In the name of God

Single-bubble sonoluminescence from air bubbles

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A. Moshaii, R. Rezaii, R. Sadighi-bonabiK. Imani, M. Silatani

13th Spring Theoretical Physics ConferenceInstitute for Studies in Theoretical Physics and Mathematics

May 3-5, 2006

Contents

1- A review of sonoluminescence phenomenon1- A review of sonoluminescence phenomenon

3- Simulation of sonoluminescence from air bubbles

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2- Bubble dynamics equations and modeling of a gas bubble evolution

2- Bubble dynamics equations and modeling of a gas bubble evolution

Barber et al., Phys. Rep., 1997SL resonator

Resonance condition3/

Sonoluminescence PhenomenonSonoluminescence Phenomenon

Measuring the bubble radius

Light (laser) scattering from the bubble surface

)()()( tVtVtR −∝

Photodetector (PMT) Voltage:

Noise level:

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Barber et al., Phys. Rev. Lett., 1992

a:PMT response (Bubble radius) b :Microphone response (sound radiation)c:Sonoluminescence radiation

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Spectrum of radiation of a typical SL bubble

Barber et al., Phys. Rep., 1997 Hiller et al., Phys. Rev. Lett. , 1992

Special characteristics of SL radiation

)()()( tVtVtR −∝

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PMT voltage of light scattering from bubble surface

Barber et al., Phys. Rev. Lett., 1992

Special characteristics of SL radiation

PMT Voltage:

Noise level:

Four important time scales in the dynamics of a SL bubble:tA ≈ 15 μstB ≈ 5 μstC ≈ 0.5 μstD ≈1 μs

Bubble dynamics description

).PP(dtd

CR

R2

RR4)tsin(PP

)aR()aR(P1R

23RR agao33

33oo2 −

ρ+

ρσ

−ρ

μ−⎥⎦

⎤⎢⎣

⎡ω−−

−−

ρ=+ γ

γ &&&&

Rayleigh Plesset Equation: (RP)

Phase parameters: Pa=1.45 atm, Ro=4.3 μm

Po=1.0 atm ρ=998.0 Kg/m3C=1483.0 m/s σ=0.0728 Kgs2μ=1.0×10-3m/s2 a=Ro/8.745γ=5/3

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Barber et al., Phys. Rep., 1997

Bubble dynamics equations and modeling of a gas bubble evolution

(A. M. and R. Sadighi, PRE, 2004) A hydrochemical ODE model:

1- Bubble radius equations:Gas

LiquidR(t)

( ) ( ) ( ) .PPdtd

C2)tsin(PPP

CR1PP

dtd

CRR

23

C3R1RR

CR1 l22

a0ll

2∞∞ −ρ

μ+λ+

ρ

ω−−⎟⎟⎠

⎞⎜⎜⎝

⎛++−

ρ=⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

&&&&&&

.244RR

RPRRP ggl

σμμ −+=+&&

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Modeling of the gas bubble evolution

,4 2th

gl

lTT

RQ−

= κπ& ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

πχ R

RRlth ,min &

.),(BNV

TKNtRP

tot

gBtotg −

=

3- Heat transfer at the bubble wall:

2- Equation of state of the gas bubble:

pCκχ =

Gas

LiquidR(t)

K: Heat Conductivity CoefficientCp: Heat Capacity

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Modeling of gas bubble evolution

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HNOONNONOHNNHNHNHN

NOHHOOOOHHHOHArtot

NNNNNNNNN

NNNNNNNNNNN

22232

2222222

+++++++++

+++++++++=

.RR

RDminl,l

nnDR4N d

d

ii,o2di ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

π=

−π=

&&

4- Mass transfer at the bubble wall:

The bubble content at the initial condition is assumed to be (4 particles):(H2O :1.55%), (O2 :20.67), (N27 : 76.78%), (Ar: 1%)

Reaction products produced at the end of collapse (15 particles);H, OH, H2, O, HO2, H2O2,

N, NH, NH2, NH3, N2H, NO, NO2, N2O,HNO

0,NNN

particles other all for0 nTk

Pn

dN

dO

dAr

0,i

lB

vOH0,

22

2

===

=

=

&&&

Modeling of gas bubble evolution

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( )[ ] ,TK

EexpTnnnk

Bn1Bn1/Bnexpr

gB

j,fcgBAtotj,f

t

tot

tottotj,f

j,f

j

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎥

⎦

⎤⎢⎣

⎡−

−=

,exp ,,, , ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

gB

jbcgCCtotjbjb TK

ETnnnkr jf

jbjfj rrr ,, −=

., jjij

ci rVN α∑=&

5- Chemical Reactions: Arrhenius Law

Modeling of gas bubble evolution

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6- Energy equation for the bubble evolution:

( )

,NhErV

NNeVPQNTe

T

dii,w

ijj

i

di

cii,th

igi

g

i,th

ig

&

&&&&&

∑+Δ∑+

+∑−−=∂∂

∑

( ) dii,formi,wi

g NehVPQE &&&& +∑+−= ( ) dii,formi,wi

Neh &+∑

( ) ,NeeE iformi,thi

+∑=

Energy loss due to mass diffusion)1Texp(

kTk

2fe

g

l,i

l,iB

lgB

ii,th

−θθ

∑+=

( ) ( )dicii,formi

di

cii,th

ii

g

i,th

ig NNeNNeNT

eTE &&&&&& +∑++∑+

∂∂

∑=

( ) 0ii,w kT2/f1h +=

Pa=1.15 atm, Ro=4.5 μm, ν=26.5 kHz

Numerical simulation results:

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Pa=1.15 atm, Ro=4.5 μm, ν=26.5 kHz

Numerical simulation results:

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Pa=1.15 atm, Ro=4.5 μm, ν=26.5 kHz

Numerical simulation results:

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Contents