Surface nanobubbles have potential applications in the manipulation of nanoscale and biological materials, waste-water treatment, and surface cleaning. These spherically capped bubbles of gas can exist in stable diffusive equilibrium on chemically patterned or rough hydrophobic surfaces, under supersaturated conditions. Previous studies have investigated their long-term response to pressure variations, which is governed by the surrounding liquid’s local supersaturation; however, not much is known about their short-term response to rapid pressure changes, i.e., their cavitation dynamics. Here, we present molecular dynamics simulations of a surface nanobubble subjected to an external oscillating pressure field. The surface nanobubble is found to oscillate with a pinned contact line, while still retaining a mostly spherical cap shape. The amplitude–frequency response is typical of an underdamped system, with a peak amplitude near the estimated natural frequency, despite the strong viscous effects at the nanoscale. This peak is enhanced by the surface nanobubble’s high internal gas pressure, a result of the Laplace pressure. We find that accurately capturing the gas pressure, bubble volume, and pinned growth mode is important for estimating the natural frequency, and we propose a simple model for the surface nanobubble frequency response, with comparisons made to other common models for a spherical bubble, a constant contact angle surface bubble, and a bubble entrapped within a cylindrical micropore. This work reveals the initial stages of growth of cavitation nanobubbles on surfaces, common in heterogeneous nucleation, where classical models based on spherical bubble growth break down.

1.
C. E.
Brennen
,
Cavitation and Bubble Dynamics
(
Cambridge University Press
,
2013
).
2.
E. Y.
Lukianova-Hleb
,
X.
Ren
,
R. R.
Sawant
,
X.
Wu
,
V. P.
Torchilin
, and
D. O.
Lapotko
, “
On-demand intracellular amplification of chemoradiation with cancer-specific plasmonic nanobubbles
,”
Nat. Med.
20
,
778
784
(
2014
).
3.
E. Y.
Lukianova-Hleb
,
Y.-S.
Kim
,
I.
Belatsarkouski
,
A. M.
Gillenwater
,
B. E.
O’Neill
, and
D. O.
Lapotko
, “
Intraoperative diagnostics and elimination of residual microtumours with plasmonic nanobubbles
,”
Nat. Nanotechnol.
11
,
525
532
(
2016
).
4.
A.
Delalande
,
S.
Kotopoulis
,
M.
Postema
,
P.
Midoux
, and
C.
Pichon
, “
Sonoporation: Mechanistic insights and ongoing challenges for gene transfer
,”
Gene
525
,
191
199
(
2013
).
5.
A.
Agarwal
,
W. J.
Ng
, and
Y.
Liu
, “
Principle and applications of microbubble and nanobubble technology for water treatment
,”
Chemosphere
84
,
1175
1180
(
2011
).
6.
M.
Dular
,
T.
Griessler-Bulc
,
I.
Gutierrez-Aguirre
,
E.
Heath
,
T.
Kosjek
,
A.
Krivograd Klemenčič
,
M.
Oder
,
M.
Petkovšek
,
N.
Rački
,
M.
Ravnikar
,
A.
Šarc
,
B.
Širok
,
M.
Zupanc
,
M.
Žitnik
, and
B.
Kompare
, “
Use of hydrodynamic cavitation in (waste)water treatment
,”
Ultrason. Sonochem.
29
,
577
588
(
2016
).
7.
F.
Hui
,
B.
Li
,
P.
He
,
J.
Hu
, and
Y.
Fang
, “
Electrochemical fabrication of nanoporous polypyrrole film on HOPG using nanobubbles as templates
,”
Electrochem. Commun.
11
,
639
642
(
2009
).
8.
C.
Huang
,
J.
Jiang
,
M.
Lu
,
L.
Sun
,
E. I.
Meletis
, and
Y.
Hao
, “
Capturing electrochemically evolved nanobubbles by electroless deposition. A facile route to the synthesis of hollow nanoparticles
,”
Nano Lett.
9
,
4297
4301
(
2009
).
9.
D.
Lohse
and
X.
Zhang
, “
Surface nanobubbles and nanodroplets
,”
Rev. Mod. Phys.
87
,
981
1035
(
2015
).
10.
S.
Brems
,
M.
Hauptmann
,
E.
Camerotto
,
A.
Pacco
,
T.-G.
Kim
,
X.
Xu
,
K.
Wostyn
,
P.
Mertens
, and
S.
De Gendt
, “
Nanoparticle removal with megasonics: A review
,”
ECS J. Solid State Sci. Technol.
3
,
N3010
N3015
(
2014
).
11.
E.
Stride
and
N.
Saffari
, “
Microbubble ultrasound contrast agents: A review
,”
Proc. Inst. Mech. Eng., Part H
217
,
429
447
(
2003
).
12.
S.
Martynov
,
E.
Kostson
,
N.
Saffari
, and
E.
Stride
, “
Forced vibrations of a bubble in a liquid-filled elastic vessel
,”
J. Acoust. Soc. Am.
130
,
2700
2708
(
2011
).
13.
M. S.
Plesset
, “
The dynamics of cavitation bubbles
,”
J. Appl. Mech.
16
,
277
282
(
1949
), available at https://resolver.caltech.edu/CaltechAUTHORS:20140808-114249321.
14.
T. B.
Benjamin
and
A. T.
Ellis
, “
The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries
,”
Philos. Trans. R. Soc., A
260
,
221
240
(
1966
).
15.
S.
Zhang
and
J. H.
Duncan
, “
On the nonspherical collapse and rebound of a cavitation bubble
,”
Phys. Fluids
6
,
2352
2362
(
1994
).
16.
P.
Koukouvinis
,
M.
Gavaises
,
O.
Supponen
, and
M.
Farhat
, “
Numerical simulation of a collapsing bubble subject to gravity
,”
Phys. Fluids
28
,
032110
(
2016
).
17.
O.
Supponen
,
D.
Obreschkow
,
M.
Tinguely
,
P.
Kobel
,
N.
Dorsaz
, and
M.
Farhat
, “
Scaling laws for jets of single cavitation bubbles
,”
J. Fluid Mech.
802
,
263
293
(
2016
).
18.
J.
Lombard
,
T.
Biben
, and
S.
Merabia
, “
Kinetics of nanobubble generation around overheated nanoparticles
,”
Phys. Rev. Lett.
112
,
105701
(
2014
).
19.
K.
Manmi
and
Q.
Wang
, “
Acoustic microbubble dynamics with viscous effects
,”
Ultrason. Sonochem.
36
,
427
436
(
2017
).
20.
J.
Dzubiella
, “
Interface dynamics of microscopic cavities in water
,”
J. Chem. Phys.
126
,
194504
(
2007
).
21.
R.
Hołyst
,
M.
Litniewski
, and
P.
Garstecki
, “
Large-scale molecular dynamics verification of the Rayleigh-Plesset approximation for collapse of nanobubbles
,”
Phys. Rev. E
82
,
066309
(
2010
).
22.
G.
Menzl
,
M. A.
Gonzalez
,
P.
Geiger
,
F.
Caupin
,
J. L. F.
Abascal
,
C.
Valeriani
, and
C.
Dellago
, “
Molecular mechanism for cavitation in water under tension
,”
Proc. Natl. Acad. Sci. U. S. A.
113
,
13582
13587
(
2016
).
23.
V. H.
Man
,
M. S.
Li
,
P.
Derreumaux
, and
P. H.
Nguyen
, “
Rayleigh-Plesset equation of the bubble stable cavitation in water: A nonequilibrium all-atom molecular dynamics simulation study
,”
J. Chem. Phys.
148
,
094505
(
2018
).
24.
N.
Ishida
,
T.
Inoue
,
M.
Miyahara
, and
K.
Higashitani
, “
Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy
,”
Langmuir
16
,
6377
6380
(
2000
).
25.
X. H.
Zhang
,
A.
Quinn
, and
W. A.
Ducker
, “
Nanobubbles at the interface between water and a hydrophobic solid
,”
Langmuir
24
,
4756
4764
(
2008
).
26.
Y.
Liu
and
X.
Zhang
, “
Nanobubble stability induced by contact line pinning
,”
J. Chem. Phys.
138
,
014706
(
2013
).
27.
H.
An
,
G.
Liu
,
R.
Atkin
, and
V. S. J.
Craig
, “
Surface nanobubbles in nonaqueous media: Looking for nanobubbles in DMSO, formamide, propylene carbonate, ethylammonium nitrate, and propylammonium nitrate
,”
ACS Nano
9
,
7596
7607
(
2015
).
28.
D.
Lohse
and
X.
Zhang
, “
Pinning and gas oversaturation imply stable single surface nanobubbles
,”
Phys. Rev. E
91
,
031003
(
2015
).
29.
P.
Attard
, “
Pinning down the reasons for the size, shape, and stability of nanobubbles
,”
Langmuir
32
,
11138
11146
(
2016
).
30.
A.
Azevedo
,
R.
Etchepare
,
S.
Calgaroto
, and
J.
Rubio
, “
Aqueous dispersions of nanobubbles: Generation, properties and features
,”
Miner. Eng.
94
,
29
37
(
2016
).
31.
P. E.
Theodorakis
and
Z.
Che
, “
Surface nanobubbles: Theory, simulation, and experiment. A review
,”
Adv. Colloid Interface Sci.
272
,
101995
(
2019
).
32.
B. M.
Borkent
,
S. M.
Dammer
,
H.
Schönherr
,
G. J.
Vancso
, and
D.
Lohse
, “
Superstability of surface nanobubbles
,”
Phys. Rev. Lett.
98
,
204502
(
2007
).
33.
D.
Dockar
,
M. K.
Borg
, and
J. M.
Reese
, “
Mechanical stability of surface nanobubbles
,”
Langmuir
35
,
9325
9333
(
2019
).
34.
M.
Minnaert
, “
XVI. On musical air-bubbles and the sounds of running water
,”
London, Edinburgh Dublin Philos. Mag. J. Sci.
16
,
235
248
(
1933
).
35.
A.
Prosperetti
, “
Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids
,”
J. Acoust. Soc. Am.
61
,
17
27
(
1977
).
36.
A.
Prosperetti
, “
The thermal behaviour of oscillating gas bubbles
,”
J. Fluid Mech.
222
,
587
616
(
1991
).
37.
J. E.
Blue
, “
Resonance of a bubble on an infinite rigid boundary
,”
J. Acoust. Soc. Am.
41
,
369
372
(
1967
).
38.
A.
Prosperetti
, “
Linear oscillations of constrained drops, bubbles, and plane liquid surfaces
,”
Phys. Fluids
24
,
032109
(
2012
).
39.
D. L.
Miller
and
W. L.
Nyborg
, “
Theoretical investigation of the response of gas-filled micropores and cavitation nuclei to ultrasound
,”
J. Acoust. Soc. Am.
73
,
1537
1544
(
1983
).
40.
H.
Gelderblom
,
A. G.
Zijlstra
,
L.
van Wijngaarden
, and
A.
Prosperetti
, “
Oscillations of a gas pocket on a liquid-covered solid surface
,”
Phys. Fluids
24
,
122101
(
2012
).
41.
J. H.
Weijs
,
J. H.
Snoeijer
, and
D.
Lohse
, “
Formation of surface nanobubbles and the universality of their contact angles: A molecular dynamics approach
,”
Phys. Rev. Lett.
108
,
104501
(
2012
).
42.
S.
Maheshwari
,
M.
van der Hoef
,
X.
Zhang
, and
D.
Lohse
, “
Stability of surface nanobubbles: A molecular dynamics study
,”
Langmuir
32
,
11116
11122
(
2016
).
43.
S.
Maheshwari
,
M.
van der Hoef
,
J.
Rodríguez Rodríguez
, and
D.
Lohse
, “
Leakiness of pinned neighboring surface nanobubbles induced by strong gas-surface interaction
,”
ACS Nano
12
,
2603
2609
(
2018
).
44.
Z.
Che
and
P. E.
Theodorakis
, “
Formation, dissolution and properties of surface nanobubbles
,”
J. Colloid Interface Sci.
487
,
123
129
(
2017
).
45.
X.
Zhu
,
R.
Verzicco
,
X.
Zhang
, and
D.
Lohse
, “
Diffusive interaction of multiple surface nanobubbles: Shrinkage, growth, and coarsening
,”
Soft Matter
14
,
2006
2014
(
2018
).
46.
S.
Plimpton
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
47.
S.-T.
Lou
,
Z.-Q.
Ouyang
,
Y.
Zhang
,
X.-J.
Li
,
J.
Hu
,
M.-Q.
Li
, and
F.-J.
Yang
, “
Nanobubbles on solid surface imaged by atomic force microscopy
,”
J. Vac. Sci. Technol., B
18
,
2573
2575
(
2000
).
48.
J. W. G.
Tyrrell
and
P.
Attard
, “
Images of nanobubbles on hydrophobic surfaces and their interactions
,”
Phys. Rev. Lett.
87
,
176104
(
2001
).
49.

While the concentric ring patterning would allow “stick-jump” motion of the contact line, as in our previous work in Ref. 33, for these simulations, where the surface nanobubble was to remain on the same pinning site, this patterning was not essential and the same could be achieved by a single patch of hydrophobic (So) atoms.

50.
A.
Stukowski
, “
Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool
,”
Modell. Simul. Mater. Sci. Eng.
18
,
015012
(
2010
).
51.
V.
Molinero
and
E. B.
Moore
, “
Water modeled as an intermediate element between carbon and silicon
,”
J. Phys. Chem. B
113
,
4008
4016
(
2009
).
52.
B.
Coasne
,
A.
Galarneau
,
F.
Di Renzo
, and
R. J. M.
Pellenq
, “
Molecular simulation of nitrogen adsorption in nanoporous silica
,”
Langmuir
26
,
10872
10881
(
2010
).
53.
R.
Sander
, “
Henry’s law constants
,” in
NIST Chemistry WebBook
, NIST Standard Reference Database Number 69, edited by
P. J.
Linstrom
and
W. G.
Mallard
(
National Institute of Standards and Technology
,
Gaithersburg
,
2017
).
54.
J. L. F.
Abascal
and
C.
Vega
, “
A general purpose model for the condensed phases of water: TIP4P/2005
,”
J. Chem. Phys.
123
,
234505
(
2005
).
55.
E. W.
Lemmon
,
M. O.
McLinden
, and
D. G.
Friend
, “
Thermophysical properties of fluid systems
,” in
NIST Chemistry WebBook
, NIST Standard Reference Database Number 69, edited by
P. J.
Linstrom
and
W. G.
Mallard
(
National Institute of Standards and Technology
,
Gaithersburg
,
2017
).
56.
F. H.
Stillinger
and
T. A.
Weber
, “
Computer simulation of local order in condensed phases of silicon
,”
Phys. Rev. B
31
,
5262
5271
(
1985
).
57.

While it is well known that water and nitrogen are polyatomic molecules, the terms “atoms” and “molecules” will be used interchangeably throughout to denote any single-particle body in the MD simulations.

58.
L.
Martínez
,
R.
Andrade
,
E. G.
Birgin
, and
J. M.
Martínez
, “
PACKMOL: A package for building initial configurations for molecular dynamics simulations
,”
J. Comput. Chem.
30
,
2157
2164
(
2009
).
59.
C. U.
Chan
,
M.
Arora
, and
C.-D.
Ohl
, “
Coalescence, growth, and stability of surface-attached nanobubbles
,”
Langmuir
31
,
7041
7046
(
2015
).
60.
S.
Nosé
, “
A unified formulation of the constant temperature molecular dynamics methods
,”
J. Chem. Phys.
81
,
511
519
(
1984
).
61.
W. G.
Hoover
, “
Canonical dynamics: Equilibrium phase-space distributions
,”
Phys. Rev. A
31
,
1695
1697
(
1985
).
62.

Contact angle is conventionally measured from the liquid side, however, for ease of analysis of the spherical cap shape, the contact angle will refer to the gas side for the remainder of this work.

63.
J. H.
Irving
and
J. G.
Kirkwood
, “
The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics
,”
J. Chem. Phys.
18
,
817
829
(
1950
).
64.
B.
Shi
,
S.
Sinha
, and
V. K.
Dhir
, “
Molecular dynamics simulation of the density and surface tension of water by particle-particle particle-mesh method
,”
J. Chem. Phys.
124
,
204715
(
2006
).
65.
M. S.
Green
, “
Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids
,”
J. Chem. Phys.
22
,
398
413
(
1954
).
66.
R.
Kubo
, “
Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems
,”
J. Phys. Soc. Jpn.
12
,
570
586
(
1957
).
67.
E. M.
Kirova
and
G. E.
Norman
, “
Viscosity calculations at molecular dynamics simulations
,”
J. Phys.: Conf. Ser.
653
,
012106
(
2015
).
68.
R.
Bolaños-Jiménez
,
M.
Rossi
,
D.
Fernandez Rivas
,
C. J.
Kähler
, and
A.
Marin
, “
Streaming flow by oscillating bubbles: Quantitative diagnostics via particle tracking velocimetry
,”
J. Fluid Mech.
820
,
529
548
(
2017
).
69.
S.
Perumanath
,
M. K.
Borg
,
M. V.
Chubynsky
,
J. E.
Sprittles
, and
J. M.
Reese
, “
Droplet coalescence is initiated by thermal motion
,”
Phys. Rev. Lett.
122
,
104501
(
2019
).
70.
P. S.
Epstein
and
M. S.
Plesset
, “
On the stability of gas bubbles in liquid-gas solutions
,”
J. Chem. Phys.
18
,
1505
1509
(
1950
).
71.
A.
Brotchie
and
X. H.
Zhang
, “
Response of interfacial nanobubbles to ultrasound irradiation
,”
Soft Matter
7
,
265
269
(
2011
).
72.

In reality, nitrogen gas is diatomic, however, the single-site nitrogen (N2) model used in these simulations is monatomic.

73.
T.-W.
Huang
,
S.-Y.
Liu
,
Y.-J.
Chuang
,
H.-Y.
Hsieh
,
C.-Y.
Tsai
,
W.-J.
Wu
,
C.-T.
Tsai
,
U.
Mirsaidov
,
P.
Matsudaira
,
C.-S.
Chang
,
F.-G.
Tseng
, and
F.-R.
Chen
, “
Dynamics of hydrogen nanobubbles in KLH protein solution studied with in situ wet-TEM
,”
Soft Matter
9
,
8856
8861
(
2013
).
74.
T. G.
Leighton
, “
The Rayleigh–Plesset equation in terms of volume with explicit shear losses
,”
Ultrasonics
48
,
85
90
(
2008
).
75.
O.
Matsuda
and
O. B.
Wright
, “
Generation and observation of GHz–THz acoustic waves in thin films and microstructures using optical methods
,” in
Frontiers in Optical Methods
, edited by
K.
Shudo
,
I.
Katayama
, and
S.
Ohno
(
Springer
,
Berlin, Heidelberg
,
2014
), Vol. 180, pp.
129
151
.

Supplementary Material

You do not currently have access to this content.