Simulating bubble dynamics impacting on obstacles is challenging because of large liquid-to-gas density ratio and complex interface deformation. In this study, a conservative phase-field model, based on a modified Allen–Cahn equation, is employed to accurately capture the bubble interface, and the lattice Boltzmann model is applied to solve the flow field. The bubble rises under the influence of buoyancy force and surface tension force, and complex topology changes, such as rotation, breakup, and squeeze deformation, are predicted in the presence of obstacles. Three dimensionless numbers, including Reynolds, Eötvös, and Morton numbers, are used to characterize bubble dynamics, and two shape indicators, including the revised Blaschke coefficient and the oblateness degree, are introduced to obtain a more systematic assessment of the bubble shape. Effects of flow parameters and obstacle geometries on bubble dynamics impacting on obstacles are investigated to render a quantitative investigation with physical insights. Model extension to the 3D case, the low-viscosity flow and non-pure fluid is further remarked, which can shed light onto future development of physically informed models for predicting the bubble behavior in more real scenarios.

1.
M. C.
Sukop
and
D. T.
Thorne
, Jr.
,
Lattice Boltzmann Modeling an Introduction for Geoscientists and Engineers
(
Springer
,
Heidelberg
,
2007
).
2.
A.
Zhang
,
J.
Du
,
X.
Zhang
,
Z.
Guo
,
Q.
Wang
, and
S.
Xiong
, “
Phase-field modeling of microstructure evolution in the presence of bubble during solidification
,”
Metall. Mater. Trans. A
51
(
3
),
1023
1037
(
2020
).
3.
S.
Wang
,
Z. P.
Guo
,
X. P.
Zhang
,
A.
Zhang
, and
J. W.
Kang
, “
On the mechanism of dendritic fragmentation by ultrasound induced cavitation
,”
Ultrason. Sonochem.
51
,
160
165
(
2019
).
4.
C. W.
Stewart
, “
Bubble interaction in low-viscosity liquids
,”
Int. J. Multiphase Flow
21
(
6
),
1037
1046
(
1995
).
5.
Y.
Sun
and
C.
Beckermann
, “
Phase-field modeling of bubble growth and flow in a Hele–Shaw cell
,”
Int. J. Heat Mass Transfer
53
(
15–16
),
2969
2978
(
2010
).
6.
A.
Zhang
,
Z.
Guo
,
Q.
Wang
, and
S.
Xiong
, “
Three-dimensional numerical simulation of bubble rising in viscous liquids: A conservative phase-field lattice-Boltzmann study
,”
Phys. Fluids
31
(
6
),
063106
(
2019
).
7.
J. G.
Hnat
and
J. D.
Buckmaster
, “
Spherical cap bubbles and skirt formation
,”
Phys. Fluids
19
(
2
),
182
(
1976
).
8.
D.
Bhaga
and
M. E.
Weber
, “
Bubbles in viscous liquids: Shapes, wakes, and velocities
,”
J. Fluid Mech.
105
,
61
85
(
1981
).
9.
T.
Maxworthy
,
C.
Gnann
,
M.
Kurten
, and
F.
Durst
, “
Experiments on the rise of air bubbles in clean viscous liquids
,”
J. Fluid Mech.
321
,
421
441
(
1996
).
10.
T.
Uchiyama
and
Y.
Ishiguro
, “
Experimental study of flow around a circular cylinder inside a bubble plume
,”
Adv. Chem. Eng. Sci.
06
(
03
),
269
280
(
2016
).
11.
M.
Cheng
,
J.
Hua
, and
J.
Lou
, “
Simulation of bubble–bubble interaction using a lattice Boltzmann method
,”
Comput. Fluids
39
(
2
),
260
270
(
2010
).
12.
J.
Hua
and
J.
Lou
, “
Numerical simulation of bubble rising in viscous liquid
,”
J. Comput. Phys.
222
(
2
),
769
795
(
2007
).
13.
Y. Q.
Zu
and
S.
He
, “
Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts
,”
Phys. Rev. E
87
(
4
),
43301
(
2013
).
14.
H. W.
Zheng
,
C.
Shu
, and
Y. T.
Chew
, “
A lattice Boltzmann model for multiphase flows with large density ratio
,”
J. Comput. Phys.
218
(
1
),
353
371
(
2006
).
15.
S.
Osher
and
R. P.
Fedkiw
, “
Level set methods: An overview and some recent results
,”
J. Comput. Phys.
169
(
2
),
463
502
(
2001
).
16.
N.
Van-Tu
and
W.
Park
, “
A volume-of-fluid (VOF) interface-sharpening method for two-phase incompressible flows
,”
Comput. Fluids
152
,
104
119
(
2017
).
17.
A.
Zhang
,
J.
Du
,
Z.
Guo
,
Q.
Wang
, and
S.
Xiong
, “
Conservative phase-field method with a parallel and adaptive-mesh-refinement technique for interface tracking
,”
Phys. Rev. E
100
(
2
),
23305
(
2019
).
18.
L.
Qian
,
Y.
Wei
, and
F.
Xiao
, “
Coupled THINC and level set method: A conservative interface capturing scheme with high-order surface representations
,”
J. Comput. Phys.
373
,
284
303
(
2018
).
19.
N.
Moelans
,
B.
Blanpain
, and
P.
Wollants
, “
An introduction to phase-field modeling of microstructure evolution
,”
CALPHAD—Comput. Coupling Phase Diagrams Thermochem.
32
(
2
),
268
294
(
2008
).
20.
A.
Zhang
,
B.
Jiang
,
Z.
Guo
,
J.
Du
,
Q.
Wang
,
F.
Pan
, and
S.
Xiong
, “
Solution to multiscale and multiphysics problems: A phase-field study of fully coupled thermal-solute-convection dendrite growth
,”
Adv. Theory Simul.
4
(3
),
2000251
(
2021
).
21.
A.
Gupta
and
R.
Kumar
, “
Lattice Boltzmann simulation to study multiple bubble dynamics
,”
Int. J. Heat Mass Transfer
51
(
21–22
),
5192
5203
(
2008
).
22.
A.
Fakhari
and
M. H.
Rahimian
, “
Investigation of deformation and breakup of a falling droplet using a multiple-relaxation-time lattice Boltzmann method
,”
Comput. Fluids
40
(
1
),
156
171
(
2011
).
23.
H.
Liang
,
B. C.
Shi
,
Z. L.
Guo
, and
Z. H.
Chai
, “
Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows
,”
Phys. Rev. E
89
,
53320
(
2014
).
24.
A.
Zhang
,
J.
Du
,
Z.
Guo
,
Q.
Wang
, and
S.
Xiong
, “
Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes
,”
Philos. Mag.
99
(
23
),
2920
2940
(
2019
).
25.
S.
Sakane
,
T.
Takaki
,
M.
Ohno
,
Y.
Shibuta
, and
T.
Aoki
, “
Two-dimensional large-scale phase-field lattice Boltzmann simulation of polycrystalline equiaxed solidification with motion of a massive number of dendrites
,”
Comput. Mater. Sci.
178
,
109639
(
2020
).
26.
A.
Zhang
,
J.
Du
,
Z.
Guo
,
Q.
Wang
, and
S.
Xiong
, “
Abnormal solute distribution near the eutectic triple point
,”
Scr. Mater.
165
,
64
67
(
2019
).
27.
A.
Zhang
,
J.
Du
,
Z.
Guo
, and
S.
Xiong
, “
Lamellar eutectic growth under forced convection: A phase-field lattice-Boltzmann study based on a modified Jackson–Hunt theory
,”
Phys. Rev. E
98
(
4
),
43301
(
2018
).
28.
M.
Alizadeh
,
S. M.
Seyyedi
,
M.
Taeibi Rahni
, and
D. D.
Ganji
, “
Three-dimensional numerical simulation of rising bubbles in the presence of cylindrical obstacles, using lattice Boltzmann method
,”
J. Mol. Liq.
236
,
151
161
(
2017
).
29.
W. Z.
Li
,
B.
Dong
,
Y. J.
Feng
, and
T.
Sun
, “
Numerical simulation of a single bubble sliding over a curved surface and rising process by the lattice Boltzmann method
,”
Numer. Heat Transfer, Part B
65
(
2
),
174
193
(
2014
).
30.
A.
Zhang
,
Z.
Guo
,
B.
Jiang
,
J.
Du
,
C.
Wang
,
G.
Huang
,
D.
Zhang
,
F.
Liu
,
S.
Xiong
, and
F.
Pan
, “
Multiphase and multiphysics modeling of dendrite growth and gas porosity evolution during solidification
,”
Acta Mater.
214
,
117005
(
2021
).
31.
R.
Han
,
A.
Zhang
,
S.
Li
, and
Z.
Zong
, “
Experimental and numerical study of the effects of a wall on the coalescence and collapse of bubble pairs
,”
Phys. Fluids
30
,
042107
(
2018
).
32.
C.
Zhang
,
J.
Li
,
L.
Luo
, and
T.
Qian
, “
Numerical simulation for a rising bubble interacting with a solid wall: Impact, bounce, and thin film dynamics
,”
Phys. Fluids
30
,
112106
(
2018
).
33.
T.
Patel
,
D.
Patel
,
N.
Thakkar
, and
A.
Lakdawala
, “
A numerical study on bubble dynamics in sinusoidal channels
,”
Phys. Fluids
31
(
5
),
052103
(
2019
).
34.
A.
Singla
and
B.
Ray
, “
Effects of surface topography on low Reynolds number droplet/bubble flow through a constricted passage
,”
Phys. Fluids
33
(
1
),
011301
(
2021
).
35.
H.
Han
,
W.
Chen
,
B.
Huang
, and
X.
Fu
, “
Numerical simulation of the influence of particle shape on the mechanical properties of rockfill materials
,”
Eng. Comput.
34
(
7
),
2228
2241
(
2017
).
36.
T.
Krüger
,
H.
Kusumaatmaja
,
A.
Kuzmin
,
O.
Shardt
,
G.
Silva
, and
E. M.
Viggen
,
The Lattice Boltzmann Method: Principles and Practice
(
Springer
,
Cham
,
2017
).
37.
H.
Huang
,
M. C.
Sukop
, and
X.
Lu
,
Multiphase Lattice Boltzmann Methods: Theory and Application
(
Wiley
,
Chichester
,
2015
).
38.
P. L.
Bhatnagar
,
E. P.
Gross
, and
M.
Krook
, “
A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems
,”
Phys. Rev.
94
(
3
),
511
525
(
1954
).
39.
A.
Fakhari
,
M.
Geier
, and
T.
Lee
, “
A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows
,”
J. Comput. Phys.
315
,
434
457
(
2016
).
40.
A.
Zhang
,
S.
Meng
,
Z.
Guo
,
J.
Du
,
Q.
Wang
, and
S.
Xiong
, “
Dendritic growth under natural and forced convection in Al-Cu alloys: From equiaxed to columnar dendrites and from 2D to 3D phase-field simulations
,”
Metall. Mater. Trans. B
50
(
3
),
1514
1526
(
2019
).
41.
L.
Zheng
,
S.
Zheng
, and
Q.
Zhai
, “
Lattice Boltzmann equation method for the Cahn–Hilliard equation
,”
Phys. Rev. E
91
(
1
),
13309
(
2015
).
42.
D. M.
Sharaf
,
A. R.
Premlata
,
M. K.
Tripathi
,
B.
Karri
, and
K. C.
Sahu
, “
Shapes and paths of an air bubble rising in quiescent liquids
,”
Phys. Fluids
29
,
122104
(
2017
).
43.
R.
Krishna
,
M. I.
Urseanu
,
J. M.
van Baten
, and
J.
Ellenberger
, “
Wall effects on the rise of single gas bubbles in liquids
,”
Int. Commun. Heat Mass Transfer
26
(
6
),
781
790
(
1999
).
44.
A.
Karma
, “
Phase-field formulation for quantitative modeling of alloy solidification
,”
Phys. Rev. Lett.
87
(
11
),
115701
(
2001
).
45.
R.
Folch
and
M.
Plapp
, “
Quantitative phase-field modeling of two-phase growth
,”
Phys. Rev. E
72
(
1
),
11602
(
2005
).
46.
M. E.
McCracken
and
J.
Abraham
, “
Multiple-relaxation-time lattice-Boltzmann model for multiphase flow
,”
Phys. Rev. E
71
,
36701
(
2005
).
47.
A.
Fakhari
and
T.
Lee
, “
Multiple-relaxation-time lattice Boltzmann method for immiscible fluids at high Reynolds numbers
,”
Phys. Rev. E
87
(
2
),
23304
(
2013
).
48.
Z.
Feng
and
E. E.
Michaelides
, “
The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems
,”
J. Comput. Phys.
195
(
2
),
602
628
(
2004
).
49.
S.
Santra
,
S.
Mandal
, and
S.
Chakraborty
, “
Phase-field modeling of multicomponent and multiphase flows in microfluidic systems: A review
,”
Int. J. Numer. Methods Heat Fluid Flow
31
,
3089
(
2020
).
50.
D.
Jacqmin
, “
Calculation of two-phase Navier–Stokes flows using phase-field modeling
,”
J. Comput. Phys.
155
(
1
),
96
127
(
1999
).
51.
S.
Santra
,
D. P.
Panigrahi
,
S.
Das
, and
S.
Chakraborty
, “
Shape evolution of compound droplet in combined presence of electric field and extensional flow
,”
Phys. Rev. Fluids
5
,
063602
(
2020
).
52.
P.
Yue
,
J. J.
Feng
,
C.
Liu
, and
J.
Shen
, “
A diffuse-interface method for simulating two-phase flows of complex fluids
,”
J. Fluid Mech.
515
(
515
),
293
317
(
2004
).
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