, 2013, San Diego, CA, USA

This study is supported by the Grant of Ministry of Education and Science of the Russian Federation

http://www.bashedu.ru/

Outline

IntroductionExperimentsTheoryComputations DiscussionConclusion

Introduction

Many practical problems are related to bubbles in acoustic fields

Surface cleaningSonochemistryEnhancement of boiling in microgravitySome micro- and nanotechnologiesMore

General scientific interest, as the problem has very rich physics and new applications can be found as a result of discovery

IntroductionOne-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 interactionSelf-organizationTheory and computations (Kobelev & Ostrovsky, Lauterborn, Akhatov, Gumerov, Mettin, Ohl, and more)Very few experiments (mostly observations of acoustic cavitation)

Present studyNew experiments and experimental observation of a self-organization phenomenon (transparency wave) predicted theoreticallySimplified model describing the phenomenonComparisons, 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

1) Imaging;2) Image filtering3) Counting;4) Average neighborhood estimation

Void fractions: 0.3-0.5%

Theory (assumptions)

Acoustic amplitude in the region of bubbly liquid is smallMass diffusion is neglectedCollisions are negligibleBubbles are sphericalTime harmonic acoustic field

Theory (linear bubble response)

Bubble response function:

Dissipation: viscousradiation thermal Polytropic exponent:

resonance radius

Theory (linear acoustic field)Helmholtz equation with space-dependent wavenumber

Multiple scattering theory (point sources, kla

Nonlinearity provides two-way interaction(closed system of self-organization)

added mass Bjerknes

buoyancy

viscous drag

Bjerknes force here includes both the primary and the secondary forces!

+ boundary conditions for the Helmholtz equation and initial conditions for bubbles

Computations

Particle-in-cell (PIC) method to get local wavenumber and void fractionSecond order finite difference solver for the Helmholtz equationTime marching: explicit scheme (the 4th order Adams-Bashforth)Three-dimensional modelOne-dimensional model used for comparisons

z y

x

z

x

x

y

0

0

15

5

155 5

14

2230

Air

WaterAcrylic

Transducer

Experimental Box Details (y and z projections)

Computational domain

-5

22

z

All sizes in mmx-20 20

y20

-2014

Model of Experimental Setup

Typical runFrequency 89 kHzVoid fraction: 0.4%Bubble size distribution from experimentsTotal number of bubbles in the system: 2,971,256FD grid 41 x 41 x 28 (1 x 1 x 1 mm boxes)X and Y-symmetries applied to accelerate500-2500 time stepsTotal 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)

What is needed for comparison:Initial void fraction and bubble size distributionFrequency and amplitude of the acoustic field in pure liquid

experiment

simulation

t = 160 ms

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?

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?

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 interbubbledistances). So small amplitude theory works well;

ConclusionExistence 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.

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Waves of Acoustically Induced Transparency in Bubbly Liquids:�Theoretical Prediction and Experimental ValidationOutlineIntroductionIntroductionExperimental SetupEffect (frames)Bubble size distribution and void fractionTheory (assumptions)Theory (linear bubble response)Theory (linear acoustic field)Nonlinearity provides two-way interaction�(closed system of self-organization)ComputationsTypical runComputational results (1)Computational results (2)Comparison with experiments�(void fraction wavefront position)DiscussionWhy the wave of acoustically induced transparency exist? Why the weakly nonlinear theory agrees with strong acoustic field experiments?Conclusion