Rectified mass diffusion serves as an important mechanism for dissolution or growth of gas bubbles under acoustic excitation with many applications in acoustical, chemical and biomedical engineering. In this paper, a general approach for predicting rectified mass diffusion phenomenon is proposed based on the equation of bubble motion with liquid compressibility. Nonuniform pressure inside gas bubbles is considered in the approach through employing a well-established framework relating with thermal effects during gas bubble oscillations. Energy dissipation mechanisms (i.e., viscous, thermal, and acoustic dissipation) and surface tension are also included in the approach. Comparing with previous analytical investigations, present approach mainly improves the predictions of rectified mass diffusion in the regions far above resonance and regions with frequencies megahertz and above. Mechanisms for the improvements are shown and discussed together with valid regions and limitations of present approach.

References

1.
Gaitan
,
D. F.
,
Crum
,
L. A.
,
Church
,
C. C.
, and
Roy
,
R. A.
,
1992
, “
Sonoluminescence and Bubble Dynamics for a Single, Stable, Cavitation Bubble
,”
J. Acoust. Soc. Am.
,
91
, pp.
3166
3183
.10.1121/1.402855
2.
Brenner
,
M. P.
,
Lohse
,
D.
,
Oxtoby
,
D.
, and
Dupont
,
T. F.
,
1996
, “
Mechanisms for Stable Single Bubble Sonoluminescence
,”
Phys. Rev. Lett.
,
76
, pp.
1158
1161
.10.1103/PhysRevLett.76.1158
3.
Roberts
,
P. H.
, and
Wu
,
C. C.
,
1998
, “
On Rectified Diffusion and Sonoluminescence
,”
Theor. Comput. Fluid Dyn.
,
10
, pp.
357
372
.10.1007/s001620050069
4.
Crum
,
L. A.
, and
Hansen
,
G. M.
,
1982
, “
Growth of Air Bubbles in Tissue by Rectified Diffusion
,”
Phys. Med. Biol.
,
27
, pp.
413
417
.10.1088/0031-9155/27/3/008
5.
Crum
,
L. A.
,
Daniels
,
S.
,
ter Haar
,
G. R.
, and
Dyson
,
M.
,
1987
, “
Ultrasonically Induced Gas Bubble Production in Agar Based Gels: Part II, Theoretical Analysis
,”
Ulrasound Med. Biol.
,
13
, pp.
541
554
.10.1016/0301-5629(87)90180-3
6.
Zhang
,
Y.
,
2012
, “
Analysis of Radial Oscillations of Gas Bubbles in Newtonian or Viscoelastic Mediums under Acoustic Excitation
,” Ph.D. thesis, University of Warwick, UK.
7.
Crum
,
L. A.
, and
Mao
,
Y.
,
1996
, “
Acoustically Enhanced Bubble Growth at Low Frequencies and Its Implications for Human Diver and Marine Mammal Safety
,”
J. Acoust. Soc. Am.
,
99
, pp.
2898
2907
.10.1121/1.414859
8.
Houser
,
D. S.
,
Howard
,
R.
, and
Ridgway
,
S.
,
2001
, “
Can Diving-Induced Tissue Nitrogen Supersaturation Increase the Chance of Acoustically Driven Bubble Growth in Marine Mammals?
,”
J. Theor. Biol.
,
213
, pp.
183
195
.10.1006/jtbi.2001.2415
9.
Crum
,
L. A.
,
Bailey
,
M. R.
,
Guan
,
J.
,
Hilmo
,
P. R.
,
Kargl
,
S. G.
,
Matula
,
T. J.
, and
Sapozhnikov
,
O. A.
,
2005
, “
Monitoring Bubble Growth in Supersaturated Blood and Tissue Ex Vivo and the Relevance to Marine Mammal Bioeffects
,”
ARLO
,
6
, pp.
214
220
.10.1121/1.1930987
10.
Ilinskii
,
Y. A.
,
Wilson
,
P. S.
, and
Hamilton
,
M. F.
,
2008
, “
Bubble Growth by Rectified Diffusion at High Gas Supersaturation Levels
,”
J. Acoust. Soc. Am.
,
124
, pp.
1950
1955
.10.1121/1.2973235
11.
Jepson
,
P. D.
,
Arbelo
,
M.
,
Deaville
,
R.
,
Patterson
, I
. A. P.
,
Castro
,
P.
,
Baker
,
J. R.
,
Degollada
,
E.
,
Ross
,
H. M.
,
Herráez
,
P.
,
Pocknell
,
A. M.
,
Rodríguez
,
F.
,
Howie
,
F. E.
,
Espinosa
,
A.
,
Reid
,
R. J.
,
Jaber
,
J. R.
,
Martin
, V
.
,
Cunningham
,
A. A.
, and
Fernández
,
A.
,
2003
, “
Gas-Bubble Lesions in Stranded Cetaceans
,”
Nature
,
425
, pp.
575
576
.10.1038/425575a
12.
Cox
,
T. M.
,
Ragen
,
T. J.
,
Read
,
A. J.
,
Vos
,
E.
,
Baird
,
R. W.
,
Balcomb
,
K.
,
Barlow
,
J.
,
Caldwell
,
J.
,
Cranford
,
T.
,
Crum
,
L. A.
,
D'Amico
,
A.
,
D'Spain
,
G.
,
Fernandez
,
A.
,
Finneran
,
J.
,
Gentry
,
R.
,
Gerth
,
W.
,
Gulland
,
F.
,
Hildebrand
,
J.
,
Houser
,
D.
,
Hullar
,
T.
,
Jepson
,
P. D.
,
Ketten
,
D.
,
MacLeod
,
C. D.
,
Miller
,
P.
,
Moore
,
S.
,
Mountain
,
D.
,
Palka
,
D.
,
Ponganis
,
P.
,
Rommel
,
S.
,
Rowles
,
T.
,
Taylor
,
B.
,
Tyack
,
P.
,
Wartzok
,
D.
,
Gisiner
,
R.
,
Mead
,
J.
,
Llowry
,
L.
, and
Benner
,
L.
,
2006
, “
Understanding the Impacts of Anthropogenic Sound on Beaked Whales
,”
J. Cetacean Res. Manage.
,
7
, pp.
177
187
.
13.
Lavon
,
I.
,
Grossman
,
N.
,
Kost
,
J.
,
Kimmel
,
E.
, and
Enden
,
G.
,
2007
, “
Bubble Growth Within the Skin by Rectified Diffusion Might Play a Significant Role in Sonophoresis
,”
J. Controlled Release
,
117
, pp.
246
255
.10.1016/j.jconrel.2006.10.027
14.
Brotchie
,
A.
, and
Zhang
,
X. H.
,
2011
, “
Response of Interfacial Nanobubbles to Ultrasound Irradiation
,”
Soft Matter
,
7
, pp.
265
269
.10.1039/c0sm00731e
15.
Okada
,
K.
,
Kudo
,
N.
,
Hassan
,
M. A.
,
Kondo
,
T.
, and
Yamamoto
,
K.
,
2009
, “
Threshold Curves Obtained Under Various Gaseous Conditions for Free Radical Generation by Burst Ultrasound-Effects of Dissolved Gas, Microbubbles and Gas Transport From the Air
,”
Ultrason. Sonochem.
,
16
, pp.
512
518
.10.1016/j.ultsonch.2008.11.010
16.
Plesset
,
M. S.
, and
Prosperetti
,
A.
,
1977
, “
Bubble Dynamics and Cavitation
,”
Annu. Rev. Fluid Mech.
,
9
, pp.
145
185
.10.1146/annurev.fl.09.010177.001045
17.
Crum
,
L. A.
,
1984
, “
Acoustic Cavitation Series: Part Five Rectified Diffusion
,”
Ultrasonics
,
22
, pp.
215
223
.10.1016/0041-624X(84)90016-7
18.
Ashokkumar
,
M.
,
Lee
,
J.
,
Kentish
,
S.
, and
Grieser
,
F.
,
2007
, “
Bubbles in an Acoustic Field: An Overview
,”
Ultrason. Sonochem.
,
14
, pp.
470
475
.10.1016/j.ultsonch.2006.09.016
19.
Fyrillas
,
M. M.
, and
Szeri
,
A. J.
,
1994
, “
Dissolution or Growth of Soluble Spherical Oscillating Bubbles
,”
J. Fluid Mech.
,
277
, pp.
381
407
.10.1017/S0022112094002806
20.
Harvey
,
E. N.
,
Barnes
,
D. K.
,
McElroy
,
W. D.
,
Whitely
,
A. H.
,
Pease
,
D. C.
, and
Cooper
,
K. W.
,
1944
,
“Bubble Formation in Animals,” J. Cell Comp. Physiol., 24
,
pp. l–40.
21.
Blake
,
F. G.
, Jr.
,
1949
, “
The Onset of Cavitation in Liquids
,” Tech. Memo. No. 12, Acoust. Res. Lab., Harvard University.
22.
Hsieh
D.-Y.
, and
Plesset
M. S.
,
1961
, “
Theory of Rectified Diffusion of Mass Into Gas Bubbles
,”
J. Acoust. Soc. Am.
,
33
, pp.
206
215
.10.1121/1.1908621
23.
Strasberg
,
M.
,
1959
, “
Onset of Ultrasonic Cavitation in Tap Water
,”
J. Acoust. Soc. Am.
,
31
, pp.
163
176
.10.1121/1.1907688
24.
Strasberg
,
M.
,
1961
, “
Rectified Diffusion: Comments on a Paper of Hsieh and Plesset
,”
J. Acoust. Soc. Am.
,
33
, pp.
359
360
.10.1121/1.1908665
25.
Eller
,
A. I.
, and
Flynn
,
H. G.
,
1965
, “
Rectified Diffusion During Nonlinear Pulsations of Cavitation Bubbles
,”
J. Acoust. Soc. Am.
,
37
, pp.
493
503
.10.1121/1.1909357
26.
Plesset
,
M. S.
, and
Zwick
,
S. A.
,
1952
, “
A Nonsteady Heat Diffusion Problem With Spherical Symmetry
,”
J. Appl. Phys.
,
23
, pp.
95
98
.10.1063/1.1701985
27.
Safar
,
M. H.
,
1968
, “
Comment on Papers Concerning Rectified Diffusion of Cavitation Bubbles
,”
J. Acoust. Soc. Am.
,
43
, pp.
1188
1189
.10.1121/1.1910961
28.
Eller
,
A. I.
,
1969
, “
Growth of Bubbles by Rectified Diffusion
,”
J. Acoust. Soc. Am.
,
46
, pp.
1246
1250
.10.1121/1.1911846
29.
Eller
,
A. I.
,
1972
, “
Bubble Growth by Diffusion in an 11-kHz Sound Field
,”
J. Acoust. Soc. Am.
,
52
, pp.
1447
1449
.10.1121/1.1913259
30.
Eller
,
A. I.
,
1975
, “
Effect of Diffusion on Gaseous Cavitation Bubbles
,”
J. Acoust. Soc. Am.
,
57
, pp.
1374
1378
.10.1121/1.380623
31.
Crum
,
L. A.
,
1980
, “
Measurements of the Growth of Air Bubbles by Rectified Diffusion
,”
J. Acoust. Soc. Am.
,
68
, pp.
203
211
.10.1121/1.384624
32.
Crum
,
L. A.
, and
Hansen
,
G. M.
,
1982
, “
Generalized Equations for Rectified Diffusion
,”
J. Acoust. Soc. Am.
,
72
, pp.
1586
1592
.10.1121/1.388494
33.
Church
,
C. C.
,
1988
, “
Prediction of Rectified Diffusion During Nonlinear Bubble Pulsations at Biomedical Frequencies
,”
J. Acoust. Soc. Am.
,
83
, pp.
2210
2217
.10.1121/1.396349
34.
Zhang
,
Y.
, and
Li
,
S. C.
,
2013
, “
Mass Transfer During Radial Oscillations of Gas Bubbles in Viscoelastic Mediums Under Acoustic Excitation
,”
Int. J. Heat Mass Transfer
,
69
, pp.
106
116
.10.1016/j.ijheatmasstransfer.2013.10.019
35.
Zhang
,
Y.
,
2012
, “
Rectified Mass Diffusion of Gas Bubbles in Liquids Under Acoustic Field With Dual Frequencies
,”
Int. Commun. Heat Mass Transfer
,
39
, pp.
1496
1499
.10.1016/j.icheatmasstransfer.2012.10.017
36.
Fyrillas
,
M.
, and
Szeri
,
A. J.
,
1995
, “
Dissolution or Growth of Soluble Spherical Oscillating Bubbles: The Effect of Surfactants
,”
J. Fluid Mech.
,
289
, pp.
295
314
.10.1017/S0022112095001340
37.
Fyrillas
,
M.
, and
Szeri
,
A. J.
,
1996
, “
Surfactant Dynamics and Rectified Diffusion of Microbubbles
,”
J. Fluid Mech.
,
311
, pp.
361
378
.10.1017/S0022112096002637
38.
Lee
,
J.
,
Kentish
,
S.
, and
Ashokkumar
,
M.
,
2005
, “
Effect of Surfactants on the Rate of Growth of an Air Bubble by Rectified Diffusion
,”
J. Phys. Chem. B
,
109
, pp.
14595
14598
.10.1021/jp051758d
39.
Leong
,
T.
,
Wu
,
S.
,
Kentish
,
S.
, and
Ashokkumar
,
M.
,
2010
, “
Growth of Bubbles by Rectified Diffusion in Aqueous Surfactant Solutions
,”
J. Phys. Chem. C
,
114
, pp.
20141
20145
.10.1021/jp107731j
40.
Leong
,
T.
,
Collis
,
J.
,
Manasseh
,
R.
,
Ooi
,
A.
,
Novell
,
A.
,
Bouakaz
,
A.
,
Ashokkumar
,
M.
, and
Kentish
,
S.
,
2011
, “
The Role of Surfactant Headgroup, Chain Length, and Cavitation Microstreaming on the Growth of Bubbles by Rectified Diffusion
,”
J. Phys. Chem. C
,
115
, pp.
24310
24316
.10.1021/jp208862p
41.
Webb
,
I. R.
,
Arora
,
M.
,
Roy
,
R. A.
,
Payne
,
S. J.
, and
Coussios
,
C. C.
,
2010
, “
Dynamics of Gas Bubbles in Time-Variant Temperature Fields
,”
J. Fluid Mech.
,
663
, pp.
209
232
.10.1017/S0022112010003472
42.
Webb
,
I. R.
,
Payne
,
S. J.
, and
Coussios
,
C. C.
,
2011
, “
Effect of Temperature on Rectified Diffusion During Ultrasound-Induced Heating
,”
J. Acoust. Soc. Am.
,
130
, pp.
3450
3457
.10.1121/1.3626153
43.
Devin
,
C.
,
1959
, “
Survey of Thermal, Radiation, and Viscous Damping of Pulsating Air Bubbles in Water
,”
J. Acoust. Soc. Am.
,
31
, pp.
1654
1667
.10.1121/1.1907675
44.
Zhang
,
Y.
, and
Li
,
S. C.
,
2013
, “
Influences of Surface Tension on Heat Transfer Across Bubble-Liquid Interface During Radial Oscillations of Gas Bubbles in Liquids Under Acoustic Excitation
” (submitted).
45.
Prosperetti
,
A.
,
1977
, “
Thermal Effects and Damping Mechanisms in the Forced Radial Oscillations of Gas Bubbles in Liquids
,”
J. Acoust. Soc. Am.
,
61
, pp.
17
27
.10.1121/1.381252
46.
Zhang
,
Y.
, and
Li
,
S. C.
,
2010
, “
Notes on Radial Oscillations of Gas Bubbles in Liquids: Thermal Effects
,”
J. Acoust. Soc. Am.
,
128
, pp.
EL306
EL309
.
47.
Zhang
,
Y.
,
2013
, “
Heat Transfer Across Interfaces of Oscillating Gas Bubbles in Liquids Under Acoustic Excitation
,”
Int. Commun. Heat Mass Transfer
,
43
, pp.
1
7
.10.1016/j.icheatmasstransfer.2013.01.007
48.
Coussios
,
C. C.
, and
Roy
,
R. A.
,
2008
, “
Applications of Acoustics and Cavitation to Noninvasive Therapy and Drug Delivery
,”
Annu. Rev. Fluid Mech.
,
40
, pp.
395
420
.10.1146/annurev.fluid.40.111406.102116
49.
Keller
,
J. B.
, and
Miksis
,
M.
,
1980
, “
Bubble Oscillations of Large Amplitude
,”
J. Acoust. Soc. Am.
,
68
, pp.
628
633
.10.1121/1.384720
50.
Epstein
,
P. S.
, and
Plesset
,
M. S.
,
1950
, “
On the Stability of Gas Bubbles in Liquid-Gas Solutions
,”
J. Chem. Phys.
,
18
, pp.
1505
1509
.10.1063/1.1747520
51.
Zhang
,
Y.
, and
Li
,
S. C.
,
2012
, “
Effects of Liquid Compressibility on Radial Oscillations of Gas Bubbles in Liquids
,”
J. Hydrodyn.
,
24
, pp.
760
766
.10.1016/S1001-6058(11)60301-6
52.
Zhang
,
Y.
,
2013
, “
A Generalized Equation for Scattering Cross Section of Spherical Gas Bubbles Oscillating in Liquids Under Acoustic Excitation
,”
ASME J. Fluids Eng.
,
135
, p.
091301
.10.1115/1.4024128
53.
Wang
,
Q. X.
, and
Blake
,
J. R.
,
2010
, “
Non-Spherical Bubble Dynamics in a Compressible Liquid. Part 1. Travelling Acoustic Wave
,”
J. Fluid Mech.
,
659
, pp.
191
224
.10.1017/S0022112010002430
54.
Wang
,
Q. X.
, and
Blake
,
J. R.
,
2011
, “
Non-Spherical Bubble Dynamics in a Compressible Liquid. Part 2. Acoustic Standing Wave
,”
J. Fluid Mech.
,
679
, pp.
559
581
.10.1017/jfm.2011.149
55.
Shaw
,
S. J.
,
2006
, “
Translation and Oscillation of a Bubble Under Axisymmetric Deformation
,”
Phys. Fluids
,
18
, p.
072104
.10.1063/1.2227047
56.
Shaw
,
S. J.
,
2009
, “
The Stability of a Bubble in a Weakly Viscous Liquid Subject to an Acoustic Traveling Wave
,”
Phys. Fluids
,
21
, p.
022104
.10.1063/1.3076932
You do not currently have access to this content.