The energy released during the bubble collapse process is used for medical and industrial purposes. The present study investigates the effects of electrohydrodynamic force on the collapse phenomenon near the rigid wall and the enhancement of the collapse energy. A solver in the OpenFoam open-source code is developed based on the volume-of-fluid model, in which the effects of compressibility, energy transfer, and electrohydrodynamic force are included. The developed solver is validated against the available experimental data, and a good agreement is seen. The effects of an electric field on the bubble collapse for the range of the electrocapillary number (CaE) of 0–5.76 and normalized wall distance (γ) of 0.8–2.0 are investigated. The results indicate that the bubble is deformed due to the presence of an electric field, and the values obtained for the maximum velocity and pressure are 33 and 35 times the state without the electric field at γ = 2 and CaE = 5.76, respectively. Also, due to the increase in velocity, the maximum shear stress on the rigid wall is increased up to seven times in the absence of the electric field. Therefore, the jet force obtained from the bubble collapse can be enhanced by applying the electric field in the continuous phase fluid. Also, the correlations are proposed to estimate the jet velocity, pressure, and wall shear stress of bubble collapse in the presence of an electric field.

1.
B.
Boyd
and
S.
Becker
, “
Numerical modeling of the acoustically driven growth and collapse of a cavitation bubble near a wall
,”
J. Phys. Fluids
31
,
032102
(
2019
).
2.
W.
Lauterborn
and
A.
Vogel
, “
Shock wave emission by laser generated bubbles
,” in
Bubble Dynamics & Shock Waves
, Shockwaves Vol.
8
(
Springer-Verlag
,
Berlin, Heidelberg
,
2013
), pp.
67
103
.
3.
S. P.
Wang
,
A. M.
Zhang
,
Y. L.
Liu
,
S.
Zhang
, and
P.
Cui
, “
Bubble dynamics and its applications
,”
J. Hydrodyn.
30
,
975
(
2018
).
4.
V.
Farhangmehr
,
M. T.
Shervani-Tabar
,
R.
Parvizi
,
S. W.
Ohl
, and
B. C.
Khoo
, “
Numerical study on ring bubble dynamics in a narrow cylinder with a compliant coating
,”
J. Fluid Dyn. Res.
47
,
025508
(
2015
).
5.
N. N.
Liu
,
A. M.
Zhang
,
Y. L.
Liu
, and
T.
Li
, “
Numerical analysis of the interaction of two underwater explosion bubbles using the compressible Eulerian finite-element method
,”
J. Phys. Fluids
32
,
046107
(
2020
).
6.
A. M.
Zhang
,
P.
Cui
,
J.
Cui
, and
Q. X.
Wang
, “
Experimental study on bubble dynamics subject to buoyancy
,”
J. Fluid Mech.
776
,
137
160
(
2015
).
7.
F.
Denner
, “
The Gilmore-NASG model to predict single-bubble cavitation in compressible liquids
,”
J. Ultrason. Sonochem.
70
,
105307
(
2021
).
8.
A. M.
Zhang
,
S.
Li
, and
J.
Cui
, “
Study on splitting of a toroidal bubble near a rigid boundary
,”
J. Phys. Fluids
27
,
062102
(
2015
).
9.
L.
Rayleigh
, “
On the pressure developed in a liquid during the collapse of a spherical cavity
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
34
,
94
98
(
1917
).
10.
A.
Osterman
,
M.
Dular
, and
B.
Sirok
, “
Numerical simulation of a near wall bubble collapse in an ultrasonic field
,”
J. Fluid Sci. Technol.
4
,
210
221
(
2009
).
11.
E. A.
Brujan
,
G. S.
Keen
,
A.
Vogel
, and
J. R.
Blake
, “
The final stage of the collapse of a cavitation bubble close to a rigid boundary
,”
J. Phys. Fluids
14
,
85
92
(
2002
).
12.
S. J.
Shaw
,
W. P.
Schiffers
,
T. P.
Gentry
, and
D. C.
Emmony
, “
The interaction of a laser-generated cavity with a solid boundary
,”
J. Acoust. Soc. Am.
107
,
3065
(
2000
).
13.
J.
Luo
,
W.
Xu
,
J.
Deng
,
Y.
Zhai
, and
Q.
Zhang
, “
Experimental study on the impact characteristics of cavitation bubble collapse on a wall
,”
J. Water
10
,
1262
(
2018
).
14.
O.
Supponen
,
D.
Obreschkow
, and
M.
Farhat
, “
Rebounds of deformed cavitation bubbles
,”
J. Phys. Rev. Fluids
3
,
103604
(
2018
).
15.
D.
Kroninger
,
K.
Kohler
,
T.
Kurz
, and
W.
Lauterborn
, “
Particle tracking velocimetry of the flow field around a collapsing cavitation bubble
,”
J. Exp. Fluids
48
,
395
408
(
2010
).
16.
J.
Yin
,
Y.
Zhang
,
J.
Zhu
,
L.
Lv
, and
L.
Tian
, “
An experimental and numerical study on the dynamical behaviors of the rebound cavitation bubble near the solid wall
,”
Int. J. Heat Mass Transfer
177
,
121525
(
2021
).
17.
Y.
Liu
and
Y.
Peng
, “
Study on the collapse process of cavitation bubbles near the concave wall by lattice Boltzmann method pseudo-potential model
,”
J. Energ.
13
,
4398
(
2020
).
18.
M.
He
,
A. M.
Zhang
, and
Y. L.
Liu
, “
Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method
,”
J. Theor. Appl. Mech. Lett.
10
,
16
(
2020
).
19.
S.
Li
,
A. M.
Zhang
,
R.
Han
, and
Q. W.
Ma
, “
3D full coupling model for strong interaction between a pulsating bubble and a movable sphere
,”
J. Comput. Phys.
392
,
713
(
2019
).
20.
J.
Cui
,
Z. P.
Chen
,
Q. X.
Wang
,
T. R.
Zhou
, and
C.
Corbett
, “
Experimental studies of bubble dynamics inside a corner
,”
J. Ultrason. Sonochem.
64
,
104951
(
2020
).
21.
H. J.
Sagar
and
O. E.
Moctar
, “
Dynamics of a cavitation bubble between oblique plates
,”
J. Phys. Fluids
35
,
013324
(
2023
).
22.
S. W.
Ohl
,
E.
Klaseboer
, and
B. C.
Khoo
, “
The dynamics of an oscillating bubble near bio-materials
,”
J. Mod. Phys. Lett. B
24
,
1365
1368
(
2010
).
23.
C.
Hirt
and
B.
Nichols
, “
VOF method for the dynamics of free boundaries
,”
J. Comput. Phys.
39
,
201
225
(
1981
).
24.
J.
Welch
,
F.
Harlow
,
J.
Shannon
, and
B.
Daly
, “
The MAC method—A computing technique for solving viscous incompressible transient fluid-flow problems involving free surfaces
,” (
Los Alamos Scientific Laboratory of the University of California
,
2000
).
25.
Z.
Wang
,
H.
Cheng
, and
B.
Ji
, “
Numerical prediction of cavitation erosion risk in an axisymmetric nozzle using a multi-scale approach
,”
J. Phys. Fluids
34
,
062112
(
2022
).
26.
C. T.
Hsiao
,
J. K.
Choi
,
S.
Singh
,
G. L.
Chahine
,
T. A.
Hay
,
Y. A.
Ilinskii
,
E. A.
Zabolotskaya
,
M. F.
Hamilton
,
G.
Sankin
,
F.
Yuan
, and
P.
Zhong
, “
Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications
,”
J. Fluid Mech.
716
,
137
170
(
2013
).
27.
B.
Han
,
K.
Kohler
,
K.
Jungnickel
,
R.
Mettin
,
W.
Lauterborn
, and
A.
Vogel
, “
Dynamics of laser-induced bubble pairs
,”
J. Fluid Mech.
771
,
706
742
(
2015
).
28.
B.
Han
,
L.
Liu
,
X. T.
Zhao
, and
X. W.
Ni
, “
Liquid jet formation through the interactions of a laser-induced bubble and a gas bubble
,”
J. Am. Inst. Phys.
7
,
1
14
(
2017
).
29.
S.
Lakshmanan
,
G. K.
Gupta
,
P.
Avci
,
R.
Chandran
,
M.
Sadasivam
,
A. E. S.
Jorge
, and
M. R.
Hamblin
, “
Physical energy for drug delivery; poration, concentration and activation
,”
Adv. Drug Delivery Rev.
71
,
98
114
(
2014
).
30.
X.
Deng
,
Y.
Ren
,
L.
Hou
,
W.
Liu
,
T.
Jiang
, and
H. J. S.
Jiang
, “
Compound-droplet-pairs-filled hydrogel microfiber for electric-field-induced selective release
,”
Small
15
,
1903098
(
2019
).
31.
C. H.
Chen
,
R. K.
Shah
,
A. R.
Abate
, and
D. A.
Weitz
, “
Janus particles templated from double emulsion droplets generated using microfluidics
,”
Langmuir
25
,
4320
4323
(
2009
).
32.
A.
San Miguel
,
J.
Scrimgeour
,
J. E.
Curtis
, and
S. H.
Behrens
, “
Smart colloidosomes with a dissolution trigger
,”
Soft Matter
6
,
3163
3166
(
2010
).
33.
M.
Huo
and
Y. J. P.
Guo
, “
Electric field enhances shear resistance of polymer melts via orientational polarization in microstructures
,”
Polymers
12
,
335
(
2020
).
34.
J.
Xie
,
J.
Jiang
,
P.
Davoodi
,
M. P.
Srinivasan
, and
C. H.
Wang
, “
Electrohydrodynamic atomization: A two-decade effort to produce and process micro-/nanoparticulate materials
,”
J. Chem. Eng. Sci.
125
,
32
57
(
2015
).
35.
K.
Ahn
,
C.
Kerbage
,
T. P.
Hunt
,
R.
Westervelt
,
D. R.
Link
, and
D.
Weitz
, “
Dielectrophoretic manipulation of drops for high-speed microfluidic sorting devices
,”
J. Appl. Phys. Lett.
88
,
024104
(
2006
).
36.
R.
Song
,
M. S.
Abbasi
, and
J. J. M.
Lee
, “
Fabrication of 3D printed modular microfluidic system for generating and manipulating complex emulsion droplets
,”
Microfluid. J. Nanofluid.
23
,
92
(
2019
).
37.
P.
Dommersnes
,
Z.
Rozynek
,
A.
Mikkelsen
,
R.
Castberg
,
K.
Kjerstad
,
K.
Hersvik
, and
J. O.
Fossum
, “
Active structuring of colloidal armour on liquid drops
,”
J. Nat. Commun.
4
,
2066
(
2013
).
38.
A.
Mikkelsen
,
P.
Dommersnes
,
Z.
Rozynek
,
A.
Gholamipour-Shirazi
, and
J. O.
Fossum
, “
Mechanics of pickering drops probed by electric field–induced stress
,”
J. Mater.
10
,
436
(
2017
).
39.
J. W.
Ha
and
S. M.
Yang
, “
Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field
,”
J. Fluid Mech.
405
,
131
156
(
2000
).
40.
H.
Paknemat
,
A.
Pishevar
, and
P.
Pournaderi
, “
Numerical simulation of drop deformations and breakup modes caused by direct current electric fields
,”
J. Phys. Fluids
24
,
102101
(
2012
).
41.
S. D.
Deshmukh
and
R. M.
Thaokar
, “
Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field
,”
J. Phys. Fluids
24
,
032105
(
2012
).
42.
J. W.
Ha
and
S. M.
Yang
, “
Breakup of a multiple emulsion drop in a uniform electric field
,”
J. Colloid Interface Sci.
213
,
92
100
(
1999
).
43.
J. W.
Ha
and
S. M.
Yang
, “
Rheological responses of oil-in-oil emulsions in an electric field
,”
J. Rheol.
44
,
235
256
(
2000
).
44.
S.
Sankaran
and
D.
Saville
, “
Experiments on the stability of a liquid bridge in an axial electric field
,”
J. Phys. Fluids A
5
,
1081
1083
(
1993
).
45.
C.
Burcham
and
D.
Saville
, “
The electrohydrodynamic stability of a liquid bridge: Microgravity experiments on a bridge suspended in a dielectric gas
,”
J. Fluid Mech.
405
,
37
56
(
2000
).
46.
S.
Mahlmann
and
D. T.
Papageorgiou
, “
Buoyancy-driven motion of a two-dimensional bubble or drop through a viscous liquid in the presence of a vertical electric field
,”
J. Theor. Comput. Fluid Dyn.
23
,
375
399
(
2009
).
47.
T.
Wang
,
H.
Li
,
Y.
Zhang
, and
D.
Shi
, “
Numerical simulation of bubble dynamics in a uniform electric field by the adaptive 3D-voset method
,”
J. Numer. Heat Transfer, Part A
67
,
1352
1369
(
2015
).
48.
Z.
Lu
,
G.
Liu
, and
B.
Wang
, “
Flow structure and heat transfer of electro-thermo-convection in a dielectric liquid layer
,”
J. Phys. Fluids
31
,
064103
(
2019
).
49.
K.
He
,
Z.
Chai
,
L.
Wang
,
B.
Ma
, and
B.
Shi
, “
Numerical investigation of electro–thermo-convection with a solid–liquid interface via the lattice Boltzmann method
,”
J. Phys. Fluids
33
,
037128
(
2021
).
50.
K.
Luo
,
J.
Wu
,
H. L.
Yi
, and
H. P.
Tan
, “
Numerical analysis of two-phase electrohydrodynamic flows in the presence of surface charge convection
,”
J. Phys. Fluids
32
,
123606
(
2020
).
51.
O.
Ozkan
and
V.
Bahadur
, “
Electrohydrodynamic analysis of bubble burst in large Leidenfrost droplets
,”
J. Phys. Fluids
32
,
122002
(
2020
).
52.
M.
Koch
,
C.
Lechner
,
F.
Reuter
,
K.
Kohler
,
R.
Mettin
, and
W.
Lauterborn
, “
Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM
,”
J. Comput. Fluids
126
,
71
90
(
2016
).
53.
T.
Li
,
S.
Wang
,
S.
Li
, and
A. M.
Zhang
, “
Numerical investigation of an underwater explosion bubble based on FVM and VOF
,”
J. Appl. Ocean Res.
74
,
49
58
(
2018
).
54.
E.
Berberovic
,
N. P.
van Hinsberg
,
S.
Jakirli
,
I. V.
Roisman
, and
C.
Tropea
, “
Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution
,”
Phys. Rev. E
79
(3),
036306
(
2009
).
55.
R.
Maddahian
,
M. J.
Cervantes
, and
D. M.
Bucur
, “
Numerical investigation of entrapped air pockets on pressure surges and flow structure in a pipe
,”
J. Hydraul. Res.
58
,
1
13
(
2020
).
56.
H. G.
Weller
, “
A new approach to VOF-based interface capturing methods for incompressible and compressible flow
,”
Report No. TR/HGW 4
(
OpenCFD Ltd
.,
2008
).
57.
B.
Lafaurie
,
C.
Nardone
,
R.
Scardovelli
,
S.
Zaleski
, and
G.
Zanetti
, “
Modelling merging and fragmentation in multiphase flows with SURFER
,”
J. Comput. Phys.
113
,
134
147
(
1994
).
58.
C. J.
Greenshields
and
H. G.
Weller
,
Notes on Computational Fluid Dynamics: General Principles
(
CFD Direct Ltd.
,
2022
).
59.
J.
Yin
,
Y.
Zhang
,
J.
Zhu
,
Y.
Zhang
, and
S.
Li
, “
On the thermodynamic behaviors and interactions between bubble pairs: A numerical approach
,”
J. Ultrason. Sonochem.
70
,
105297
(
2021
).
60.
B.
Shin
,
Y.
Iwata
, and
T.
Ikohagi
, “
Numerical simulation of unsteady cavitating flows using a homogenous equilibrium model
,”
J. Comput. Mech.
30
,
388
395
(
2003
).
61.
T.
Yamamoto
,
S. I.
Hatanaka
, and
S. V.
Komarov
, “
Fragmentation of cavitation bubble in ultrasound field under small pressure amplitude
,”
J. Ultrason. Sonochem.
58
,
104684
(
2019
).
62.
H. T.
Chen
and
R.
Collins
, “
Shock wave propagation past an ocean surface
,”
J. Comput. Phys.
7
,
89
101
(
1971
).
63.
I.
Akhatov
,
O.
Lindau
,
A.
Topolnikov
,
R.
Mettin
,
N.
Vakhitova
, and
W.
Lauterborn
, “
Collapse and rebound of a laser-induced cavitation bubble
,”
J. Phys. Fluids
13
,
2805
(
2001
).
64.
J. R.
Melcher
,
Continuum Electromechanics
(MITR Press, Cambridge, MA,
1981
).
65.
L. D.
Landau
and
E. M.
Lifshitz
,
Electrodynamics of Continuous Media
(
Elsevier Science
,
1984
), Vol.
8
.
66.
C. J.
Greenshields
,
OpenFOAM User Guide Version 4.0
(
OpenFOAM, Foundation Ltd
.,
London
,
2016
).
67.
N.
Samkhaniani
and
M.
Ansari
, “
Numerical simulation of superheated vapor bubble rising in stagnant liquid
,”
J. Heat Mass Transfer
53
,
2885
2899
(
2017
).
68.
D. A.
Hoang
,
V.
van Steijn
,
L. M.
Portela
,
M. T.
Kreutzer
, and
C. R.
Kleijn
, “
Benchmark numerical simulations of segmented two-phase flows in microchannels using the volume of fluid method
,”
J. Comput. Fluids
86
,
28
36
(
2013
).
69.
M.
Ivings
,
D.
Causon
, and
E.
Toro
, “
On Riemann solvers for compressible liquids
,”
Int. J. Numer. Methods Fluids
28
,
395
418
(
1998
).
70.
M. J.
Del Razo
and
R. J.
LeVeque
, “
Computational study of shock waves propagating through air-plastic-water interfaces
,”
Bull. Braz. Math. Soc. New Ser.
47
,
685
700
(
2016
).
71.
I. B.
Celik
,
U.
Ghia
,
P. J.
Roache
, and
C. J.
Freitas
, “
Procedure for estimation and reporting of 26 uncertainty due to discretization in CFD applications
,”
J. Fluids Eng.
130
,
078001
(
2008
).
72.
A.
Philipp
and
W.
Lauterborn
, “
Cavitation erosion by single laser-produced bubbles
,”
J. Fluid Mech.
361
,
75
116
(
1998
).
73.
P.
Koukouvinis
,
G.
Strotos
,
Q.
Zeng
,
S. R.
Gonzalez-Avila
,
A.
Theodorakakos
,
M.
Gavaises
, and
C.
Dieter-Ohl
, “
Parametric investigations of the induced shear stress by a laser generated bubble
,”
J. Langmuir
34
,
6428
(
2018
).
74.
T.
Li
,
A. M.
Zhang
,
S. P.
Wang
,
S.
Li
, and
W. T.
Liu
, “
Bubble interactions and bursting behaviors near a free surface
,”
J. Phys. Fluids
31
,
042104
(
2019
).
75.
edited by
C.
Rolf
and
E. C.
Johan
, “
Response surface methods
,” in
Data Handling in Science and Technology
(
Elsevier
,
2005
), Chap. 12, pp.
243
19
.
76.
B.
Wahdame
et al, “
Analysis of a PEMFC durability test under low humidity conditions and stack behaviour modelling using experimental design techniques
,”
J. Power Sources
182
,
429
440
(
2008
).
77.
I.
Taymaz
,
F.
Akgun
, and
M.
Benli
, “
Application of response surface methodology to optimize and investigate the effects of operating conditions on the performance of DMFC
,”
J. Energy
36
,
1155
1160
(
2011
).
78.
F. G.
Boyaci San
,
I.
Isik-Gulsac
, and
O.
Okur
, “
Analysis of the polymer composite bipolar plate properties on the performance of PEMFC (polymer electrolyte membrane fuel cells) by RSM (response surface methodology)
,”
J. Energy
55
,
1067
1075
(
2013
).
79.
S.
Bozorgmehri
and
M.
Hamedi
, “
Analysis of design parameters in anode-supported solid oxide fuel cells using response surface methodology
,”
J. Fuel Cells
13
,
751
760
(
2013
).
80.
E. E.
Kahveci
and
I.
Taymaz
, “
Experimental investigation on water and heat management in a PEM fuel cell using response surface methodology
,”
J. Hydrogen Energy
39
,
10655
10663
(
2014
).
81.
A.
Martin
,
M.
Reggio
, and
J. Y.
Trepanier
, “
Numerical solution of axisymmetric multi-species compressible gas flow: Towards improved circuit breaker simulation
,”
J. Comput. Fluid Dyn.
22
,
259
271
(
2008
).
82.
D.
Kröninger
, “
Particle-tracking-velocimetry-Messungen an kollabierenden kavitationsblasen
,” Ph.D. thesis (
Drittes Physikalisches Institut Universität Göttingen
,
2008
).
83.
S.
Muller
,
M.
Bachmann
,
D.
Kroninger
,
T.
Kurz
, and
P.
Helluy
, “
Comparison and validation of compressible flow simulations of laser-induced cavitation bubbles
,”
J. Comput. Fluids
38
,
1850
1862
(
2009
).
84.
D. A.
Saville
, “
Electrohydrodynamics: The Taylor–Melcher leaky dielectric model
,”
J. Annu. Rev. Fluid Mech.
29
,
27
64
(
1997
).
85.
G.
Taylor
, “
Studies in electrohydrodynamics—I: The circulation produced in a droplet by electric field
,”
Proc. R. Soc. London Ser. A
291
,
159
166
(
1966
).
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