Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T22:13:12.358Z Has data issue: false hasContentIssue false
  • English
  • Français

Lattice Boltzmann Simulation of Droplet Generation in a Microfluidic Cross-Junction

Published online by Cambridge University Press:  20 August 2015

Haihu Liu and
Yonghao Zhang
Haihu Liu*
Affiliation:
Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
Yonghao Zhang*
Affiliation:
Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
*
Email:haihu.liu@strath.ac.uk
Corresponding author.Email:yonghao.zhang@strath.ac.uk
Get access

Abstract

Using the lattice Boltzmann multiphase model, numerical simulations have been performed to understand the dynamics of droplet formation in a microfluidic cross-junction. The influence of capillary number, flow rate ratio, viscosity ratio, and viscosity of the continuous phase on droplet formation has been systematically studied over a wide range of capillary numbers. Two different regimes, namely the squeezinglike regime and the dripping regime, are clearly identified with the transition occurring at a critical capillary number Cacr. Generally, large flow rate ratio is expected to produce big droplets, while increasing capillary number will reduce droplet size. In the squeezing-like regime (Ca ≤ Cacr), droplet breakup process is dominated by the squeezing pressure and the viscous force; while in the dripping regime (Ca ≤ Cacr), the viscous force is dominant and the droplet size becomes independent of the flow rate ratio as the capillary number increases. In addition, the droplet size weakly depends on the viscosity ratio in both regimes and decreases when the viscosity of the continuous phase increases. Finally, a scaling law is established to predict the droplet size.

Keywords

47.55.db47.55.df47.61.-k47.61.JdDroplet generationmicrodroplet technologylattice Boltzmann methodmultiphase flow

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011, pp. 1235 - 1256
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Song, H., Chen, D. L., and Ismagilov, R. F., Reactions in droplets in microfluidic channels, Angew. Chem. Int. Ed., 45 (2006), 7336–7356.CrossRefGoogle ScholarPubMed
[2]deMello, A. J., Microfluidics: DNA amplification moves on, Nature., 422 (2003), 28–29.CrossRefGoogle Scholar
[3]Huebner, A., Sharma, S., Srisa-Art, M., Hollfelder, F., Edel, J. B., and deMello, A. J., Micro-droplets: a sea of applications?, Lab. Chip., 8 (2008), 1244–1254.Google Scholar
[4]Stone, H., Stroock, A., and Ajdari, A., Engineering flows in small devices microfluidics toward a Lab-on-a-chip, Annu. Rev. Fluid. Mech., 36 (2004), 381–411.CrossRefGoogle Scholar
[5]Yasuno, M., Sugiura, S., Iwamoto, S., Nakajima, M., Shono, A., and Satoh, K., Monodispersed microbubble formation using microchannel technique, AIChE J., 50 (2004), 3227–3233.Google Scholar
[6]Sugiura, S., Nakajima, M., and Seki, M., Predictionof droplet diameter for microchannel emul-sification: prediction model for complicated microchannel geometries, Ind. Eng. Chem. Res., 43 (2004), 8233–8238.Google Scholar
[7]Anna, S. L., Bontoux, N., and Stone, H. A., Formation of dispersions using “flow focusing” in microchannels, Appl. Phys. Lett., 82 (2003), 364–366.CrossRefGoogle Scholar
[8]Cubaud, T., Tatineni, M., Zhong, X., and Ho, C.-M., Bubble dispenser in microfluidic devices, Phys. Rev. E., 72 (2005), 037302.CrossRefGoogle ScholarPubMed
[9]Garstecki, P., Stone, H. A., and Whitesides, G. M., Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions, Phys. Rev. Lett., 94 (2005), 164501.CrossRefGoogle ScholarPubMed
[10]Fu, T., Ma, Y., Funfschilling, D., and Li, H. Z., Bubble formation and breakup mechanism in a microfluidic flow-focusing device, Chem. Eng. Sci., 64(10) (2009), 2392–2400.Google Scholar
[11]Thorsen, T., Roberts, R. W., Arnold, F. H., and Quake, S. R., Dynamic pattern formation in a vesicle-generating microfluidic device, Phys. Rev. Lett., 86 (2001), 4163–4166.CrossRefGoogle Scholar
[12]Nisisako, T., Torii, T., and Higuchi, T., Droplet formation in a microchannel network, Lab. Chip., 2 (2002), 24–26.Google Scholar
[13]Xu, J. H., Luo, G. S., Li, S. W., and Chen, G. G., Shear force induced monodisperse droplet formation in a microfluidic device by controlling wetting properties, Lab. Chip., 6 (2005), 131–136.Google Scholar
[14]Garstecki, P., Fuerstman, M. J., Stone, H. A., and Whitesides, G. M., Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up, Lab. Chip., 6 (2006), 437–446.Google Scholar
[15]Graaf, S. van der, Nisisako, T., Schrön, C. G. P. H., van der Sman, R. G. M., and Boom, R. M., Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel, Langmuir., 22 (2006), 4144–4152.Google Scholar
[16]Christopher, G. F., Noharuddin, N. N., Taylor, J. A., and Anna, S. L., Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions, Phys. Rev. E., 78 (2008), 036317.Google Scholar
[17]Umbanhowar, P. B., Prasad, V., and Weitz, D. A., Monodisperse emulsion generation via drop break off in a coflowing stream, Langmuir., 16 (2000), 347–351.Google Scholar
[18]Hua, J., Zhang, B., and Lou, J., Numerical simulation of microdroplet formation in coflowing immiscible liquids, AIChE J., 53 (2007), 2534–2548.Google Scholar
[19]Tan, J., Xu, J., Li, S., and Luo, G., Drop dispenser in a cross-junction microfluidic device: scaling and mechanism of break-up, Chem. Eng. J., 136 (2008), 306–311.Google Scholar
[20]Davidson, M. R., Harvie, D. J. E., and Cooper-White, J. J., Flow focusing in microchannels, ANZIAM J., 46 (2004), C47–C58.Google Scholar
[21]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford, Oxford University Press, 2001.CrossRefGoogle Scholar
[22]Chen, S., and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid. Mech., 30 (1998), 329–364.Google Scholar
[23]Dupin, M. M., Halliday, I., and Care, C. M., Simulation of a microfluidic flow-focusing device, Phys. Rev. E., 73 (2006) 055701.CrossRefGoogle ScholarPubMed
[24]Yu, Z., Hemminger, O., and Fan, L.-S., Experiment and lattice Boltzmann simulation of two-phase gas-liquid flows in microchannels, Chem. Eng. Sci., 62 (2007), 7172–7183.Google Scholar
[25]Wu, L., Tsutahara, M., Kim, L. S., and Ha, M., Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel, Int. J. Multiphase. Flow., 34 (2008), 852–864.Google Scholar
[26]Kim, L., Jeong, H., Ha, M., and Kim, K., Numerical simulation of droplet formation in a microchannel using the lattice Boltzmann method, J. Mech. Sci. Tech., 22 (2008), 770–779.Google Scholar
[27]Liu, H., and Zhang, Y., Droplet formation in a T-shaped microfluidic junction, J. Appl. Phys., 106 (2009), 034906.Google Scholar
[28]Gupta, A., Murshed, S. M. S., and Kumar, R., Droplet formation and stability of flows in a microfluidic T-junction, Appl. Phys. Lett., 94 (2009), 164107.Google Scholar
[29]Cahn, J. W., Critical point wetting, J. Chem. Phys., 66 (1977), 3667–3672.Google Scholar
[30]Menech, M. D., Modeling of droplet breakup in a microfluidic T-shaped junction with a phase-field model, Phys. Rev. E., 73 (2006), 031505.Google Scholar
[31]Zhou, C., Yue, P., and Feng, J. J., Formation of simple and compound drops in microfluidic devices, Phys. Fluids., 18 (2006), 092105.Google Scholar
[32]Yu, W., and Zhou, C., Coalescence of droplets in viscoelastic matrix with diffuse interface under simple shear flow, J. Polym. Sci. Part. B. Polym. Phys., 45 (2007), 1856–1869.Google Scholar
[33]van der Sman, R., and van der Graaf, S., Emulsion droplet deformation and breakup with lattice Boltzmann model, Comput. Phys. Commun., 178 (2008), 492–504.CrossRefGoogle Scholar
[34]Swift, M. R., Orlandini, E., Osborn, W. R., and Yeomans, J. M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev. E., 54(5) (1996), 5041–5052.Google Scholar
[35]Rowlinson, J. S., and Widom, B., Molecular Theory of Capillarity, London, Clarendon Press, 1989.Google Scholar
[36]Kendon, V. M., Cates, M. E., Pagonabarraga, I., Desplat, J. C., and Bladon, P., Inertial effects in three-dimensional spinodal. decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study, J. Fluid. Mech., 440 (2001), 147–203.CrossRefGoogle Scholar
[37]Guo, Z., Zheng, C., and Shi, B., Discrete lattice effects on the forcing term in the lattice Boltz-mann method, Phys. Rev. E., 65 (2002), 046308.Google Scholar
[38]van der Sman, R. G. M., Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices, Phys. Rev. E., 74 (2006), 026705.Google Scholar
[39]Zou, Q., and He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids., 9 (1997), 1591–1598.Google Scholar
[40]Hao, L., and Cheng, P., Lattice Boltzmann simulations of liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel, J. Power. Sources., 190 (2009), 435–446.Google Scholar
[41]Pooley, C. M., and Furtado, K., Eliminating spurious velocities in the free-energy lattice Boltz-mann method, Phys. Rev. E., 77 (2008), 046702.Google Scholar
[42]Lishchuk, S. V., Care, C. M., and Halliday, I., Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents, Phys. Rev. E., 67 (2003), 036701.Google Scholar
[43]Gunstensen, A. K., Rothman, D. H., Zaleski, S., and Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A., 43(8) (1991), 4320–4327.Google Scholar
[44]Shan, X., and Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E., 47(3) (1993), 1815–1819.Google Scholar
[45]Roths, T., Friedrich, C., Marth, M., and Honerkamp, J., Dynamics and rheology of the morphology of immiscible polymer blends-on modeling and simulation, Rheol. Acta., 41(3) (2002), 211–222.Google Scholar
[46]Zhou, H., and Pozrikidis, C., The flow of suspensions in channels: single files of drops, Phys. Fluids. A., 5(2) (1993), 311–324.Google Scholar
[47]Christopher, G. F., and Anna, S. L., Microfluidic methods for generating continuous droplet streams, J. Phys. D. Appl. Phys., 40 (2007), R319–R336.Google Scholar
[48]Gupta, A., and Kumar, R., Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction, Microfluid. Nanofluid., 8(6) (2010), 799–812.CrossRefGoogle Scholar
[49]Menech, M.D., Garstecki, P., Jousse, F., and Stone, H. A., Transition from squeezing to dripping in a microfluidic T-shaped junction, J. Fluid. Mech., 595 (2008), 141–161.Google Scholar
[50]Stone, H. A., Dynamics of drop deformation and breakup in viscous fluids, Annu. Rev. Fluid. Mech., 26 (1994), 65–102.Google Scholar
[51]Tomotika, S., On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid, Proc. R. Soc. London. Ser. A., 150 (1935), 322–337.Google Scholar