Bubble breakup in viscous liquids at a microfluidic T-junction

doi:10.1016/j.cjche.2024.10.026

Abstract

Abstract: Bubble breakup at T-junction microchannels is the basis for the numbering-up of gas-liquid two-phase flow in parallelized microchannels. This article presents the bubble breakup in viscous liquids at a microfluidic T-junction. Nitrogen is used as the gas phase, and glycerol-water mixtures with different mass concentration of glycerol as the liquid phase. The evolution of the gas-liquid interface during bubble breakup at the microfluidic T-junction is explored. The thinning of the bubble neck includes the squeezing stage and the rapid pinch-off stage. In the squeezing stage, the power law relation is found between the minimum width of the bubble neck and the time, and the values of exponents α₁ and α₂ are influenced by the viscous force. The values of pre-factors m₁ and m₂ are negatively correlated with the capillary number. In the rapid pinch-off stage, the thinning of the bubble neck is predominated by the surface tension, and the minimum width of the bubble neck can be scaled with the remaining time as power-law. The propagation of the bubble tip can be characterized by the power law between the movement distance and the time, with decreasing exponent as increased liquid viscosity.

Key words: Bubble, Microfluidics, Microchannel, Breakup, Viscous fluid

摘要： Bubble breakup at T-junction microchannels is the basis for the numbering-up of gas-liquid two-phase flow in parallelized microchannels. This article presents the bubble breakup in viscous liquids at a microfluidic T-junction. Nitrogen is used as the gas phase, and glycerol-water mixtures with different mass concentration of glycerol as the liquid phase. The evolution of the gas-liquid interface during bubble breakup at the microfluidic T-junction is explored. The thinning of the bubble neck includes the squeezing stage and the rapid pinch-off stage. In the squeezing stage, the power law relation is found between the minimum width of the bubble neck and the time, and the values of exponents α₁ and α₂ are influenced by the viscous force. The values of pre-factors m₁ and m₂ are negatively correlated with the capillary number. In the rapid pinch-off stage, the thinning of the bubble neck is predominated by the surface tension, and the minimum width of the bubble neck can be scaled with the remaining time as power-law. The propagation of the bubble tip can be characterized by the power law between the movement distance and the time, with decreasing exponent as increased liquid viscosity.

关键词: Bubble, Microfluidics, Microchannel, Breakup, Viscous fluid

Hongwei Zhu, Junjie Feng, Ziyi Xu, Chunying Zhu, Youguang Ma, Wei Xu, Bing Sun, Taotao Fu. Bubble breakup in viscous liquids at a microfluidic T-junction[J]. Chinese Journal of Chemical Engineering, 2025, 78(2): 44-57.

Hongwei Zhu, Junjie Feng, Ziyi Xu, Chunying Zhu, Youguang Ma, Wei Xu, Bing Sun, Taotao Fu. Bubble breakup in viscous liquids at a microfluidic T-junction[J]. 中国化学工程学报, 2025, 78(2): 44-57.

References

[1] F.Z. Chaouche, B. Bensebia, S.K. Moustefai, Computational fluid dynamics for microreactors used in nitration of phenol, Theor. Found. Chem. Eng. 56 (6) (2022) 1215-1235.
[2] A. Kazan, Supercritical CO₂ applications in microfluidic systems, Microfluid. Nanofluid. 26 (9) (2022) 68.
[3] M. Movsisyan, E.I.P. Delbeke, J.K.E.T. Berton, C. Battilocchio, S.V. Ley, C.V. Stevens, Taming hazardous chemistry by continuous flow technology, Chem. Soc. Rev. 45 (18) (2016) 4892-4928.
[4] R. Xu, Q. Song, C. Li, J. Li, H. Yang, J. Chen, Z. Mao, Highly efficient approach to the synthesis of 2-Chloro-2-methylbutane in a continuous-flow microreactor, Can. J. Chem. Eng. 101(7) (2023) 3813-3820.
[5] A.D. Bick, J.W. Khor, Y. Gai, S.K.Y. Tang, Strategic placement of an obstacle suppresses droplet break up in the hopper flow of a microfluidic soft crystal, Proc. Natl. Acad. Sci. USA 118 (19) (2021) e2017822118.
[6] M. Kalli, L. Chagot, P. Angeli, Comparison of surfactant mass transfer with drop formation times from dynamic interfacial tension measurements in microchannels, J. Colloid Interface Sci. 605 (2022) 204-213.
[7] J. Mandal, S. Sarkar, S. Sen, A deterministic model for bubble propagation through simple and cascaded loops of microchannels in power-law fluids, Phys. Fluids 33 (7) (2021) 072008.
[8] E. Um, M. Kim, H. Kim, J.H. Kang, H.A. Stone, J. Jeong, Phase synchronization of fluid-fluid interfaces as hydrodynamically coupled oscillators, Nat. Commun. 11 (1) (2020) 5221.
[9] Q.Y. Shen, C. Zhang, M.F. Tahir, S.K. Jiang, C.Y. Zhu, Y.G. Ma, T.T. Fu, Numbering-up strategies of micro-chemical process: Uniformity of distribution of multiphase flow in parallel microchannels, Chem. Eng. Process. Process. Intensif. 132 (2018) 148-159.
[10] D.R. Link, S.L. Anna, D.A. Weitz, H.A. Stone, Geometrically mediated breakup of drops in microfluidic devices, Phys. Rev. Lett. 92 (5) (2004) 054503.
[11] A.M. Leshansky, L.M. Pismen, Breakup of drops in a microfluidic T junction, 21 (2) (2009) 023303.
[12] M.C. Jullien, M.J. Tsang Mui Ching, C. Cohen, L. Menetrier, P. Tabeling, Droplet breakup in microfluidic T-junctions at small capillary numbers, Phys. Fluids 21 (7) (2009) 072001.
[13] A.M. Leshansky, S. Afkhami, M.C. Jullien, P. Tabeling, Obstructed breakup of slender drops in a microfluidic T junction, Phys. Rev. Lett. 108 (26) (2012) 264502.
[14] D.A. Hoang, L.M. Portela, C.R. Kleijn, M.T. Kreutzer, V. van Steijn, Dynamics of droplet breakup in a T-junction, J. Fluid Mech. 717 (2013) R4.
[15] Y.P. Chen, Z.L. Deng, Hydrodynamics of a droplet passing through a microfluidic T-junction, J. Fluid Mech. 819 (2017) 401-434.
[16] X. Sun, C.Y. Zhu, T.T. Fu, Y.G. Ma, H.Z. Li, Dynamics of droplet breakup and formation of satellite droplets in a microfluidic T-junction, Chem. Eng. Sci. 188 (2018) 158-169.
[17] T.T. Fu, Y.G. Ma, D. Funfschilling, H.Z. Li, Dynamics of bubble breakup in a microfluidic T-junction divergence, Chem. Eng. Sci. 66 (18) (2011) 4184-4195.
[18] Y.T. Lu, T.T. Fu, C.Y. Zhu, Y.G. Ma, H.Z. Li, Dynamics of bubble breakup at a T junction, Phys. Rev. E 93 (2) (2016) 022802.
[19] X.D. Wang, C.Y. Zhu, T.T. Fu, Y.G. Ma, Critical lengths for the transition of bubble breakup in microfluidic T-junctions, Chem. Eng. Sci. 111 (2014) 244-254.
[20] X.D. Wang, C.Y. Zhu, Y.N. Wu, T.T. Fu, Y.G. Ma, Dynamics of bubble breakup with partly obstruction in a microfluidic T-junction, Chem. Eng. Sci. 132 (2015) 128-138.
[21] X.D. Wang, C.Y. Zhu, T.T. Fu, Y.G. Ma, Bubble breakup with permanent obstruction in an asymmetric microfluidic T-junction, AlChE. J. 61 (3) (2015) 1081-1091.
[22] R.F. Day, E.J. Hinch, J.R. Lister, Self-similar capillary pinchoff of an inviscid fluid, Phys. Rev. Lett. 80 (4) (1998) 704-707.
[23] J.R. Lister, H.A. Stone, Capillary breakup of a viscous thread surrounded by another viscous fluid, 10 (11) (1998) 2758-2764.
[24] Y.J. Fei, C.Y. Zhu, T.T. Fu, X.Q. Gao, Y.G. Ma, Slug bubble deformation and its influence on bubble breakup dynamics in microchannel, Chin. J. Chem. Eng. 50 (2022) 66-74.
[25] C.Q. Yao, Y.C. Zhao, G.W. Chen, Multiphase processes with ionic liquids in microreactors: Hydrodynamics, mass transfer and applications, Chem. Eng. Sci. 189 (2018) 340-359.
[26] Y.N. Wu, T.T. Fu, C.Y. Zhu, Y.T. Lu, Y.G. Ma, H.Z. Li, Asymmetrical breakup of bubbles at a microfluidic T-junction divergence: Feedback effect of bubble collision, Microfluid. Nanofluid. 13 (5) (2012) 723-733.
[27] L. Sheng, Y. Chang, J. Deng, G.S. Luo, Taylor bubble generation rules in liquids with a higher viscosity in a T-junction microchannel, Ind. Eng. Chem. Res. 61 (6) (2022) 2623-2632.