Semi-obstructed splitting behaviors of droplet in an asymmetric microfluidic T-junction

Deng Zi-Long; Li Peng-Yu; Zhang Xuan; Liu Xiang-Dong

doi:10.7498/aps.70.20201171

Abstract

Asymmetric droplet splitting is a common method to obtain micro-droplets of different sizes. The study of droplet asymmetric splitting behaviors is of great significance to the fields of biomedicine, energy, chemical industry and food engineering. In this paper, the control flow is introduced into a branch of the T-shaped microchannel to control the pressure distribution in the channel and precisely control the size of the daughter droplets. The method is simple to operate and is a preferred method for asymmetric microfluidic splitting. Existing studies have analyzed droplet splitting modes, critical conditions for flow pattern transitions, and splitting dynamics, but the theoretical prediction of droplet asymmetric splitting behaviors needs to be strengthened. Moreover, compared with tunnel splitting and obstructed splitting, which are more abundantly studied, neither semi-obstructed splitting as an intermediate state of tunnel splitting nor obstructed splitting is analyzed sufficiently. Therefore, a microfluidic T-junction chip is designed and fabricated, with which asymmetrical splitting behaviors of droplets with a tunnel in a microfluidic T-junction are investigated experimentally. The influence of flow rate regulation on the droplet splitting ratio is studied. And a theoretical model is also established to predict the splitting ratio. The results are concluded as follows: 1) the process of asymmetrical droplet splitting is divided into three stages i.e. early squeezing, late squeezing and rapid pinch-off stage. In the early stage of squeezing, the radius of curvature of the droplet neck is sizable, and the additional pressure of interfacial tension is minor. Compared with the additional pressure that hinders neck contraction, the upstream continuous phase driving force is dominant, and the width of the neck changes linearly with time; in the process of late squeezing, the upstream pressure driving effect is still greater than the hindering effect of the additional tension, and the neck width changes exponentially with time; However, in the rapid pinch-off stage, the interfacial tension pointing to the center of the cross section of droplet neck dominates the pinch-off stage. Then, the droplet neck shrinks sharply. 2) Adjusting the flow rate of the branch channel can effectively control the asymmetric splitting ratio of the droplets, and under the current semi-obstructed asymmetric splitting of the droplets, the regulation effect is less affected by the size of the mother droplet, but more affected by the capillary number. 3) The prediction model of droplet splitting ratio based on the pressure drop model can effectively predict the droplet splitting ratio.

Keywords:

Authors and contacts

1.
Key Laboratory of Energy Thermal Conversion and Control, Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China
2.
College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China

Corresponding author: Liu Xiang-Dong, liuxd@yzu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51725602, 51906039), the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK20180405, BK20180102), and the Fundamental Research Funds for the Central Universities (Grant No. 2242019k1G008)

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References

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[2]	Wang J, Gao W, Zhang H, Zou M H, Chen Y P, Zhao Y J 2018 Sci. Adv. 4 eaat7392 Google Scholar
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图 1 微流控芯片结构　(a)示意图, I-流动聚焦微通道, II-辅助微通道, III-T型分裂微通道, IV-调控微通道; (b)实物图, 其中Q_c为连续相体积流量, Q_d为离散相体积流量, Q_f为辅助流量, Q_t为调控流量

Figure 1. Geometric structure of the microfluidic chip: (a) Schematic diagram, I-flow focusing microchannel, II-T-shaped splitting microchannel, III-tuning microchannel; (b) actual chip, Q_c is volumetric flow rate of continuous phase, Q_d is volumetric flow rate of dispersed phase, Q_f is volumetric flow rate of supporting continuous phase, Q_t is volumetric flow rate of controlling continuous phase

DownLoad: Full-Size Img PowerPoint

图 2 液滴半阻塞不对称分裂示意图(u为流体速度, l_m为母液滴长度, w为微通道宽度, Δx为子液滴头部位移, d为液滴颈部宽度, l_d为子液滴长度, l_c为子液滴间距)

Figure 2. Schematic of droplet asymmetrical splitting with a tunnel in a T-junciton (u is velocity of the fluid, l_m is length of the mother droplet, w is width of the microchannel, Δx is displacement of the head of the daughter droplets, d is width of the droplet neck, l_d is length of the daughter droplet, l_c is interval of daughter droplets).

DownLoad: Full-Size Img PowerPoint

图 3 实验系统图

Figure 3. Schematic of the experimental system.

DownLoad: Full-Size Img PowerPoint

图 4 典型半阻塞不对称分裂过程 (Q_c = 400 μL/h, Q_d = 40 μL/h, Ca = 5.53 × 10^–4, l_m/w = 4.08)

Figure 4. Typical droplet assymetrical splitting with a tunnel in a microfluidic T-junction (Q_c = 400 μL/h, Q_d = 40 μL/h, Ca = 5.53 × 10^–4, l_m /w = 4.08).

DownLoad: Full-Size Img PowerPoint

图 5 液滴颈部宽度演变过程(Q_c = 400 μL/h, Q_d = 40 μL/h, Q_t = 0 μL/h, Ca = 5.53 × 10^–4, l_m /w = 4.08, T = 0.2592 s), 其中(t–t₄)/T = 0时表示颈部刚开始收缩

Figure 5. Evolution of neck width d/w with dimensionless time (t–t₄)/T (Q_c = 400 μL/h, Q_d = 40 μL/h, Q_t = 0 μL/h, Ca = 5.53 × 10^–4, l_m/w = 4.08, T = 0.2592 s), where (t–t₄)/T = 0 represents the neck starts contracting.

DownLoad: Full-Size Img PowerPoint

图 6 分裂过程中液滴前端位移(Q_c = 400 μL/h, Q_d = 40 μL/h, Q_t = 0 μL/h, Ca = 5.53 × 10^–4, l_m/w = 4.08, T = 0.2592 s), 其中(t–t₄)/T = 0表示液滴头部刚开始进入分支通道

Figure 6. Motion of droplet front cap during splitting process (Q_c = 400 μL/h, Q_d = 40 μL/h, Q_t = 0 μL/h, Ca = 5.53 × 10^–4, l_m/w = 4.08, T = 0.2592 s), where (t–t₄)/T = 0 represents the head of the droplet has just entered the branch channel.

DownLoad: Full-Size Img PowerPoint

图 7 调控流量Q_t对液滴分裂比的影响(Q_d = 50 μL/h)

Figure 7. Active regulation of droplet splitting ratio by tuning flow Q_t (Q_d = 50 μL/h).

DownLoad: Full-Size Img PowerPoint

图 8 液滴不对称分裂模型　(a)实物图; (b)简化图

Figure 8. Asymmetrical droplet splitting model: (a) Actual microchannel; (b) simplified diagram.

DownLoad: Full-Size Img PowerPoint

图 9 调控流量Q_t变化时液滴不对称分裂比预测值与实验值对比　(a) l_m/w = 4.37, Ca = 5.24 × 10^–3; (b) l_m/w = 4.99, Ca = 3.88 × 10^–3; (c) l_m/w = 5.44, Ca = 3.04 × 10^–3; (d) l_m/w = 6.24, Ca = 2.22 × 10^–3; (e) l_m/w = 7.50, Ca = 1.32 × 10^–3

Figure 9. Comparison of predicted value and experimental value of droplet asymmetric split ratio when Q_t changes: (a) l_m/w = 4.37, Ca = 5.24 × 10^–3; (b) l_m/w = 4.99, Ca = 3.88 × 10^–3; (c) l_m/w = 5.44, Ca = 3.04 × 10^–3; (d) l_m/w = 6.24, Ca = 2.22 × 10^–3; (e) l_m/w = 7.50, Ca = 1.32 × 10^–3.

DownLoad: Full-Size Img PowerPoint

[1]	Chen Y P, Zhang C B, Shi M H, Yang Y C 2010 AlChE J. 56 2018
[2]	Wang J, Gao W, Zhang H, Zou M H, Chen Y P, Zhao Y J 2018 Sci. Adv. 4 eaat7392 Google Scholar
[3]	Pan D, Liu M, Li F, Chen Q, Liu X, Liu Y, Zhang Z, Huang W, Li B 2018 Chem. Eng. Sci. 176 254 Google Scholar
[4]	Sharei A, Zoldan J, Adamo A, et al. 2013 Proc. Natl. Acad Sci. USA 110 2082 Google Scholar
[5]	Tao Y, Rotem A, Zhang H, et al. 2015 Lab Chip 15 3934 Google Scholar
[6]	Holland-Moritz D A, Wismer M K, Mann B F, et al. 2020 Angew. Chem. Int. Ed. Engl. 59 4470 Google Scholar
[7]	Wang J, Sun L Y, Zou M H, Gao W, Liu C H, Shang L R, Gu Z Z, Zhao Y J 2017 Sci. Adv. 3 e1700004 Google Scholar
[8]	Zuo Y, He X, Yang Y, Wei D, Sun J, Zhong M, Xie R, Fan H, Zhang X 2016 Acta Biomater. 38 153 Google Scholar
[9]	Lan K, Liu J, Li Z C, et al. 2016 Matter and Radiat. at Extremes 1 8 Google Scholar
[10]	Liu M F, Su L, Li J, Chen S F, Liu Y Y, Li J, Li B, Chen Y P, Zhang Z W 2016 Matter and Radiat. at Extremes 1 213 Google Scholar
[11]	Zhang C B, Gao W, Zhao Y J, Chen Y P 2018 Appl. Phys. Lett. 113 203702 Google Scholar
[12]	Shang L, Cheng Y, Zhao Y 2017 Chem. Rev. 117 7964 Google Scholar
[13]	Park J, Jung J H, Park K, Destgeer G, Ahmed H, Ahmad R, Sung H J 2018 Lab Chip 18 422 Google Scholar
[14]	Jung J H, Destgeer G, Ha B, Park J, Sung H J 2016 Lab Chip 16 3235 Google Scholar
[15]	Chaudhuri J, Timung S, Dandamudi C B, Mandal T K, Bandyopadhyay D 2017 Electrophoresis 38 278 Google Scholar
[16]	崔于桐, 王宁宁, 刘海湖 2017 工程热物理学报 38 1564 Cui Y T, Wang N N, Liu H H 2017 J. Eng. Thermophys. 38 1564
[17]	Cui Y T, Wang N N, Liu H H 2019 Phys. Fluids 31 022105 Google Scholar
[18]	Rogers C I, Oxborrow J B, Anderson R R, Tsai L F, Nordin G P, Woolley A T 2014 Sens. Actuators B Chem. 191 438 Google Scholar
[19]	Raveshi M R, Agnihotri S N, Sesen M, Bhardwaj R, Neild A 2019 Sensors Actuators B: Chem. 292 233 Google Scholar
[20]	高崴, 于程, 姚峰 2020 中国物理B 29 054702 Google Scholar Gao W, Yu C, Yao F 2020 Chin. Phys. B 29 054702 Google Scholar
[21]	Chen Y P, Gao W, Zhang C B, Zhao Y J 2016 Lab Chip 16 1332 Google Scholar
[22]	Yamada M, Doi S, Maenaka H, Yasuda M, Seki M 2008 J. Colloid Interface Sci. 321 401 Google Scholar
[23]	王维萌, 马一萍, 王澎, 陈斌 2015 工程热物理学报 36 338 Wang W M, Ma Y P, Wang P, Chen B 2015 J. Eng. Thermophys. 36 338
[24]	Wang X, Liu Z M, Pang Y 2018 Chem. Eng. Sci. 188 11 Google Scholar
[25]	梁宏, 柴振华, 施保昌 2016 物理学报 65 204701 Google Scholar Liang H, Chai Z H, Shi B C 2016 Acta Phys. Sin. 65 204701 Google Scholar
[26]	Fu Y H, Bai L, Jin Y, Cheng Y 2017 Phys. Fluids 29 032003 Google Scholar
[27]	Cheng W L, Sadr R, Dai J, Han A 2018 Biomed. Microdevices 20 72 Google Scholar
[28]	Chen B, Li G, Wang W, Wang P 2015 Appl. Therm. Eng. 88 94 Google Scholar
[29]	俞炜, 邓梓龙, 吴苏晨, 于程, 王超 2019 物理学报 68 054701 Google Scholar Yu W, Deng Z L, Wu S C, Yu C, Wang C 2019 Acta Phys. Sin. 68 054701 Google Scholar
[30]	Leshansky A M, Afkhami S, Jullien M C, Tabeling P 2012 Phys. Rev. Lett. 108 264502 Google Scholar
[31]	Jousse F, Lian G, Janes R, Melrose J 2005 Lab Chip 5 646 Google Scholar
[32]	Fuerstman M J, Lai A, Thurlow M E, Shevkoplyas S S, Stone H A, Whitesides G M 2007 Lab Chip 7 1479 Google Scholar
[33]	Ladosz A, von Rohr P R 2018 Chem. Eng. Sci. 191 398 Google Scholar
[34]	Mortensen N A, Okkels F, Bruus H 2005 Phys. Rev. E Stat Nonlin. Soft Matter Phys. 71 057301 Google Scholar
[35]	Warnier M J F, de Croon M, Rebrov E V, Schouten J C 2010 Microfluid. Nanofluid. 8 33 Google Scholar
[36]	Wong H, Radke C J, Morris S 1995 J. Fluid Mech. 292 95 Google Scholar

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