Numerical simulation of double emulsion formation in cross-junctional flow-focusing microfluidic device using Lattice Boltzmann method

References

• Aserin, A. Multiple Emulsions: Technology and Applications. Mult. Emuls. Technol. Appl. 2007, 326, 1–326. DOI: 10.1002/9780470209264.
   Google Scholar
• Dams, S. S.; Walker, I. M. Multiple Emulsions as Targetable Delivery Systems. Methods Enzymol. 1987, 149, 51–64. DOI: 10.1016/0076-6879(87)49043-5.
   PubMed Web of Science ®Google Scholar
• Zhao, C. X. Multiphase Flow Microfluidics for the Production of Single or Multiple Emulsions for Drug Delivery. Adv. Drug Deliv. Rev. 2013, 65, 1420–1446. DOI: 10.1016/j.addr.2013.05.009.
   PubMed Web of Science ®Google Scholar
• Gallarate, M.; Carlotti, M. E.; Trotta, M.; Bovo, S. On the Stability of Ascorbic Acid in Emulsified Systems for Topical and Cosmetic Use. Int. J. Pharm. 1999, 188, 233–241. DOI: 10.1016/S0378-5173(99)00228-8.
   PubMed Web of Science ®Google Scholar
• Edris, A.; Bergnståhl, B. Encapsulation of Orange Oil in a Spray Dried Double Emulsion. Nahrung. 2001, 45, 133–137. DOI: 10.1002/1521-3803(20010401)45:2 < 133::AID-FOOD133 > 3.0.CO;2-C.
   PubMedGoogle Scholar
• Vladisavljevic, G. T. Recent Advances in the Production of Controllable Multiple Emulsions Using Microfabricated Devices. Particuology. 2016, 24, 1–17. DOI: 10.1016/j.partic.2015.10.001.
   Web of Science ®Google Scholar
• Utada, A. S. Monodisperse Double Emulsions Generated from a Microcapillary Device, Science (80-.). Science 2005, 308, 537–541. DOI: 10.1126/science.1109164.
   PubMed Web of Science ®Google Scholar
• Abate, A. R.; Thiele, J.; Weitz, D. A. One-Step Formation of Multiple Emulsions in Microfluidics. Lab Chip. 2011, 11, 253–258. DOI: 10.1039/C0LC00236D.
   PubMed Web of Science ®Google Scholar
• Okushima, S.; Nisisako, T.; Torii, T.; Higuchi, T. Controlled Production of Monodisperse Double Emulsions by Two-Step Droplet Breakup in Microfluidic Devices. Langmuir. 2004, 20, 9905–9908. DOI: 10.1021/la0480336.
   PubMed Web of Science ®Google Scholar
• Nisisako, T.; Okushima, S.; Torii, T. Controlled Formulation of Monodisperse Double Emulsions in a Multiple-Phase Microfluidic System. Soft Matter. 2005, 1, 23. DOI: 10.1039/b501972a.
   PubMed Web of Science ®Google Scholar
• Chu, L. Y.; Utada, A. S.; Shah, R. K.; Kim, J. W.; Weitz, D. A. Controllable Monodisperse Multiple Emulsions. Angew. Chem. Int. Ed. 2007, 46, 8970–8974. DOI: 10.1002/anie.200701358.
   PubMed Web of Science ®Google Scholar
• Chang, Z.; Serra, C. A.; Bouquey, M.; Prat, L.; Hadziioannou, G. Co-Axial Capillaries Microfluidic Device for Synthesizing Size- and Morphology-Controlled Polymer Core-Polymer Shell Particles. Lab Chip. 2009, 9, 3007. DOI: 10.1039/b913703c.
   PubMed Web of Science ®Google Scholar
• Abate, A. R.; Weitz, D. A. High-Order Multiple Emulsions Formed in Poly(Dimethylsiloxane) Microfluidics. Small 2009, 5, 2030–2032. DOI: 10.1002/smll.200900569.
   PubMed Web of Science ®Google Scholar
• Kim, S. H.; Kim, J. W.; Kim, D. H.; Han, S. H.; Weitz, D. A. Enhanced-Throughput Production of Polymersomes Using a Parallelized Capillary Microfluidic Device. Microfluid. Nanofluid. 2013, 14, 509–514. DOI: 10.1007/s10404-012-1069-5.
   Web of Science ®Google Scholar
• Shao, T.; Feng, X.; Jin, Y.; Cheng, Y. Controlled Production of Double Emulsions in Dual-Coaxial Capillaries Device for Millimeter-Scale Hollow Polymer Spheres. Chem. Eng. Sci. 2013, 104, 55–63. DOI: 10.1016/j.ces.2013.09.001.
   Web of Science ®Google Scholar
• Zhang, L.; Hao, S.; Liu, B.; Shum, H. C.; Li, J.; Chen, H. Fabrication of Ceramic Microspheres by Diffusion-Induced Sol-Gel Reaction in Double Emulsions. ACS Appl. Mater. Interfaces. 2013, 5, 11489–11493. DOI: 10.1021/am402028w.
   PubMed Web of Science ®Google Scholar
• Kim, S. H.; Kim, B. Controlled Formation of Double-Emulsion Drops in Sudden Expansion Channels. J. Colloid Interface Sci. 2014, 415, 26–31. DOI: 10.1016/j.jcis.2013.10.020.
   PubMed Web of Science ®Google Scholar
• Wu, N.; Oakeshott, J. G.; Easton, C. J.; Peat, T. S.; Surjadi, R.; Zhu, Y. A Double-Emulsion Microfluidic Platform for in Vitro Green Fluorescent Protein Expression. J. Micromech. Microeng. 2011, 21, 054032. DOI: 10.1088/0960-1317/21/5/
   Web of Science ®Google Scholar
• Sun, B. J.; Shum, H. C.; Holtze, C.; Weitz, D. A. Microfluidic Melt Emulsification for Encapsulation and Release of Actives. ACS Appl. Mater. Interfaces. 2010, 2, 3411–3416. DOI: 10.1021/am100860b.
   PubMed Web of Science ®Google Scholar
• Seo, M.; Paquet, C.; Nie, Z.; Xu, S.; Kumacheva, E. Microfluidic Consecutive Flow-Focusing Droplet Generators. Soft Matter. 2007, 3, 986. DOI: 10.1039/b700687j.
   PubMed Web of Science ®Google Scholar
• Nie, Z.; Xu, S.; Seo, M.; Lewis, P. C.; Kumacheva, E. Polymer Particles with Various Shapes and Morphologies Produced in Continuous Microfluidic Reactors. J. Am. Chem. Soc. 2005, 127, 8058–8063. DOI: 10.1021/ja042494w.
   PubMed Web of Science ®Google Scholar
• Tan, J.; Xu, J. H.; Li, S. W.; Luo, G. S. Drop Dispenser in a Cross-Junction Microfluidic Device: Scaling and Mechanism of Break-up. Chem. Eng. J. 2008, 136, 306–311. DOI: 10.1016/j.cej.2007.04.011.
   Web of Science ®Google Scholar
• van Loo, S.; Stoukatch, S.; Kraft, M.; Gilet, T. Droplet Formation by Squeezing in a Microfluidic Cross-Junction. Microfluid. Nanofluid. 2016, 20, 146. DOI: 10.1007/s10404-016-1807-1.
   Web of Science ®Google Scholar
• Thiele, J.; Abate, A. R.; Shum, H. C.; Bachtler, S.; Förster, S.; Weitz, D. A. Fabrication of Polymersomes Using Double-Emulsion Templates in Glass-Coated Stamped Microfluidic Devices. Small 2010, 6, 1723–1727. DOI: 10.1002/smll.201000798.
   PubMed Web of Science ®Google Scholar
• Higuera, F. J.; Succi, S.; Benzi, R. Lattice Gas Dynamics with Enhanced Collisions. Europhys. Lett. 1989, 9, 345–349. DOI: 10.1209/0295-5075/9/4/008.
   Google Scholar
• Higuera, F. J.; Jiménez, J. Boltzmann Approach to Lattice Gas Simulations. Europhys. Lett. 1989, 9, 663–668. DOI: 10.1209/0295-5075/9/7/009.
   Google Scholar
• Benzi, R.; Succi, S.; Vergassola, M. The Lattice Boltzmann Equation: theory and Applications. Phys. Rep. 1992, 222, 145–197. DOI: 10.1016/0370-1573(92)90090-M.
   Web of Science ®Google Scholar
• Benzi, R.; Sbragaglia, M.; Succi, S.; Bernaschi, M.; Chibbaro, S. Mesoscopic Lattice Boltzmann Modeling of Soft-Glassy Systems: Theory and Simulations. J. Chem. Phys. 2009, 131, 104903. DOI: 10.1063/1.3216105.
   Web of Science ®Google Scholar
• Benzi, R.; Chibbaro, S.; Succi, S. Mesoscopic Lattice Boltzmann Modeling of Flowing Soft Systems. Phys. Rev. Lett. 2009, 102, 026002. DOI: 10.1103/PhysRevLett.102.026002.
   PubMed Web of Science ®Google Scholar
• Gunstensen, A. K.; Rothman, D. H.; Zaleski, S.; Zanetti, G. Lattice Boltzmann Model of Immiscible Fluids. Phys. Rev. A. 1991, 43, 4320–4327. DOI: 10.1103/PhysRevA.43.4320.
   PubMed Web of Science ®Google Scholar
• Rothman, D. H.; Keller, J. M. Immiscible Cellular-Automaton Fluids. J. Stat. Phys. 1988, 52, 1119–1127. DOI: 10.1007/BF01019743.
   Web of Science ®Google Scholar
• Huang, H.; Wang, L.; Lu, X. Evaluation of Three Lattice Boltzmann Models for Multiphase Flows in Porous Media. Comput. Math. Appl. 2011, 61, 3606–3617. DOI: 10.1016/j.camwa.2010.06.034.
   Web of Science ®Google Scholar
• Shan, X.; Chen, H. Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components. Phys. Rev. E. 1993, 47, 1815–1819. DOI: 10.1103/PhysRevE.47.1815.
   PubMed Web of Science ®Google Scholar
• Swift, M. R.; Orlandini, E.; Osborn, W. R.; Yeomans, J. M. Lattice Boltzmann Simulations of Liquid-Gas and Binary Fluid Systems. Phys. Rev. E. 1996, 54, 5041–5052. DOI: 10.1103/PhysRevE.54.5041.
   PubMed Web of Science ®Google Scholar
• He, X.; Chen, S.; Zhang, R. A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability. J. Comput. Phys. 1999, 152, 642–663. DOI: 10.1006/jcph.1999.6257.
   Web of Science ®Google Scholar
• Yan, Y. Y.; Zu, Y. Q.; Dong, B. LBM, a Useful Tool for Mesoscale Modelling of Single-Phase and Multiphase Flow, in. Appl. Therm. Eng. 2011, 31, 649–655. DOI: 10.1016/j.applthermaleng.2010.10.010.
   Web of Science ®Google Scholar
• Leclaire, S.; Reggio, M.; Trépanier, J. Y. Progress and Investigation on Lattice Boltzmann Modeling of Multiple Immiscible Fluids or Components with Variable Density and Viscosity Ratios. J. Comput. Phys. 2013, 246, 318–342. DOI: 10.1016/j.jcp.2013.03.039.
   Web of Science ®Google Scholar
• Liu, H.; Zhang, Y. Droplet Formation in Microfluidic Cross-Junctions. Phys. Fluids. 2011, 23, 082101. DOI: 10.1063/1.3615643.
   Web of Science ®Google Scholar
• Fu, Y.; Zhao, S.; Bai, L.; Jin, Y.; Cheng, Y. Numerical Study of Double Emulsion Formation in Microchannels by a Ternary Lattice Boltzmann Method. Chem. Eng. Sci. 2016, 146, 126–134. DOI: 10.1016/j.ces.2016.02.036.
   Web of Science ®Google Scholar
• Azarmanesh, M.; Farhadi, M.; Azizian, P. Double Emulsion Formation through Hierarchical Flow-Focusing Microchannel. Phys. Fluids. 2016, 28, 032005. DOI: 10.1063/1.4944058.
   Web of Science ®Google Scholar
• Bhatnagar, P. L.; Gross, E. P.; Krook, M. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Phys. Rev. 1954, 94, 511–525. DOI: 10.1103/PhysRev.94.511.
   Web of Science ®Google Scholar
• Reis, T.; Phillips, T. N. Lattice Boltzmann Model for Simulating Immiscible Two-Phase Flows. J. Phys. A: Math. Theor. 2007, 40, 4033–4053. DOI: 10.1088/1751-8113/40/14/018.
   Web of Science ®Google Scholar
• Sbragaglia, M.; Benzi, R.; Biferale, L.; Succi, S.; Sugiyama, K.; Toschi, F. Generalized Lattice Boltzmann Method with Multirange Pseudopotential. Phys. Rev. E. 2007, 75, 026702. DOI: 10.1103/PhysRevE.75.026702.
   Web of Science ®Google Scholar
• Leclaire, S.; Reggio, M.; Trépanier, J. Y. Isotropic Color Gradient for Simulating Very High-Density Ratios with a Two-Phase Flow Lattice Boltzmann Model. Comput. Fluids. 2011, 48, 98–112. DOI: 10.1016/j.compfluid.2011.04.001.
   Web of Science ®Google Scholar
• Guzowski, J.; Korczyk, P. M.; Jakiela, S.; Garstecki, P. The Structure and Stability of Multiple Micro-Droplets. Soft Matter. 2012, 8, 7269. DOI: 10.1039/c2sm25838b.
   Web of Science ®Google Scholar
• D’Ortona, U.; Salin, D.; Cieplak, M.; Rybka, R. B.; Banavar, J. R. Two-Color Nonlinear Boltzmann Cellular Automata: Surface Tension and Wetting. Phys. Rev. E. 1995, 51, 3718–3728. DOI: 10.1103/PhysRevE.51.3718.
   PubMed Web of Science ®Google Scholar
• Wu, L.; Tsutahara, M.; Kim, L. S.; Ha, M. Three-Dimensional Lattice Boltzmann Simulations of Droplet Formation in a Cross-Junction Microchannel. Int. J. Multiph. Flow. 2008, 34, 852–864. DOI: 10.1016/j.ijmultiphaseflow.2008.02.009.
   Web of Science ®Google Scholar
• Zou, Q.; He, X. On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model. Phys. Fluids. 1997, 9, 1591–1598. DOI: 10.1063/1.869307.
   Web of Science ®Google Scholar
• Ladd, A. J. C. Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation. Part 1. Theoretical Foundation. J. Fluid Mech. 1994, 271, 285. DOI: 10.1017/S0022112094001771.
   Web of Science ®Google Scholar