Numerical study of asymmetric breakup behavior of bubbles in Y-shaped branching microchannels

Pan Wen-Tao; Wen Lin; Li Shan-Shan; Pan Zhen-Hai

doi:10.7498/aps.71.20210832

Abstract

Microfluidic technology based on microchannel two-phase flow has been widely used. The precise control of the bubble or droplet size in the channel plays a crucial role in designing the microfluidic systems. In this work, the bubble breakup behavior in Y-shaped microchannel is reconstructed based on the volume of fluid method (VOF), and the effects of bubble dimensionless size (1.2–2.7), outlet flow ratio (1–4) and main channel Reynolds number (100–600) on the bubble breakup behavior are systematically investigated. The bubble asymmetric breakup process is found to be divided into three stages: extension stage, squeeze stage, and rapid pinch-off stage. In the case of small initial bubble size or relatively high outlet flow rate, the bubble does not break, but only experiences the extension stage and the squeezing stage. Four flow patterns of bubble breakup are further revealed for the bubbles with different sizes and outlet flow ratios: tunnel-tunnel breakup, obstruction-obstruction breakup, tunnel-obstruction breakup, and non-breakup. With the increase of outlet flow ratio, the breakup process of the bubble gradually becomes asymmetrical, and the flow pattern shifts along the tunnel-tunnel breakup and the obstruction-obstruction breakup, gradually turns toward the tunnel-obstruction breakup and non-breakup. On this basis, the critical flow ratio of bubble breakup and the variation of daughter bubble volume ratio with outlet flow ratio are obtained for different Reynolds numbers and initial bubble sizes, and the corresponding criterion correlation equation is refined, which can provide theoretical guidance for accurately regulating the daughter bubble size after breakup.

Keywords:

Authors and contacts

1.
School of Perfume and Aroma Technology, Shanghai Institute of Technology, Shanghai 201418, China
2.
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: Li Shan-Shan, liss@sit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51706136) and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, China.

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References

[1]	涂善东, 周帼彦, 于新海 2007 化工进展 26 2 Tu S T, Zhou G Y, Yu X H 2007 Chem. Ind. Eng. Prog. 26 2
[2]	Teh S Y, Lin R, Hung L H, Lee A P 2008 Lab on Chip 8 198 Google Scholar
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[4]	王长亮, 靳遵龙, 王永庆, 王定标 2017 化工进展 36 S1 Wang C L, Jin Z L, Wang Y Q, Wang D B 2017 Chem. Ind. Eng. Prog 36 S1
[5]	乐军, 陈光文, 袁权, 罗灵爱, Hervé L G 2006 化工学报 57 6 Google Scholar Le J, Chen G W, Yuan Q 2006 J. Chem. Ind. Eng. (China) 57 6 Google Scholar
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[7]	Wang H 2019 Langmuir 35 32
[8]	Zhang J Z, Li W 2016 Int. Commun. Heat Mass Transf. 74 1 Google Scholar
[9]	Talimi V, Muzychka Y S, Kocabiyik S 2012 Int. J. Multiphase Flow 39 88104
[10]	Seemann R, Brinkmann M, Pfohl T, Herminghaus S 2012 Rep. Prog. Phys. 75 016601 Google Scholar
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[14]	Tan J, Du L, Xu J H, Wang K, Luo G S 2011 AIChE J. 57 2647 Google Scholar
[15]	刘赵淼, 刘丽昆, 申峰 2014 机械工程学报 50 8 Liu Z M, Liu L K, Shen F 2014 Chin. J. Mech. Eng. 50 8
[16]	王维萌, 马一萍, 王澎, 陈斌 2015 工程热物理学报 36 2 Wang W M, Ma Y P, Wang P, Chen B 2015 J. Eng. Therm. 36 2
[17]	Ma D F, Liang D, Zhu C Y, Fu T T, Ma Y G 2020 Chem. Eng. Sci. 10 1016
[18]	Carlson A, Do-Quang M, Amberg G 2010 Int. J. Multiphase Flow 36 397 Google Scholar
[19]	Samie M, Salari A, Shafii M B 2013 Phys. Rev. E 87 053003 Google Scholar
[20]	Zheng M M, Ma Y L, Jin T M, Wang J T 2016 Microfluid Nanofluid 20 107 Google Scholar
[21]	温宇, 朱春英, 付涛涛, 马友光 2016 高校化学工程学报 30 19 Google Scholar Wen Y, Zhu C Y, Fu T T, Ma Y G 2016 J. Chem. Eng. Chin. Univ. 30 19 Google Scholar
[22]	Calderon A J, Heo Y S, Huh D, Futai N, Takayama S, Fowlkes J B 2006 Appl. Phys. Lett. 89 299
[23]	丛振霞, 朱春英, 付涛涛, 马友光 2014 化工学报 65 93 Google Scholar Cong Z X, Zhu C Y, Fu T T, Ma Y G 2014 J. Chem. Ind. Eng. (China) 65 93 Google Scholar
[24]	Menetrier-Deremble L, Tabeling P 2006 Phys Rev. E 74 035303
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[26]	Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335 Google Scholar
[27]	Fluent, ANSYS FLUENT 17.0: User's Guide, 2016, ANSYS-Fluent Inc., Canonsburg, PA.
[28]	Xu Z Y, Fu T T, Zhu C Y, Jiang S K, Wang K 2019 Electrophoresis 40 376 Google Scholar
[29]	Gupta R, Fletcher D F, Haynes B S 2009 Chem. Eng. Sci. 64 29
[30]	Pan Z H, Weibel J A, Garimella S V 2015 Numerical Heat Transfer, Part A 67 1
[31]	Wang X, Liu Z M, Pang Y 2019 Chem. Eng. Sci. 197 258 Google Scholar
[32]	Wang X, Zhu C, Wu Y, Fu T, Ma Y 2015 Chem. Eng. Sci. 132 128 Google Scholar
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[34]	Leshansky A M, Pismen L M 2009 Phys. Fluids 21 023303 Google Scholar

Cited By

图 1 (a) 孤立气泡通过Y型分支微通道的示意图; (b) Y型结区域的网格模型

Figure 1. (a) Schematic illustration of an isolated bubble traveling through a Y-shaped branching microchannel; (b) mesh generation in Y-junction region.

DownLoad: Full-Size Img PowerPoint

图 2 气液两相流模型的验证: 数值结果与实验结果的比较^[28]

Figure 2. Validation of hydrodynamic model: Comparison between numerical results (by present model) and experimental results^[28]

DownLoad: Full-Size Img PowerPoint

图 3 网格无关性检验: $t^* $ = 27.8时的气泡轮廓

Figure 3. Mesh independence study: Bubble profile at the dimensionless time instant of 27.8.

DownLoad: Full-Size Img PowerPoint

图 4 Y型分支微通道中气泡轮廓的演化　(a) Re = 100, λ = 1; (b) Re = 300, λ = 1; (c) Re = 300, λ = 2; (d) Re = 300, λ = 4

Figure 4. Evolution of bubble profile in Y-junction region: (a) Re = 100, λ = 1; (b) Re = 300, λ = 1; (c) Re = 300, λ = 2; (d) Re = 300, λ = 4.

DownLoad: Full-Size Img PowerPoint

图 5 气泡的4种破裂模式　(a) 隧道-隧道破裂; (b) 阻塞-阻塞破裂; (c) 隧道-阻塞破裂; (d) 不破裂

Figure 5. Different flow patterns of bubble breakup: (a) Tunnel-tunnel breakup; (b) obstruction-obstruction breakup; (c) tunnel-obstruction breakup; (d) non-breakup.

DownLoad: Full-Size Img PowerPoint

图 6 液相的挤压力和剪切力分布　(a) 隧道-隧道破裂; (b) 阻塞-阻塞破裂; (c) 隧道-阻塞破裂

Figure 6. Liquid-phase squeezing pressure and shear force distribution during bubble motion: (a) Tunnel-tunnel breakup; (b) obstruction-obstruction breakup; (c) tunnel-obstruction breakup.

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图 7 不同流量比下气泡的破裂模式相图　(a) λ = 1.0; (b) λ = 1.5; (c) λ = 2.0; (d) λ = 2.5

Figure 7. Bubble breakup modes at different flow ratios: (a) λ = 1.0; (b) λ = 1.5; (c) λ = 2.0; (d) λ = 2.5.

DownLoad: Full-Size Img PowerPoint

图 8 不同流量比(λ)下分支通道中子气泡的体积比(R_v)　(a) $V^* $= 2.7; (b) $V^* $= 2.2; (c) $V^* $= 1.7

Figure 8. Volume ratio (R_v) of daughter bubbles in branching channel with different outlet flow ratio (λ): (a) $V^* $= 2.7; (b) $V^* $= 2.2; (c) $V^* $= 1.7.

DownLoad: Full-Size Img PowerPoint

图 9 不同气泡尺寸下的临界破裂流量比(λ^c)

Figure 9. Critical fracture flow ratio (λ^c) at different bubble volume.

DownLoad: Full-Size Img PowerPoint

表 1 水和空气的物理性质(20 ℃)

Table 1. Physical parameters of water and air (20 ℃)

流体类型	密度/(kg·m^–3)	黏性系数/(Pa·s)	表面张力系数/(N·m^–1)
空气	1.225	0.000018
水	998.2	0.001005	0.07275

DownLoad: CSV

表 2 网格无关性验证: 气泡长度对比

Table 2. Mesh-independent study: Comparison of bubble length.

算例	网格 1		网格 2		网格 3		网格 4
网格数	499890		1003170		1586530		2401453
雷诺数	100	600	100	600	100	600	100	600
气泡长度$l^* $	2.122	2.563	2.196	2.595	2.187	2.589	2.190	2.592
\|误差($l^* $)\|/%	3.11	1.12	0.27	0.12	0.14	0.12	—	—

DownLoad: CSV

表 3 经验公式(11)的拟合参数值

Table 3. Fitting parameter values of empirical formula (11).

	Re
	100	200	300	400	500	600
a₁	1.47	1.45	1.35	1.30	1.25	1.22
b₁	5.0 × 10^–7	1.1 × 10^–7	1.0 × 10^–4	5.8 × 10^–3	4.6 × 10^–3	2.2 × 10^–4
c₁	0.42	0.57	1.15	2.08	2.25	2.65
a₂	0.001	0.001	0.001	0.02	0.02	0.02
b₂	9.9 × 10^–5	1.20	1.58	1.07	0.66	0.81
c₂	0.50	0.98	1.23	2.05	2.24	2.50
a₃	—	0.001	0.001	0.001	0.005	0.010
b₃	—	0.47	–0.36	0.15	0.03	–0.13
c₃	—	0.85	1.00	1.20	1.63	1.98

DownLoad: CSV

表 4 经验公式(12)的拟合参数值

Table 4. Fitting parameter values of empirical formula (12).

	i	j
$V^* $= 1.7	–0.79	0.025
$V^* $= 2.2	–0.44	0.034
$V^* $= 2.7	–1.54	0.054

DownLoad: CSV

[1]	涂善东, 周帼彦, 于新海 2007 化工进展 26 2 Tu S T, Zhou G Y, Yu X H 2007 Chem. Ind. Eng. Prog. 26 2
[2]	Teh S Y, Lin R, Hung L H, Lee A P 2008 Lab on Chip 8 198 Google Scholar
[3]	王琳琳, 李国君, 田辉, 叶阳辉 2011 西安交通大学学报 45 9 Wang L L, Li G J, Tian H, Ye Y H 2011 J. Xi'an Jiaotong. Univ. 45 9
[4]	王长亮, 靳遵龙, 王永庆, 王定标 2017 化工进展 36 S1 Wang C L, Jin Z L, Wang Y Q, Wang D B 2017 Chem. Ind. Eng. Prog 36 S1
[5]	乐军, 陈光文, 袁权, 罗灵爱, Hervé L G 2006 化工学报 57 6 Google Scholar Le J, Chen G W, Yuan Q 2006 J. Chem. Ind. Eng. (China) 57 6 Google Scholar
[6]	梁宏, 柴振华, 施保昌 2016 物理学报 65 204701 Google Scholar Liang H, Cai Z H, Shi B C 2016 Acta Phys. Sin. 65 204701 Google Scholar
[7]	Wang H 2019 Langmuir 35 32
[8]	Zhang J Z, Li W 2016 Int. Commun. Heat Mass Transf. 74 1 Google Scholar
[9]	Talimi V, Muzychka Y S, Kocabiyik S 2012 Int. J. Multiphase Flow 39 88104
[10]	Seemann R, Brinkmann M, Pfohl T, Herminghaus S 2012 Rep. Prog. Phys. 75 016601 Google Scholar
[11]	Squires T M, Quake S R 2005 Rev. Mod. Phys. 77 977 Google Scholar
[12]	Stone H A, Kim S 2001 AIChE J. 47 1250 Google Scholar
[13]	侯璟鑫, 钱刚, 周兴贵 2013 化工学报 64 6 Hou J X, Qian G, Zhou X G 2013 J. Chem. Ind. Eng. (China) 64 6
[14]	Tan J, Du L, Xu J H, Wang K, Luo G S 2011 AIChE J. 57 2647 Google Scholar
[15]	刘赵淼, 刘丽昆, 申峰 2014 机械工程学报 50 8 Liu Z M, Liu L K, Shen F 2014 Chin. J. Mech. Eng. 50 8
[16]	王维萌, 马一萍, 王澎, 陈斌 2015 工程热物理学报 36 2 Wang W M, Ma Y P, Wang P, Chen B 2015 J. Eng. Therm. 36 2
[17]	Ma D F, Liang D, Zhu C Y, Fu T T, Ma Y G 2020 Chem. Eng. Sci. 10 1016
[18]	Carlson A, Do-Quang M, Amberg G 2010 Int. J. Multiphase Flow 36 397 Google Scholar
[19]	Samie M, Salari A, Shafii M B 2013 Phys. Rev. E 87 053003 Google Scholar
[20]	Zheng M M, Ma Y L, Jin T M, Wang J T 2016 Microfluid Nanofluid 20 107 Google Scholar
[21]	温宇, 朱春英, 付涛涛, 马友光 2016 高校化学工程学报 30 19 Google Scholar Wen Y, Zhu C Y, Fu T T, Ma Y G 2016 J. Chem. Eng. Chin. Univ. 30 19 Google Scholar
[22]	Calderon A J, Heo Y S, Huh D, Futai N, Takayama S, Fowlkes J B 2006 Appl. Phys. Lett. 89 299
[23]	丛振霞, 朱春英, 付涛涛, 马友光 2014 化工学报 65 93 Google Scholar Cong Z X, Zhu C Y, Fu T T, Ma Y G 2014 J. Chem. Ind. Eng. (China) 65 93 Google Scholar
[24]	Menetrier-Deremble L, Tabeling P 2006 Phys Rev. E 74 035303
[25]	Lou Q, Li T, Yang M 2019 J. Appl. Phys. 126 034301 Google Scholar
[26]	Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335 Google Scholar
[27]	Fluent, ANSYS FLUENT 17.0: User's Guide, 2016, ANSYS-Fluent Inc., Canonsburg, PA.
[28]	Xu Z Y, Fu T T, Zhu C Y, Jiang S K, Wang K 2019 Electrophoresis 40 376 Google Scholar
[29]	Gupta R, Fletcher D F, Haynes B S 2009 Chem. Eng. Sci. 64 29
[30]	Pan Z H, Weibel J A, Garimella S V 2015 Numerical Heat Transfer, Part A 67 1
[31]	Wang X, Liu Z M, Pang Y 2019 Chem. Eng. Sci. 197 258 Google Scholar
[32]	Wang X, Zhu C, Wu Y, Fu T, Ma Y 2015 Chem. Eng. Sci. 132 128 Google Scholar
[33]	Jullien M C, Tsang Mui Ching M J, Cohen C, Menetrier L, Tabeling P 2009 Phys. Fluids 21 072001 Google Scholar
[34]	Leshansky A M, Pismen L M 2009 Phys. Fluids 21 023303 Google Scholar

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