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Transition from squeezing to dripping in a microfluidic T-shaped junction

Published online by Cambridge University Press:  08 January 2008

M. DE MENECH
Affiliation:
Max–Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany
P. GARSTECKI
Affiliation:
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland
F. JOUSSE
Affiliation:
Unilever Corporate Research, Colworth House, Sharnbrook, Bedfordshire, MK44 1LQ, UK
H. A. STONE
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

Abstract

We describe the results of a numerical investigation of the dynamics of breakup of streams of immiscible fluids in the confined geometry of a microfluidic T-junction. We identify three distinct regimes of formation of droplets: squeezing, dripping and jetting, providing a unifying picture of emulsification processes typical for microfluidic systems. The squeezing mechanism of breakup is particular to microfluidic systems, since the physical confinement of the fluids has pronounced effects on the interfacial dynamics. In this regime, the breakup process is driven chiefly by the buildup of pressure upstream of an emerging droplet and both the dynamics of breakup and the scaling of the sizes of droplets are influenced only very weakly by the value of the capillary number. The dripping regime, while apparently homologous to the unbounded case, is also significantly influenced by the constrained geometry; these effects modify the scaling law for the size of the droplets derived from the balance of interfacial and viscous stresses. Finally, the jetting regime sets in only at very high flow rates, or with low interfacial tension, i.e. higher values of the capillary number, similar to the unbounded case.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse–interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139165.CrossRefGoogle Scholar
Anna, S. L., Bontoux, N. & Stone, H. A. 2003 Formation of dispersions using flow focusing in microchannels. Appl. Phys. Lett. 82, 364366.CrossRefGoogle Scholar
Badalassi, V. E., Ceniceros, H. D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190, 371.CrossRefGoogle Scholar
Basaran, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 18421848.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Blackmore, B., Li, D. Q. & Gao, J. 2001 Detachment of bubbles in slit microchannels by shearing flow. J. Colloid Interface Sci. 241, 514520.CrossRefGoogle Scholar
Cahn, J. W. 1965 Phase separation by spinodal decomposition in isotropic systems. J. Chem. Phys. 42, 9399.CrossRefGoogle Scholar
Cahn, J. W. 1977 Critical point wetting. J. Chem. Phys. 66, 36673672.CrossRefGoogle Scholar
Christopher, G. F. & Anna, S. L. 2007 Microfluidic methods for generating continuous droplet streams. J. Phys. D: Appl. Phys. 40, R319R336.CrossRefGoogle Scholar
Cornish, V. W. 2006 Catalytic competition for cells. Nature 440, 156157.CrossRefGoogle ScholarPubMed
Cramer, C., Fischer, P. & Windhab, E. J. 2004 Drop formation in a co-flowing ambient fluid. Chem Engng Sci. 59, 30453058.CrossRefGoogle Scholar
Cristini, V., Balwzdziewicz, J. & Loewenberg, M. 1998 Drop breakup in three-dimensional viscous flows. Phys. Fluids 10, 17811783.CrossRefGoogle Scholar
Cristini, V. & Tan, Y.-C. 2004 Theory and numerical simulation of droplet dynamics in complex flows – a review. Lab Chip 4, 257264.CrossRefGoogle ScholarPubMed
Cubaud, T. & Ho, C. M. 2004 Transport of bubbles in square microchannels. Phys. Fluids 16, 45754585.CrossRefGoogle Scholar
Cubaud, T., Tatieni, M. T., Zhong, X. & Ho, C. M. 2005 Bubble dispenser in microfluidic devices. Phys. Rev. E 172, 037302.Google Scholar
Cygan, Z. T., Cabral, J. T., Beers, K. L. & Amis, E. J. 2005 Microfluidic platform for the generation of organic-phase microreactors. Langmuir 21, 36293634.CrossRefGoogle ScholarPubMed
De Menech, M. 2006 Modeling of droplet breakup in a microfluidic T-shaped junction. Phys. Rev. E 73, 031505.Google Scholar
Dendukuri, D., Tsoi, K., Hatton, T. A. & Doyle, P. S. 2005 Controlled synthesis of nonspherical microparticles using microfluidics. Langmuir 21, 21132116.CrossRefGoogle ScholarPubMed
Dreyfus, R., Tabeling, P. & Willaime, H. 2003 Ordered and disordered patterns in two-phase flows in microchannels. Phys. Rev. Lett. 90, 144505.CrossRefGoogle ScholarPubMed
Duffy, D. C., McDonald, J. C., Schueller, O. J. A. & Whitesides, G. M. 1998 Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Ann. Chem. 70, 49744984.CrossRefGoogle ScholarPubMed
Dupuis, A. & Yeomans, J. M. 2004 Lattice Boltzmann modelling of droplets on chemically heterogeneous surfaces. Future Generation Comput. Syst. 20, 9931001.CrossRefGoogle Scholar
Engl, W., Roche, M., Colin, A., Panizza, P. & Ajdari, A. 2005 Droplet traffic at a simple junction at low capillary numbers. Phys. Rev. Lett. 95, 208305.CrossRefGoogle Scholar
Feng, J. Q. & Basaran, O. A. 1994 Shear flow over a translationally-symmetric cylindrical bubble pinned on a slot in a plane wall. J. Fluid Mech. 275, 351378.CrossRefGoogle Scholar
Ganán-Calvo, A. M. & Gordillo, J. M. 2001 Perfectly monodisperse microbubbling by capillary flow focusing. Phys. Rev. Lett. 87, 274501.CrossRefGoogle ScholarPubMed
Garstecki, P., Gitlin, I., DiLuzio, W., Whitesides, G., Kumacheva, E. & Stone, H. A. 2004 Formation of monodisperse bubbles in a microfluidic flow–focusing device. Appl. Phys. Lett. 85, 26492651.CrossRefGoogle Scholar
Garstecki, P., Fuerstman, M. & Whitesides, G. M. 2005 a Design for mixing using bubbles in branched microfluidic channels. Appl. Phys. Lett. 86, 244108.CrossRefGoogle Scholar
Garstecki, P., Fuerstman, M. & Whitesides, G. M. 2005 b Nonlinear dynamics of a microfluidic flow-focusing bubble generator. Phys. Rev. Lett. 94, 234502.CrossRefGoogle Scholar
Garstecki, P., Fuerstman, M. & Whitesides, G. M. 2005 c Oscillations with uniquely long periods in a microfluidic bubble generator. Nature Phys. 1, 168171.CrossRefGoogle Scholar
Garstecki, P., Stone, H. A. & Whitesides, G. M. 2005 d Mechanisms for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys. Rev. Lett. 94, 164501.CrossRefGoogle ScholarPubMed
Garstecki, P., Feuerstman, M., Stone, H. A. & Whitesides, G. M. 2006 Formation of droplets and bubbles in a microfluidic T-junction: scaling and mechanism of breakup. Lab Chip 6, 437446.CrossRefGoogle Scholar
Gerdts, C. J., Sharoyan, D. E. & Ismagilov, R. F. 2004 A synthetic reaction network: chemical amplification using nonequilibrium autocatalytic reactions coupled in time. J. Am. Chem. Soc. 126, 63276331.CrossRefGoogle ScholarPubMed
van der Graaf, S., Nisisako, T., Schroen, C. G. P. H., van der Sman, R. G. M. & Boom, R. M. 2006 Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. Langmuir 22, 41444152.CrossRefGoogle Scholar
Guillot, P. & Colin, A. 2005 Stability of parallel flows in a microchannel after a T junction. Phys. Rev. E 72, 066301.Google Scholar
Gunther, A. & Jensen, K. F. 2006 Multiphase microfluidics: from flow characteristics to chemical and materials synthesis. Lab Chip 6, 14871503.CrossRefGoogle ScholarPubMed
Gunther, A., Kahn, S. A., Thalmann, M., Trachsel, F. & Jensen, K. F. 2004 Transport and reaction in microscale segmented gas–liquid. Lab Chip 4, 278286.CrossRefGoogle ScholarPubMed
He, M. Y., Edgar, J. S., Jeffries, G. D. M., Lorenz, R. M., Shelby, J. P. & Chiu, D. T. 2005 Selective encapsulation of single cells and subcellular organelles into picoliter-and femtoliter-volume droplets. Ann. Chem. 77, 15391544.CrossRefGoogle ScholarPubMed
Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modelling. J. Comput. Phys. 155, 96127.CrossRefGoogle Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 5788.CrossRefGoogle Scholar
Jensen, M. J., Stone, H. A. & Bruus, H. 2006 A numerical study of two-phase Stokes flow in an axisymmetric flow-focusing device. Phys. Fluids 18, 077103.CrossRefGoogle Scholar
Jeong, W., Kim, J. Y., Kim, S., Lee, S., Mensing, G. & Beebe, D. J. 2004 Hydrodynamic microfabrication via ‘on the fly’ photopolymerization of microscale fibers and tubes. Lab Chip 4, 576580.CrossRefGoogle Scholar
Jeong, W. J., Kim, J. Y., Choo, J., Lee, E. K., Han, C. S., Beebe, D. J., Seong, G. H. & Lee, S. H. 2005 Continuous fabrication of biocatalyst immobilized microparticles using photopolymerization and immiscible liquids in microfluidic systems. Langmuir 21, 37383741.CrossRefGoogle ScholarPubMed
Kenis, P. J. A., Ismagilov, R. F. & Whitesides, G. M. 1999 Microfabrication inside capillaries using multiphase laminar flow patterning. Science 285, 8385.CrossRefGoogle ScholarPubMed
Kim, J. 2005 A continuous surface tension force formulation for diffuse-interface models. J. Comput. Phys. 204, 784804.CrossRefGoogle Scholar
Kuksenok, O., Jasnow, D., Yeomans, J. & Balazs, A. C. 2003 Periodic droplet formation in chemically patterned microchannels. Phys. Rev. Lett. 91, 108303.CrossRefGoogle ScholarPubMed
Li, M., Zheng, L. & Harris, M. T. 2000 Modeling the synthesis of porous spherical shells and microspheres of zirconia by electrodispersion precipitation. J. Powder Technol. 110, 1521.CrossRefGoogle Scholar
Li, X. & Pozrikidis, C. 1996 Shear flow over a liquid drop adhering to a solid surface. J. Fluid Mech. 307, 167190.CrossRefGoogle Scholar
Link, D. R., Anna, S. L., Weitz, D. A. & Stone, H. A. 2004 Geometrically mediated breakup of drops in microfluidic devices. Phys. Rev. Lett. 92, 053403.CrossRefGoogle ScholarPubMed
McDonald, J. C., Duffy, D. C., Anderson, J. R., Chiu, D. T., Wu, H., Schueller, O. J. A. & Whitesides, G. M. 2000 Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21–40, 27.3.0.CO;2-C>CrossRefGoogle Scholar
Nisisako, T., Torii, T. & Higuchi, T. 2004 Novel microreactors for functional polymer beads. Chem. Engng J. 101, 2329.CrossRefGoogle Scholar
Okushima, S., Nisisako, T., Torii, T. & Higuchi, T. 2004 Controlled production of monodisperse double emulsions by two-step breakup in microfluidic devices. Langmuir 20, 99059908.CrossRefGoogle ScholarPubMed
Osher, S. & Fedkiw, R. P. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169, 463502.CrossRefGoogle Scholar
Pedersen, H. & Horvath, C. 1981 Axial dispersion in a segmented gas–liquid flow. Ind. Engng Chem. Fund. 20, 181186.CrossRefGoogle Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in viscous flow. Annu. Rev. Fluid. Mech. 16, 4566.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free-surface and interfacial flows. Annu. Rev. Fluid Mech 31, 567603.CrossRefGoogle Scholar
Schleizer, A. D. & Bonnecaze, R. T. 1999 Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows. J. Fluid Mech. 383, 2954.CrossRefGoogle Scholar
Sia, S. K., Linder, V., Parviz, B. A., Siegel, A. & Whitesides, G. M. 2004 An integrated approach to a portable low-cost immunoassay for resource-poor settings. Angew. Chem. Intl Edn 43, 498502.CrossRefGoogle ScholarPubMed
Song, H. & Ismagilov, R. F. 2003 Millisecond kinetics on a microfluidic chip in multiphase microfluidics at low values of the Reynolds and capillary numbers. J. Am. Chem. Soc. 125, 14 61314 619.CrossRefGoogle Scholar
Song, H., Bringer, M. R., Tice, J. D., Gerdts, C. J. & Ismagilov, R. F. 2003 Experimental test of scaling of mixing by chaotic advection moving through microfluidic channels. Appl. Phys. Lett. 83, 46644666.CrossRefGoogle ScholarPubMed
Song, H., Chen, D. L. & Ismagilov, R. F. 2006 Reactions in droplets in microfluidic channels. Angew. Chem. Intl Edn 45, 73367356.CrossRefGoogle ScholarPubMed
Squires, T. & Quake, S. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 9771026.CrossRefGoogle Scholar
Stone, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid. Mech. 26, 65102.CrossRefGoogle Scholar
Stone, H. A. 2005 On lubrication flows in geometries with zero curvature. Chem. Engng Sci. 60, 48384845.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid. Mech 36, 381411.CrossRefGoogle Scholar
Subramaniam, A. B., Abkarian, M. & Stone, H. A. 2005 Controlled assembly of jammed colloidal shells on fluid droplets. Nature Materials 4, 553556.CrossRefGoogle ScholarPubMed
Sugiura, S., Nakajima, M., Iwamoto, S. & Seki, M. 2001 Interfacial tension driven monodisperse droplet formation from microfabricated channel array. Langmuir 17, 55625566.CrossRefGoogle Scholar
Sugiura, S., Oda, T., Izumida, Y., Aoyagi, Y., Satake, M., Ochiai, A. & Ohkohchi, N. 2005 Size control of calcium alginate beads containing living cells using micro-nozzle array. Biomaterials 26, 33273331.CrossRefGoogle ScholarPubMed
Suryo, R. & Basaran, O. A. 2006 Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18, 082102.CrossRefGoogle Scholar
Takeuchi, S., Garstecki, P., Weibel, D. B. & Whitesides, G. M. 2005 An axisymmetric flow–focusing microfluidic device. Adv. Materials 17, 10671072.CrossRefGoogle Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501523.Google Scholar
Thorsen, T., Roberts, R. W., Arnold, F. H. & Quake, S. R. 2001 Dynamic pattern formation in a vesicle-generating microfluidic device. Phys. Rev. Lett. 86, 41634166.CrossRefGoogle Scholar
Tice, J. D., Lyon, A. D. & Ismagilov, R. F. 2004 Effects of viscosity on droplet formation and mixing in microfluidic channels. An. Chim. Acta 507, 7377.CrossRefGoogle Scholar
Umbanhowar, P. B., Prasad, V. & Weitz, D. A. 2000 Monodisperse emulsion generation via drop break off in a coflowing stream. Langmuir 16, 347351.CrossRefGoogle Scholar
Utada, A. S., Lorenceau, E., Link, D. R., Kaplan, P. D, Stone, H. A. & Weitz, D. A. 2005 Monodisperse double emulsions generated from a microcapillary device. Science 308, 537541.CrossRefGoogle ScholarPubMed
Utada, A. S., Fernandez-Nieves, A., Stone, H. A. & Weitz, D. A. 2007 Dripping to jetting transitions in co-flowing liquid streams. Phys. Rev. Lett. 99, 094502.CrossRefGoogle Scholar
Wagner, A. J. & Yeomans, Y. M. 1997 Effect of shear on droplets in a binary mixture. Intl J. Mod. Phys. C 8, 773782.CrossRefGoogle Scholar
Wagner, A. J., Wilson, L. M. & Cates, M. E. 2003 Role of inertia in two-dimensional deformation and breakdown of a droplet. Phys. Rev. E 68, 045301(R).Google ScholarPubMed
Ward, T., Faivre, M., Abkarian, M. & Stone, H. A. 2005 Microfluidic flow focusing: drop size and scaling in pressure versus flow-rate-driven pumping. Electrophoresis 26, 37163724.CrossRefGoogle ScholarPubMed
Wilkes, E. D., Phillips, S. & Basaran, O. 1999 Computational and experimental analysis of dynamics of drop formation. Phys. Fluids 11, 35773598.CrossRefGoogle Scholar
Xu, Q. & Nakajima, M. 2004 The generation of highly monodisperse droplets through the breakup of hydrodynamically focused microthread in a microfluidic device. Appl. Phys. Lett. 85, 37263728.CrossRefGoogle Scholar
Xu, S. Q., Nie, Z. H., Seo, M., Lewis, P., Kumacheva, E., Stone, H. A., Garstecki, P., Weibel, D. B., Gitlin, I. & Whitesides, G. M. 2005 Generation of monodisperse particles by using microfluidics: control over size, shape, and composition. Angew. Chem. Intl Edn 44, 724728.CrossRefGoogle ScholarPubMed
Zhang, D. F. & Stone, H. A. 1997 Drop formation in viscous flows at a vertical capillary tube. Phys. Fluids 9, 22342242.CrossRefGoogle Scholar
Zheng, B. & Ismagilov, R. F. 2005 A microfluidic approach for screening submicroliter volumes against multiple reagents by using preformed arrays of nanoliter plugs in a three-phase liquid/liquid/gas flow. Angew. Chem. Intl Edn 44, 25202523.CrossRefGoogle Scholar
Zheng, B., Roach, L. S. & Ismagilov, R. F. 2003 Screening of protein crystallization conditions on a microfluidic chip using nanoliter-size droplets. J. Am. Chem. Soc. 125, 11 17011 171.CrossRefGoogle ScholarPubMed
Zhou, C., Yue, P. & Feng, J. J. 2006 Formation of simple and compound drops in microfluidic devices. Phys. Fluids 18, 092105.CrossRefGoogle Scholar