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Lattice Boltzmann Simulations of Thermocapillary Motion of Droplets in Microfluidic Channels

Published online by Cambridge University Press:  03 June 2015

Jonathan Li ,
Haihu Liu ,
Nikolaos Ioannou ,
Yonghao Zhang  and
Jason M. Reese
Jonathan Li
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, United Kingdom
Haihu Liu*
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, United Kingdom School of Energy and Power Engineering, Xi’an Jiaotong University; 28 West Xianning Road, Xi’an 710049, China
Nikolaos Ioannou
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, United Kingdom
Yonghao Zhang
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, United Kingdom
Jason M. Reese
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh, EH9 3JT, United Kingdom
*
*Corresponding author. Email addresses: [email protected] (H. Liu), [email protected] (J. Li), [email protected] (N. Ioannou), [email protected] (Y. Zhang), [email protected] (J. M. Reese)
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Abstract

Our recently developed lattice Boltzmann model is used to simulate droplet dynamical behaviour governed by thermocapillary force in microchannels. One key research challenge for developing droplet-based microfluidic systems is control of droplet motion and its dynamic behaviour. We numerically demonstrate that the thermocapillary force can be exploited for microdroplet manipulations including synchronisation, sorting, and splitting. This work indicates that the lattice Boltzmann method provides a promising design simulation tool for developing complex droplet-based microfluidic devices.

Keywords

76T99Lattice Boltzmann methodthermocapillary forcedroplet manipulationmicrofluidics
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 5 , May 2015 , pp. 1113 - 1126
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Fair, R. B., Digital microfluidics: is a true lab-on-a-chip possible?, Microfluid. Nanofluidics, 3(2007), 245–281.Google Scholar
[2]Song, H., Chen, D. L. and Ismagilov, R. F., Reactions in droplets in microfluidic channels, Angew. Chem., Int. Ed., 45(2006), 7336–7356.Google Scholar
[3]Agresti, J. J., Antipov, E., Abate, A. R., Ahn, K., Rowat, A. C., Baret, J.-C., Marquez, M., Klibanov, A. M., Griffiths, A. D. and Weitz, D. A., Ultrahigh-throughput screening in drop-based microfluidics for directed evolution, PNAS, 107(2010), 4004–4009.Google Scholar
[4]Prakash, M. and Gershenfeld, N., Microfluidic bubble logic, Science, 315(2007) 832–835.Google Scholar
[5]Cheow, L. F., Yobas, L. and Kwong, D.-L., Digital microfluidics: Droplet based logic gates, Appl. Phys. Lett., 90(2007), 054107.CrossRefGoogle Scholar
[6]Choi, K., Ng, A. H.C., Fobel, R. and Wheeler, A. R., Digital microfluidics, Annu. Rev. Anal. Chem., 5(2012), 413–440.CrossRefGoogle ScholarPubMed
[7]Jiao, Z. J., Huang, X. Y. and Nguyen, N.-T., Manipulation of a droplet in a planar channel by periodic thermocapillary actuation, J. Micromech. Microeng. 18(2008), 045027.Google Scholar
[8]Liu, M.-C., Wu, J.-G., Tsai, M.-F., Yu, W.-S., Lin, P.-C., Chiu, I-C., Chin, H.-A., Cheng, I-C., Tung, Y.-C. and Chen, J.-Z., Two dimensional thermoelectric platforms for thermocapillary droplet actuation, RSC Adv., 2(2012), 1639–1642.CrossRefGoogle Scholar
[9]Cordero, M. L., Burnham, D. R., Baroud, C. N. and McGloin, D., Thermocapillary manipulation of droplets using holographic beam shaping: microfluidic pin ball, Appl. Phys. Lett., 93(2008), 034107.Google Scholar
[10]Baroud, C., Delville, J.-P., Gallaire, F. and Wunenburger, R., Thermocapillary valve for droplet production and sorting, Phys. Rev. E, 75(2007), 046302.CrossRefGoogle ScholarPubMed
[11]Baroud, C., Vincent, M. R. de Saint and Delville, J.-P., An optical toolbox for total control of droplet microfluidics, Lab Chip, 7(2007), 1029–1033.Google Scholar
[12]Vincent, M. R. de Saint, Wunenburger, R. and Delville, J.-P., Laser switching and sorting for high speed digital microfluidics, Appl. Phys. Lett., 92(2008), 154105.CrossRefGoogle Scholar
[13]Hirt, C. and Nichols, B., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39(1981), 201–225.Google Scholar
[14]Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79(1988), 12–49.Google Scholar
[15]Shyy, W., Smith, R. W., Udaykumar, H. S. and Rao, M. M., Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Washington, DC (1996).Google Scholar
[16]Chen, H.-Y., Jasñow, D. and Vinals, J., Interface and contact line motion in a two phase fluid under shear flow, Phys. Rev. Lett., 85(2000), 1686–1689.Google Scholar
[17]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30(1998), 329–364.Google Scholar
[18]Gunstensen, A. K., Rothman, D. H., Zaleski, S. and Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A, 43(1991), 4320–4327.Google Scholar
[19]Swift, M. R., Osborn, W. R. and Yeomans, J. M., Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75(1995), 830–833.CrossRefGoogle ScholarPubMed
[20]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(1996), 5041–5052.Google Scholar
[21]Shan, X. and Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47(1993), 1815–1819.Google Scholar
[22]He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152(1999), 642–663.Google Scholar
[23]Zhang, J., Lattice Boltzmann method for microfluidics: models and applications, Microfluid. Nanofluidics, 10(2011), 1–28.Google Scholar
[24]Liu, H., Zhang, Y. and Valocchi, A. J., Modeling and simulation of thermocapillary flows using lattice Boltzmann method, J. Comput. Phys., 231(2012), 4433–4453.Google Scholar
[25]Latva-Kokko, M. and Rothman, D. H., Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids, Phys. Rev. E, 71(2005), 056702.Google Scholar
[26]Liu, H., Valocchi, A. J., Zhang, Y. and Kang, Q., A phase-field-based lattice-Boltzmann finite-difference model for simulating thermocapillary flows, Phys. Rev. E, 87(2013), 013010.CrossRefGoogle ScholarPubMed
[27]Liu, H., Valocchi, A. J., Zhang, Y. and Kang, Q., Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel, J. Comput. Phys., 256(2014), 334–356.Google Scholar
[28]McNamara, G. R. and Zanetti, G., Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61(1988), 2332–2335.CrossRefGoogle ScholarPubMed
[29]Higuera, F. J. and Jiménez, J., Boltzmann approach to lattice gas simulations, Europhys. Lett., 9(1989), 663–668.CrossRefGoogle Scholar
[30]Bhatnagar, P. L., Gross, E. P. and Krook, M., A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94(1954), 511–525.Google Scholar
[31]Qian, Y. H., d’Humieres, D. and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17(1997), 479–484.Google Scholar
[32]Koelman, J. M. V. A., A simple lattice Boltzmann scheme for Navier-Stokes fluid flow, Europhys. Lett., 15(1991), 603–607.Google Scholar
[33]Brackbill, J. U., Kothe, D. B. and Zemach, C., A continuum method for modeling surface tension, J. Comp. Phys., 100(1992), 335–354.Google Scholar
[34]Guo, Z., Zheng, C. and Shi, B., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65(2002), 046308.Google Scholar
[35]Ginzburg, I. and Adler, P. M., Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. Phys. II France, 4(1994), 191–214.Google Scholar
[36]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
[37]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. and Toschi, F., Generalized lattice Boltzmann method with multirange pseudopotential, Phys. Rev. E, 75(2007), 026702.CrossRefGoogle Scholar
[38]Halliday, I., Hollis, A. P. and Care, C. M., Lattice Boltzmann algorithm for continuum multi-component flow, Phys. Rev. E, 76(2007), 026708.CrossRefGoogle Scholar
[39]Liu, H. and Zhang, Y., Droplet formation in microfluidic cross-junctions, Phys. Fluids, 23 (2011), 082101.Google Scholar
[40]Aidun, C. K. and Clausen, J. R., Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. 42(2010), 439–472Google Scholar
[41]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
[42]Liu, C.-H., Lin, K.-H, Mai, H.-C. and Lin, C.-A., Thermal boundary conditions for thermal lattice Boltzmann simulations, Comput. Math. Appl., 59(2010), 2178–2193.CrossRefGoogle Scholar
[43]Ahn, B., Lee, K., Panchapakesan, R. and Oh, K. W., Parallel synchronization of two trains of droplets using a railroad-like channel network, Lab Chip, 11(2011), 3956–3962CrossRefGoogle ScholarPubMed
[44]Maddala, J., Srinivasan, B., Bithi, S. S., Vananalli, S. A. and Rengaswamy, R., Design of a model-based feedback controller for active sorting and synchronising of droplets in a microfluidic loop, AICHE Journal, 58(2012), 2120–2130.Google Scholar
[45]Yap, Y. F., Tan, S. H., Nguyen, N. T., Murshed, S. M. Sohel, Wong, T. N. and Yobas, L., Thermally mediated control of liquid microdroplets at a bifurcation, J. Phys. D: Appl. Phys., 42(2009) 065503.Google Scholar
[46]Meng, J., Zhang, Y., Hadjiconstantinou, N. G., Radtke, G. A. and Shan, X., Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows, J. Fluid Mech., 718(2013), 347–370Google Scholar