液珠式微流體廣泛應用於生化微反應、藥物傳輸等領域，特定反應通常藉由液珠融合來驅動，透過流道幾何製造液珠碰撞融合為被動式控制，但目前被動式融合仍以單層乳化液珠為主，少有研究針對雙層乳化系統內部融合進行討論，因此本研究藉由突縮突擴流道，探討流道幾何對於雙重乳化液珠內部融合的影響。
本研究先使用兩階段流動聚焦型結構生成雙重乳化液珠，設定突縮段寬度200 μm與250 μm(W200, W250)，長度800 μm與1600 μm(L800, L1600)，使用微粒子影像測速儀依序探討寬度、長度與液珠尺寸對於加速過程流場變化情形，以及突擴後內部液珠融合行為的影響。在寬度的比較中，寬度除了改變加速效果，也造成壁面阻力與溝流驅動力主導程度不同，W200造成外部界面明顯頸縮，而W250則較為緩和；當長度增加至L1600，W200界面頸縮造成局部阻力降低，內部液珠在加速過程相互分離，W250則不受突縮段長度影響，內部液珠始終保持接觸。在突擴階段比較中，提高加速幅度或尺寸都會增加內部液珠擠壓程度，但內部液珠接觸面排液流動並未顯著增強，而是恢復形變時產生反向排液流動，此反向流動讓W200無法實現內部液珠融合，W250內部液珠則在碰撞後陸續觀測到融合現象。根據本研究結果顯示，W250突縮段更利於促進內部液珠融合，對於被動式融合元件設計，增加液珠接觸時間以及降低碰撞形變仍為主要考量，此實驗結果期望能提供後續被動式操控、液珠融合晶片設計之參考。

Droplet-based microfluidics is widely used in biochemical reactions, and drug delivery. The specific reaction is usually driven by the coalescence of droplets. The fusion of droplets can be passively controlled through channel geometry. However, the current passive fusion is still based on the single-emulsion system. Therefore, this study investigates the internal fusion behavior of double-emulsion droplets through convergent-divergent channel geometry.
In this study, a two-stage flow-focusing structure was used to generate double-emulsion droplets. We used two widths of convergent section (W200, W250), and two lengths of convergent section (L800, L1600) to investigate flow field variation by a micro-PIV system. We found that the width of convergent section not only changes the acceleration magnitude but affects the dominance of wall resistance and gutter flow driving stress. The W200 convergent section causes significant necking of the outer droplet, while the necking phenomenon is moderate in W250 convergent section. As the length of convergent section increases to 1600 m, the interface necking partially reduces the wall resistance. The inner droplets of W200 convergent section separate during the acceleration process. In contrast, the inner droplets of W250 convergent section will remain in contact. During the divergence stage, the squeezing effect of the inner droplets increases with the acceleration amplitude or size. However, the drainage flow at the contact surface was not significantly enhanced. Instead, a reverse drainage flow occurs as the droplets recover from deformation. This reverse flow prevents internal fusion in the W200 structure, while we observed internal fusion after collision in the W250 structure. According to the results of this study, the W250 structure is more conducive to promote internal fusion. For the passive fusion component design, increasing the droplet contact time and reducing the collision deformation are still the main considerations. The experimental results provide a reference for subsequent passive control and microfluidic device design.

[1] R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Reports on Progress in Physics, vol. 75, no. 1, Jan. 2012, doi: 10.1088/0034-4885/75/1/016601.
[2] F. Shen, Y. Li, Z. Liu, and X. J. Li, “Study of flow behaviors of droplet merging and splitting in microchannels using Micro-PIV measurement,” Microfluid Nanofluidics, vol. 21, no. 4, Apr. 2017, doi: 10.1007/s10404-017-1902-y.
[3] H. Song, D. L. Chen, and R. F. Ismagilov, “Reactions in droplets in microfluidic channels,” Angewandte Chemie - International Edition, vol. 45, no. 44. pp. 7336–7356, Nov. 13, 2006. doi: 10.1002/anie.200601554.
[4] J. K. Nunes, S. S. H. Tsai, J. Wan, and H. A. Stone, “Dripping and jetting in microfluidic multiphase flows applied to particle and fibre synthesis,” J Phys D Appl Phys, vol. 46, no. 11, Mar. 2013, doi: 10.1088/0022-3727/46/11/114002.
[5] H. Chen et al., “Reactions in double emulsions by flow-controlled coalescence of encapsulated drops,” Lab Chip, vol. 11, no. 14, pp. 2312–2315, Jul. 2011, doi: 10.1039/c1lc20265k.
[6] F. Sarrazin, L. Prat, N. di Miceli, G. Cristobal, D. R. Link, and D. A. Weitz, “Mixing characterization inside microdroplets engineered on a microcoalescer,” Chem Eng Sci, vol. 62, no. 4, pp. 1042–1048, Feb. 2007, doi: 10.1016/j.ces.2006.10.013.
[7] P. Ma, D. Liang, C. Zhu, T. Fu, and Y. Ma, “An effective method to facile coalescence of microdroplet in the symmetrical T-junction with expanded convergence,” Chem Eng Sci, vol. 213, Feb. 2020, doi: 10.1016/j.ces.2019.115389.
[8] K. Wang, Y. Lu, C. P. Tostado, L. Yang, and G. Luo, “Coalescences of microdroplets at a cross-shaped microchannel junction without strictly synchronism control,” Chemical Engineering Journal, vol. 227, pp. 90–96, Jul. 2013, doi: 10.1016/j.cej.2012.09.060.
[9] C. Wang, N. T. Nguyen, and T. N. Wong, “Optical measurement of flow field and concentration field inside a moving nanoliter droplet,” Sens Actuators A Phys, vol. 133, no. 2 SPEC. ISS., pp. 317–322, Feb. 2007, doi: 10.1016/j.sna.2006.06.026.
[10] B. J. Jin and J. Y. Yoo, “Visualization of droplet merging in microchannels using micro-PIV,” Exp Fluids, vol. 52, no. 1, pp. 235–245, Jan. 2012, doi: 10.1007/s00348-011-1221-0.
[11] J. Tao, X. Song, J. Liu, and J. Wang, “Microfluidic rheology of the multiple-emulsion globule transiting in a contraction tube through a boundary element method,” Chem Eng Sci, vol. 97, pp. 328–336, Jun. 2013, doi: 10.1016/j.ces.2013.04.043.
[12] H. Gu, M. H. G. Duits, and F. Mugele, “Droplets formation and merging in two-phase flow microfluidics,” International journal of molecular sciences, vol. 12, no. 4. pp. 2572–2597, 2011. doi: 10.3390/ijms12042572.
[13] R. M. Erb, D. Obrist, P. W. Chen, J. Studer, and A. R. Studart, “Predicting sizes of droplets made by microfluidic flow-induced dripping,” Soft Matter, vol. 7, no. 19, pp. 8757–8761, Oct. 2011, doi: 10.1039/c1sm06231j.
[14] R. K. Shah et al., “Designer emulsions using microfluidics,” Elsevier, 2008.
[15] S. A. Nabavi, G. T. Vladisavljević, S. Gu, and E. E. Ekanem, “Double emulsion production in glass capillary microfluidic device: Parametric investigation of droplet generation behaviour,” Chem Eng Sci, vol. 130, pp. 183–196, Jul. 2015, doi: 10.1016/j.ces.2015.03.004.
[16] G. T. Vladisavljević, R. al Nuumani, and S. A. Nabavi, “Microfluidic production of multiple emulsions,” Micromachines, vol. 8, no. 3. MDPI AG, 2017. doi: 10.3390/mi8030075.
[17] T. Thorsen, R. W. Roberts, F. H. Arnold, and S. R. Quake, “Dynamic pattern formation in a vesicle-generating microfluidic device,” Phys Rev Lett, vol. 86, no. 18, pp. 4163–4166, Apr. 2001, doi: 10.1103/PhysRevLett.86.4163.
[18] P. Garstecki, M. J. Fuerstman, H. A. Stone, and G. M. Whitesides, “Formation of droplets and bubbles in a microfluidic T-junction - Scaling and mechanism of break-up,” Lab Chip, vol. 6, no. 3, pp. 437–446, 2006, doi: 10.1039/b510841a.
[19] C. N. Baroud, F. Gallaire, and R. Dangla, “Dynamics of microfluidic droplets,” Lab on a Chip, vol. 10, no. 16. Royal Society of Chemistry, pp. 2032–2045, Aug. 21, 2010. doi: 10.1039/c001191f.
[20] S. L. Anna, N. Bontoux, and H. A. Stone, “Formation of dispersions using ‘flow focusing’ in microchannels,” Appl Phys Lett, vol. 82, no. 3, pp. 364–366, Jan. 2003, doi: 10.1063/1.1537519.
[21] D. Hernández-Cid, V. H. Pérez-González, R. C. Gallo-Villanueva, J. González-Valdez, and M. A. Mata-Gómez, “Modeling droplet formation in microfluidic flow-focusing devices using the two-phases level set method,” Mater Today Proc, Oct. 2020, doi: 10.1016/j.matpr.2020.09.417.
[22] Liu Zhaomiao and Yang Yang, “Influence of geometry configurations on the microdroplets in flow focusing microfluidics,” Chinese Journal of Theoretical and Applied Mechanics, vol. 48, no. 4, pp. 867–876, 2016.
[23] S. Okushima, T. Nisisako, T. Torii, and T. Higuchi, “Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices,” Langmuir, vol. 20, no. 23, pp. 9905–9908, Nov. 2004, doi: 10.1021/la0480336.
[24] S. Okushima, T. Nisisako, T. Torii, and T. Higuchi, “One-step wettability patterning of PDMS microchannels for generation of monodisperse alginate microbeads by in Situ external gelation in double emulsion microdroplets,” Sens Actuators B Chem, vol. 291, pp. 418–425, Jul. 2019, doi: 10.1016/j.snb.2019.04.100.
[25] M. Azarmanesh, M. Farhadi, and P. Azizian, “Double emulsion formation through hierarchical flow-focusing microchannel,” Physics of Fluids, vol. 28, no. 3, Mar. 2016, doi: 10.1063/1.4944058.
[26] S. C. Kim, D. J. Sukovich, and A. R. Abate, “Patterning microfluidic device wettability with spatially-controlled plasma oxidation,” Lab Chip, vol. 15, no. 15, pp. 3163–3169, Jun. 2015, doi: 10.1039/c5lc00626k.
[27] D. Wu, Y. Luo, X. Zhou, Z. Dai, and B. Lin, “Multilayer poly(vinyl acohol)-adsorbed coating on poly(dimethylsiloxane) microfluidic chips for biopolymer separation,” Electrophoresis, vol. 26, no. 1, pp. 211–218, Jan. 2005, doi: 10.1002/elps.200406157.
[28] T. Trantidou, Y. Elani, E. Parsons, and O. Ces, “Hydrophilic surface modification of pdms for droplet microfluidics using a simple, quick, and robust method via pva deposition,” Microsyst Nanoeng, vol. 3, 2017, doi: 10.1038/micronano.2016.91.
[29] H. Kinoshita, S. Kaneda, T. Fujii, and M. Oshima, “Three-dimensional measurement and visualization of internal flow of a moving droplet using confocal micro-PIV,” Lab Chip, vol. 7, no. 3, pp. 338–346, 2007, doi: 10.1039/b617391h.
[30] W. Thielicke and E. J. Stamhuis, “PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB,” J Open Res Softw, vol. 2, Oct. 2014, doi: 10.5334/jors.bl.
[31] C. D. Meinhart, S. T. Wereley, and M. H. B. Gray, “Volume illumination for two-dimensional particle image velocimetry,” 2000.
[32] M. Hein, M. Moskopp, and R. Seemann, “Flow field induced particle accumulation inside droplets in rectangular channels,” Lab Chip, vol. 15, no. 13, pp. 2879–2886, Jul. 2015, doi: 10.1039/c5lc00420a.
[33] M. Oishi, H. Kinoshita, T. Fujii, and M. Oshima, “Simultaneous measurement of internal and surrounding flows of a moving droplet using multicolour confocal micro-particle image velocimetry (micro-PIV),” Meas Sci Technol, vol. 22, no. 10, 2011, doi: 10.1088/0957-0233/22/10/105401.
[34] Q. Q. Xiong, Z. Chen, S. W. Li, Y. D. Wang, and J. H. Xu, “Micro-PIV measurement and CFD simulation of flow field and swirling strength during droplet formation process in a coaxial microchannel,” Chem Eng Sci, vol. 185, pp. 157–167, Aug. 2018, doi: 10.1016/j.ces.2018.04.022.
[35] J.-C. Baret, “Surfactants in droplet-based microfluidics,” Lab Chip, vol. 12, no. 3, pp. 422–433, 2012, doi: 10.1039/c1lc20582j.
[36] M. K. Mulligan and J. P. Rothstein, “The effect of confinement-induced shear on drop deformation and breakup in microfluidic extensional flows,” Physics of Fluids, vol. 23, no. 2, Feb. 2011, doi: 10.1063/1.3548856.
[37] N. M. Kovalchuk and M. J. H. Simmons, “Effect of surfactant dynamics on flow patterns inside drops moving in rectangular microfluidic channels,” Colloids and Interfaces, vol. 5, no. 3, Sep. 2021, doi: 10.3390/colloids5030040.
[38] M. Li et al., “Flow topology and its transformation inside droplets traveling in rectangular microchannels,” Physics of Fluids, vol. 32, no. 5, May 2020, doi: 10.1063/5.0004549.
[39] Y. Chen, X. Liu, C. Zhang, and Y. Zhao, “Enhancing and suppressing effects of an inner droplet on deformation of a double emulsion droplet under shear,” Lab Chip, vol. 15, no. 5, pp. 1255–1261, Mar. 2015, doi: 10.1039/c4lc01231c.
[40] S. Ma, W. T. S. Huck, and S. Balabani, “Deformation of double emulsions under conditions of flow cytometry hydrodynamic focusing,” Lab Chip, vol. 15, no. 22, pp. 4291–4301, 2015, doi: 10.1039/c5lc00693g.
[41] W. A. C. Bauer, M. Fischlechner, C. Abell, and W. T. S. Huck, “Hydrophilic PDMS microchannels for high-throughput formation of oil-in-water microdroplets and water-in-oil-in-water double emulsions,” Lab Chip, vol. 10, no. 14, pp. 1814–1819, 2010, doi: 10.1039/c004046k.
[42] E. Lorenceau, A. S. Utada, D. R. Link, G. Cristobal, M. Joanicot, and D. A. Weitz, “Generation of polymerosomes from double-emulsions,” Langmuir, vol. 21, no. 20, pp. 9183–9186, Sep. 2005, doi: 10.1021/la050797d.
[43] J. Wang, X. Li, X. Wang, and J. Guan, “Possible oriented transition of multiple-emulsion globules with asymmetric internal structures in a microfluidic constriction,” Phys Rev E Stat Nonlin Soft Matter Phys, vol. 89, no. 5, May 2014, doi: 10.1103/PhysRevE.89.052302.
[44] W. Wang, C. Yang, and C. M. Li, “On-demand microfluidic droplet trapping and fusion for on-chip static droplet assays,” Lab Chip, vol. 9, no. 11, pp. 1504–1506, 2009, doi: 10.1039/b903468d.
[45] A. A. García et al., “Magnetic movement of biological fluid droplets,” J Magn Magn Mater, vol. 311, no. 1 SPEC. ISS., pp. 238–243, 2007, doi: 10.1016/j.jmmm.2006.10.1149.
[46] H. Yi, C. Zhu, T. Fu, and Y. Ma, “Efficient coalescence of microdroplet in the cross-focused microchannel with symmetrical chamber,” J Taiwan Inst Chem Eng, vol. 112, pp. 52–59, Jul. 2020, doi: 10.1016/j.jtice.2020.07.010.
[47] E. Klaseboer, J. P. Chevaillier, C. Gourdon, and O. Masbernat, “Film drainage between colliding drops at constant approach velocity: Experiments and modeling,” J Colloid Interface Sci, vol. 229, no. 1, pp. 274–285, Sep. 2000, doi: 10.1006/jcis.2000.6987.
[48] L.-H. Hung, K. M. Choi, W.-Y. Tseng, Y.-C. Tan, K. J. Shea, and A. P. Lee, “Alternating droplet generation and controlled dynamic droplet fusion in microfluidic device for CdS nanoparticle synthesis,” Lab Chip, vol. 6, no. 2, p. 174, 2006, doi: 10.1039/b513908b.
[49] L. G. Leal, “Flow induced coalescence of drops in a viscous fluid,” Physics of Fluids, vol. 16, no. 6, pp. 1833–1851, 2004, doi: 10.1063/1.1701892.
[50] S. Narayan, I. Makhnenko, D. B. Moravec, B. G. Hauser, A. J. Dallas, and C. S. Dutcher, “Insights into the microscale coalescence behavior of surfactant-stabilized droplets using a microfluidic hydrodynamic trap,” Langmuir, vol. 36, no. 33, pp. 9827–9842, Aug. 2020, doi: 10.1021/acs.langmuir.0c01414.
[51] N. Bremond, A. R. Thiam, and J. Bibette, “Decompressing emulsion droplets favors coalescence,” Phys Rev Lett, vol. 100, no. 2, Jan. 2008, doi: 10.1103/PhysRevLett.100.024501.
[52] D. Z. Gunes, X. Clain, O. Breton, G. Mayor, and A. S. Burbidge, “Avalanches of coalescence events and local extensional flows - Stabilisation or destabilisation due to surfactant,” J Colloid Interface Sci, vol. 343, no. 1, pp. 79–86, Mar. 2010, doi: 10.1016/j.jcis.2009.11.035.
[53] L. Mazutis and A. D. Griffiths, “Selective droplet coalescence using microfluidic systems,” Lab Chip, vol. 12, no. 10, pp. 1800–1806, Apr. 2012, doi: 10.1039/c2lc40121e.
[54] Z. Liu, X. Wang, R. Cao, and Y. Pang, “Droplet coalescence at microchannel intersection chambers with different shapes,” Soft Matter, vol. 12, no. 26, pp. 5797–5807, 2016, doi: 10.1039/c6sm01158f.
[55] 林明俊、莊勝雄、游士諄、周祖亮, “SU-8光阻在矽晶圓基材上製作微流道面板之研究,” 南亞學報, no. 26, pp. 23–36, 2006.
[56] MicroChem, “SU-8 2000 Permanent Epoxy Negative Photoresist PROCESSING GUIDELINES FOR: SU-8 2025, SU-8 2035, SU-8 2050 and SU-8 2075.” [Online]. Available: www.atgc.co.jp
[57] T. Fu, Y. Wu, Y. Ma, and H. Z. Li, “Droplet formation and breakup dynamics in microfluidic flow-focusing devices: From dripping to jetting,” Chem Eng Sci, vol. 84, pp. 207–217, Dec. 2012, doi: 10.1016/j.ces.2012.08.039.
[58] T. Geoffrey Ingram, “The formation of emulsions in definable fields of flow,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 146, no. 858, pp. 501–523, Oct. 1934, doi: 10.1098/RSPA.1934.0169.