This work is motivated by an experiment of microbubble transport in a polymer microfluidic gas generation device where coalescence-induced detachment exhibits. We numerically study three-dimensional microbubble coalescence using the graphics processing unit accelerating free energy lattice Boltzmann method with cubic polynomial boundary conditions. The focus is on the coalescence-induced microbubble detachment (CIMD) in microfluidics. From the experimental observation, we identified that size inequality between two-parent bubbles and the size of the father (large) bubble are key factors to determine if a CIMD will occur. First, the analytical relationship between equilibrium contact angle and dimensionless wetting potential and experimental results of coalescence with and without CIMD are employed for the verification and validation, respectively. From eighteen experimental and computational cases, we derive a new criterion for CIMD: CIMD occurs when the two-parent bubbles are (nearly) equal with a relatively large radius. The underlying mechanism behind this criterion is explored by the time evolution of the velocity vector field, vorticity field, and kinetic energy in the entire coalescence. It is found that the symmetric capillary force drives the formation of vertical flow stream to the horizontal alignment of parent bubbles and the blockage of the downward stream due to the solid interface promotes the intensity of the upward stream. Meanwhile, large-sized parent bubbles transfer a large amount of kinetic energy from the initial free surface energy, which is essential to lead a CIMD in the post-coalescence stage. Such a new criterion is expected to impact the design and optimization of microfluidics in various applications.
References
1.
L.
Zhu
, N.
Kroodsma
, J.
Yeom
, J.
Haan
, M.
Shannon
, and D.
Meng
, “An on-demand microfluidic hydrogen generator with self-regulated gas generation and self-circulated reactant exchange with a rechargeable reservoir
,” Microfluid. Nanofluid.
11
, 569
(2011
).2.
S.
Garimella
, T.
Persoons
, J.
Weibel
, and V.
Gektin
, “Electronics thermal management in information and communications technologies: Challenges and future directions
,” IEEE Trans. Compon., Packag., Manuf. Technol.
7
, 1191
(2017
).3.
C.
Hidrovo
, T.
Kramer
, E.
Wang
, S.
Vigneron
, J.
Steinbrenner
, J.
Koo
, F.
Wang
, D.
Fogg
, R.
Flynn
, E.
Lee
, C.
Cheng
, T.
Kenny
, J.
Eaton
, and K.
Goodson
, “Two-phase microfluidics for semiconductor circuits and fuel cells
,” Heat Transfer Eng.
27
, 53
(2006
).4.
S.
Kadam
, I.
Hassan
, R.
Kumar
, and M. A.
Rahman
, “Bubble dynamics in microchannel: An overview of the state-of-the-art
,” Meccanica
56
, 481
–433
(2021
).5.
H.
Flemming
, “Biofouling in water systems–cases, causes and countermeasures
,” Appl. Microbiol. Biotechnol.
59
, 629
(2002
).6.
A.
Agarwal
, W.
Ng
, and Y.
Liu
, “Cleaning of biologically fouled membranes with self-collapsing microbubbles
,” Biofouling
29
, 69
(2013
).7.
P.
Sharma
, M.
Gibcus
, H. C.
Van DM
, and H.
Busscher
, “Microbubble-induced detachment of coadhering oral bacteria from salivary pellicles
,” Eur. J. Oral Sci.
113
, 326
(2005
).8.
N.
Vyas
, M.
Grewal
, S.
Kuehne
, R.
Sammons
, and A.
Walmsley
, “High speed imaging of biofilm removal from a dental implant model using ultrasonic cavitation
,” Dent. Mater.
36
, 733
–743
(2020
).9.
A.
Georgoulas
, M.
Andredaki
, and M.
Marengo
, “An enhanced VOF method coupled with heat transfer and phase change to characterise bubble detachment in saturated pool boiling
,” Energies
10
, 272
(2017
).10.
L.
Guillaume
, Y.
Luan
, G.
Erik
, D.
Benjamin
, M.
Frits
, D.
Heleen
, L.
Ine
, D. J.
Nico
, and V.
Michel
, “Non-spherical oscillations drive the ultrasound-mediated release from targeted microbubbles
,” Commun. Phys.
1
, 22
(2018
).11.
J.
Chen
, L.
Guo
, X.
Hu
, Z.
Cao
, and Y.
Wang
, “Dynamics of single bubble departure from TiO2 nanorod-array photoelectrode
,” Electrochim. Acta
274
, 57
(2018
).12.
E.
Wang
, S.
Devasenathipathy
, C.
Hidrovo
, D.
Fogg
, J.
Koo
, J.
Santiago
, K.
Goodson
, and T.
Kenny
, “Liquid velocity field measurements in two-phase microchannel convection
,” in Proceedings of the 3rd International Symposium on Two-Phase Flow Modeling and Experimentation
, Pisa, Italy (2004
).13.
J.
Xu
, B.
Chen
, and T.
Xie
, “Experimental and theoretical analysis of bubble departure behavior in narrow rectangular channel
,” Prog. Nucl. Energy
77
, 1
(2014
).14.
Á.
Soto
, T.
Maddalena
, A.
Fraters
, D.
Van Der Meer
, and D.
Lohse
, “Coalescence of diffusively growing gas bubbles
,” J. Fluid Mech.
846
, 143
(2018
).15.
F.
Liu
, G.
Ghigliotti
, J.
Feng
, and C.
Chen
, “Self-propelled jumping upon drop coalescence on Leidenfrost surfaces
,” J. Fluid Mech.
752
, 22
(2014
).16.
S.
Farokhirad
, J.
Morris
, and T.
Lee
, “Coalescence-induced jumping of droplet: Inertia and viscosity effects
,” Phys. Fluids
27
, 102102
(2015
).17.
M.
Moradi
, M. H.
Rahimian
, and S. F.
Chini
, “Coalescence-induced droplet detachment on low-adhesion surfaces: A three-phase system study
,” Phys. Rev. E
99
, 063102
(2019
).18.
X.
Wang
, B.
Xu
, Z.
Chen
, Y.
Yang
, and Q.
Cao
, “Effects of gravitational force and surface orientation on the jumping velocity and energy conversion efficiency of coalesced droplets
,” Microgravity Sci. Technol.
32
, 1185
–1197
(2020
).19.
K.
Wang
, Q.
Liang
, R.
Jiang
, Y.
Zheng
, Z.
Lan
, and X.
Ma
, “Numerical simulation of coalescence-induced jumping of multidroplets on superhydrophobic surfaces: Initial droplet arrangement effect
,” Langmuir
33
, 6258
(2017
).20.
F.
Xie
, G.
Lu
, X.
Wang
, and B.
Wang
, “Coalescence-induced jumping of two unequal-sized nanodroplets
,” Langmuir
34
, 2734
–2740
(2018
).21.
S.
Zhou
, Y.
Cao
, R.
Chen
, T.
Sun
, K.
Fezzaa
, H.
Yu
, and L.
Zhu
, “Study on coalescence dynamics of unequal-sized microbubbles captive on solid substrate
,” Exp. Therm. Fluid Sci.
98
, 362
(2018
).22.
J.
Paulsen
, R.
Carmigniani
, A.
Kannan
, J.
Burton
, and S.
Nagel
, “Coalescence of bubbles and drops in an outer fluid
,” Nat. Commun.
5
, 3182
(2014
).23.
S.
An
, H.
Yu
, Z.
Wang
, R.
Chen
, B.
Kapadia
, and J.
Yao
, “Unified mesoscopic modeling and GPU-accelerated computational method for image-based pore-scale porous media flows
,” Int. J. Heat Mass Transfer
115
, 1192
(2017
).24.
R.
Chen
, H.
Yu
, L.
Zhu
, L.
Taehun
, and R.
Patil
, “Spatial and temporal scaling of unequal microbubble coalescence
,” AIChE J.
63
, 1441
(2017
).25.
H.
Yu
, L.-S.
Luo
, and S.
Girimaji
, “Scalar mixing and chemical reaction simulations using lattice Boltzmann method
,” Int. J. Comput. Eng. Sci.
03
, 73
(2002
).26.
H.
Yu
and S.
Girimaji
, “Study of axis-switching and stability of laminar rectangular jets using lattice Boltzmann method
,” Comput. Math. Appl.
55
, 1611
(2008
).27.
H.
Yu
, X.
Chen
, Z.
Wang
, D.
Deep
, E.
Lima
, Y.
Zhao
, and D.
Teague
, “Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries
,” Phys. Rev. E
89
, 063304
(2014
).28.
Z.
Wang
, N.
Chen
, Y.
Zhao
, and H.
Yu
, “GPU-accelerated lattice Boltzmann method for extracting real biomechanical geometry and volumetric boundary condition
,” Comput. Fluids
115
, 192
(2015
).29.
K. A. K.
Gunstensen
, H. D. H.
Rothman
, S.
Zaleski
, and G.
Zanetti
, “Lattice Boltzmann model of immiscible fluids
,” Phys. Rev. A
43
, 4320
(1991
).30.
X.
Shan
and H.
Chen
, “Lattice Boltzmann model for simulating flows with multiphases and components
,” Phys. Rev. E
47
, 1815
(1993
).31.
X.
He
, X.
Shan
, and G.
Doolen
, “Discrete Boltzmann equation model for nonideal gases
,” Phys. Rev. E
57
, R13
(1998
).32.
M.
Swift
, W.
Osborn
, and J.
Yeomans
, “Lattice Boltzmann simulation of nonideal fluids
,” Phys. Rev. Lett.
75
, 830
(1995
).33.
A.
Mazloomi
, S.
Chikatamarla
, and I.
Karlin
, “Entropic lattice Boltzmann method for multiphase flows
,” Phys. Rev. Lett.
114
, 174502
(2015
).34.
Q.
Kang
, D.
Zhang
, and S.
Chen
, “Displacement of a three-dimensional immiscible droplet in a duct
,” J. Fluid Mech.
545
, 41
(2005
).35.
M.
Schaap
, M.
Porter
, B.
Christensen
, and D.
Wildenschild
, “Comparison of pressure-saturation characteristics derived from computed tomography and lattice Boltzmann simulations
,” Water Resour. Res.
43
, W12S06
, (2007
).36.
M.
Latva-Kokko
and D.
Rothman
, “Static contact angle in lattice Boltzmann models of immiscible fluids
,” Phys. Rev. E
72
, 046701
(2005
).37.
A.
Briant
, A.
Wagner
, and J.
Yeomans
, “Lattice Boltzmann simulations of contact line motion. I. Liquid-gas systems
,” Phys. Rev. E
69
, 031602
(2004
).38.
A.
Dupuis
and J.
Yeomans
, “Lattice Boltzmann modelling of droplets on chemically heterogeneous surfaces
,” Future Gener. Comput. Syst.
20
, 993
(2004
).39.
A.
Yiotis
, J.
Psihogios
, M.
Kainourgiakis
, A.
Papaioannou
, and A.
Stubos
, “A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media
,” Colloids Surf. A
300
, 35
(2007
).40.
L.
Wang
, H.
Huang
, and X.
Lu
, “Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method
,” Phys. Rev. E
87
, 013301
(2013
).41.
H.
Huang
, M.
Sukop
, and X.
Lu
, Multiphase Lattice Boltzmann Methods: Theory and Application
(John Wiley & Sons
, 2015
).42.
L.
Liu
and T.
Lee
, “Wall free energy based polynomial boundary conditions for non-ideal gas lattice Boltzmann equation
,” Int. J. Mod. Phys. C
20
, 1749
(2009
).43.
T.
Lee
and C.-L.
Lin
, “A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
,” J. Comput. Phys.
206
, 16
(2005
).44.
T.
Lee
and L.
Liu
, “Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces
,” J. Comput. Phys.
229
, 8045
(2010
).45.
L.
Baroudi
and T.
Lee
, “Effect of interfacial mass transport on inertial spreading of liquid droplets
,” Phys. Fluids
32
, 032101
(2020
).46.
R.
Chen
, H.
Yu
, J.
Zeng
, and L.
Zhu
, “General power-law temporal scaling for unequal-size microbubble coalescence
,” Phys. Rev. E
101
, 023106
(2020
).47.
R.
Chen
, H.
Yu
, and L.
Zhu
, “Effects of initial conditions on the coalescence of micro-bubbles
,” Proc. Inst. Mech. Eng., Part C
232
, 457
(2018
).48.
T.
Lee
, “Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids
,” Comput. Math. Appl.
58
, 987
(2009
).49.
M. O.
Carpinlioǧlu
and M.
Gündoǧdu
, “A critical review on pulsatile pipe flow studies directing towards future research topics
,” Flow Meas. Instrum.
12
, 163
(2001
).50.
J.
Yang
, D.
Hubball
, M.
Ward
, E.
Rundensteiner
, and W.
Ribarsky
, “Value and relation display: Interactive visual exploration of large datasets with hundreds of dimensions
,” IEEE Trans. Visualization Comput. Graph.
13
, 494
(2007
).51.
J.
Rowlinson
and B.
Widom
, Molecular Theory of Capillarity
(Oxford University Press
, Oxford, UK
, 1989
).52.
D.
Jamet
, O.
Lebaigue
, N.
Coutris
, and J.
Delhaye
, “The second gradient method for the direct numerical simulation of liquid–vapor flows with phase change
,” J. Comput. Phys.
169
, 624
(2001
).53.
Y.
Cao
, J.
Bontrager-Singer
, and L.
Zhu
, “A 3D microfluidic device fabrication method using thermopress bonding with multiple layers of polystyrene film
,” J. Micromech. Microeng.
25
, 065005
(2015
).54.
S.
An
, H.
Yu
, and J.
Yao
, “GPU-accelerated volumetric lattice Boltzmann method for porous media flow
,” J. Pet. Sci. Eng.
156
, 546
(2017
).55.
M. M. I.
Khan
, “Image based computational hemodynamics for non-invasive and patient-specific assessment of arterial stenosis
,” Master's thesis (Purdue University
, 2019
).56.
D.
Chen
, L.
Pan
, and S.
Ren
, “Prediction of bubble detachment diameter in flow boiling based on force analysis
,” Nucl. Eng. Des.
243
, 263
(2012
).57.
J.
Towns
, T.
Cockerill
, M.
Dahan
, I.
Foster
, K.
Gaither
, A.
Grimshaw
, V.
Hazlewood
, S.
Lathrop
, D.
Lifka
, G.
Peterson
, R.
Roskies
, J.
Scott
, and N.
Wilkins-Diehr
, “XSEDE: Accelerating scientific discovery
,” Comput. Sci. Eng.
16
, 62
(2014
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
