Abstract
This study’s aim is to improve the understanding of the dynamical behavior of a multi-core compound droplet traveling in an axisymmetric channel consisting of a diffuser element. The compound droplet typically consisting of two inner droplets distributed one after another is initially located at a certain distance from the entrance of the channel. A front-tracking method is used to handle the movement and deformation of the droplet. The numerical simulation results show that the compound droplet is stretched in the channel, and it takes a certain time, “the transit time”, to pass through the diffuser. The compound droplet has the largest deformation in the diffuser region and tends to return to its nearly original shape after leaving the diffuser. The deformation and transit time of the compound droplet are affected by some typical parameters, such as the capillary number and the diffuser angle. For small capillary numbers, the leading inner droplet takes a shorter transit time than the rear one does. The transit time also increases with an increase in the diffuser angle and the number of inner droplets enclosed in the compound droplet.
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References
J. Wang, J. Liu, J. Han and J. Guan, Rheology investigation of the globule of multiple emulsions with complex internal structures through a boundary element method, Chem. Eng. Sci., 96 (2013) 87–97.
A. Aserin, Multiple Emulsion: Technology and Applications, Wiley-Interscience, New Jersey (2007).
A. R. Abate and D. A. Weitz, High-order multiple emulsions formed in poly(dimethylsiloxane) microfluidics, Small, 5(18) (2009) 2030–2032.
L.-Y. Chu, A. S. Utada, R. K. Shah, J.-W. Kim and D. A. Weitz, Controllable monodisperse multiple emulsions, Angewandte Chemie, 119(47) (2007) 9128–9132.
G. Su, P. W. Longest and R. M. Pidaparti, A novel micropump droplet generator for aerosol drug delivery: design simulations, Biomicrofluidics, 4(4) (2010) 044108.
L. Shang, Y. Cheng and Y. Zhao, Emerging droplet microfluidics, Chem. Rev., 117(12) (2017) 7964–8040.
S. Li, J. Liu and D. Jiang, Dynamic characterization of a valveless micropump considering entrapped gas bubbles, J. Heat Transfer, 135(9) (2013) 091403.
T. C. Yih, C. Wei and B. Hammad, Modeling and characterization of a nanoliter drug-delivery MEMS micropump with circular bossed membrane, Nanomedicine: NBM, 1(2) (2005) 164–175.
M. Sun, M. Zhao and W. Gao, Hydrodynamics of compound droplet flowing in the curved minichannel, Adv. Condens. Matter. Phys., 2019 (2019) 5726974.
T. Darvishzadeh and N. V. Priezjev, Effects of crossflow velocity and transmembrane pressure on microfiltration of oil-in-water emulsions, J. Membr. Sci., 423–424 (2012) 468–476.
I.-L. Ngo, S. W. Joo and C. Byon, Effects of junction angle and viscosity ratio on droplet formation in microfluidic cross-junction, J. Fluids Eng., 138(5) (2016) 051202.
Z. Che, Y. F. Yap and T. Wang, Flow structure of compound droplets moving in microchannels, Phys. Fluids, 30(1) (2018) 012114.
J. Li, H. Chen and H. A. Stone, Breakup of double emulsion droplets in a tapered nozzle, Langmuir, 27(8) (2011) 4324–4327.
H. D. Nguyen, T. V. Vu, P. H. Nguyen, B. D. Pham, N. X. Ho, C. T. Nguyen and V. T. Nguyen, Numerical study of the indentation formation of a compound droplet in a constriction, J. of Mechanical Science and Technology, 35(4) (2021) 1515–1526.
M. Tang, Q. Bao, J. Zhang, L. Lai and Q. Ning, Simulation of raindrop-shaped flow tube valveless piezoelectric pump, Journal of Physics: Conference Series, 1314 (2019) 012047.
M. Wörner, Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications, Microfluid Nanofluid, 12(6) (2012) 841–886.
T. M. Tran, F. Lan, C. S. Thompson and A. R. Abate, From tubes to drops: droplet-based microfluidics for ultrahigh-throughput biology, J. Phys. D: Appl. Phys., 46(11) (2013) 114004.
J. Han and G. Tryggvason, Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force, Phys. Fluids, 11(12) (1999) 3650.
T. V. Vu and P. H. Pham, Numerical study of a compound droplet moving toward a rigid wall in an axisymmetric channel, Int. J. Heat Fluid Flow, 82 (2020) 108542.
N. X. Ho, T. V. Vu, V. T. Nguyen, C. T. Nguyen and H. V. Vu, A numerical study of liquid compound filament contraction, Phys. Fluids, 33(2) (2021) 023314.
G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas and Y.-J. Jan, A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169(2) (2001) 708–759.
T.-V. Vu, T. V. Vu, C. T. Nguyen and P. H. Pham, Deformation and breakup of a double-core compound droplet in an axisymmetric channel, Int. J. Heat Mass. Transfer, 135 (2019) 796–810.
S. O. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100(1) (1992) 25–37.
A. R. Abate, J. Thiele and D. A. Weitz, One-step formation of multiple emulsions in microfluidics, Lab Chip, 11(2) (2011) 253–258.
T. M. Tran, S. Cater and A. R. Abate, Coaxial flow focusing in poly(dimethylsiloxane) microfluidic devices, Biomicrofluidics, 8(1) (2014) 016502.
C. T. Nguyen, H. V. Vu, T. V. Vu, T. V. Truong, N. X. Ho, B. D. Pham, H. D. Nguyen and V. T. Nguyen, Numerical analysis of deformation and breakup of a compound droplet in microchannels, Eur. J. Mech. B Fluids, 88 (2021) 135–147.
R. R. Gidde, P. M. Pawar and V. P. Dhamgaye, Fully coupled modeling and design of a piezoelectric actuation based valveless micropump for drug delivery application, Microsyst. Technol., 26(2) (2020) 633–645.
E. Stemme and G. Stemme, A valveless diffuser/nozzle-based fluid pump, Sensors and Actuators A: Physical, 39(2) (1993) 159–167.
H. W. Lee and I. H. A. Azid, Neuro-genetic optimization of the diffuser elements for applications in a valveless diaphragm micropumps system, Sensors, 9(9) (2009) 7481–7497.
M. Tahmasebipour and A. A. Paknahad, Unidirectional and bidirectional valveless electromagnetic micropump with PDMS-Fe3O4 nanocomposite magnetic membrane, J. Micromech. Microeng., 29(7) (2019) 075014.
Y.-Y. Tsui and S.-L. Lu, Evaluation of the performance of a valveless micropump by CFD and lumped-system analyses, Sensor Actuat. A-Phys., 148(1) (2008) 138–148.
Y. H. Mori, Configurations of gas-liquid two-phase bubbles in immiscible liquid media, Int. J. Multiphase Flow, 4(4) (1978) 383–396.
M. P. Borthakur, G. Biswas and D. Bandyopadhyay, Dynamics of deformation and pinch-off of a migrating compound droplet in a tube, Phys. Rev. E, 97(4) (2018) 043112.
T. V. Vu, D. T. Bui, Q. D. Nguyen and P. H. Pham, Numerical study of rheological behaviors of a compound droplet in a conical nozzle, Int. J. Heat Fluid Flow, 85 (2020) 108655.
T. V. Vu, Parametric study of the collision modes of compound droplets in simple shear flow, Int. J. Heat Mass Transfer, 79 (2019) 108470.
C. Zhou, P. Yue and J. J. Feng, Deformation of a compound drop through a contraction in a pressure-driven pipe flow, Int. J. Multiphase Flow, 34(1) (2008) 102–109.
N. X. Ho and T. V. Vu, Numerical simulation of the deformation and breakup of a two-core compound droplet in an axisymmetric T-junction channel, Int. J. Heat Fluid Flow, 86 (2020) 108702.
M. N. Hamdan, S. Abdallah and A. Al-Qaisia, Modeling and study of dynamic performance of a valveless micropump, Journal of Sound and Vibration, 329(15) (2010) 3121–3136.
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This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number: 13/2019/TN.
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Dang T. Bui is an Associate Professor and a Lecturer at Hanoi University of Science and University (HUST). He received his Master’s in Instrumentation and Control from Hanoi University of Science and Technology (HUST), Vietnam, in 2011, and Ph.D. from Ecole Normale Superieure de Cachan, France, in 2011. His main research interests include numerical simulations (CFD), control system design, embedded systems and AI, IoT for smart agriculture.
Truong V. Vu is a Lecturer in the Faculty of Vehicle and Energy Engineering, Phenikaa University, Hanoi, Vietnam. He received his Ph.D. in Integrated Science and Engineering from Ritsumeikan University, Japan. His research interests include multiphase and free surface flows, phase change heat transfer and numerical methods.
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Bui, D.T., Vu, H.V., Nguyen, Q.D. et al. A multi-core compound droplet passing through a diffuser channel. J Mech Sci Technol 35, 5049–5060 (2021). https://doi.org/10.1007/s12206-021-1022-1
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DOI: https://doi.org/10.1007/s12206-021-1022-1