Application of lattice Boltzmann method for simulation of multiphase/multicomponent flow in microfluidics

doi:10.3969/j.issn.0438-1157.2014.07.015

Abstract

Abstract: Multiphase/multicomponent systems have been widely applied in chemical engineering field, generally involving complex physical processes (such as species transfer, phase change, generation and movement of interface) as well as chemical reactions. It is of great challenge to model and simulate such complex systems. Lattice Boltzmann method (LBM) has attracted more and more attention as a relatively new method in recent years. Compared with traditional methods, multiphase/multicomponent lattice Boltzmann models have certain advantages, such as the convenience of tracking dynamic fluid interfaces and the easy definition of solid boundaries. It is an ideal approach for meso-scale and scale-bridging simulations, especially successful in the applications of fluid flow simulations involving interfacial dynamics and complex boundaries in the multiphase/multicomponent systems in micro-chemical engineering areas. Based on the methodology scheme of LBM, this review introduces the state-of-the-art development of LB models applied to simulate the gas-liquid and liquid-liquid micro-flow systems.

Key words: multiphase flow, microfluidics, micro-droplet, simulation, lattice Boltzmann method

摘要： 多相/多组分流体在化工领域中广泛应用，通常伴随有组分传递、相变、界面的产生与运动、化学反应等复杂的物理、化学过程，建立描述相应复杂体系的理论模型和模拟方法面临着极大的挑战。格子Boltzmann方法（lattice Boltzmann method，LBM）是近年来备受关注的一种介观模拟方法；多相/多组分格子Boltzmann模型具有易于追踪多相动态界面、壁面性质设定简单等优点，从物理模型到计算精度和速度都有很大的优势，尤其适合于模拟微化工系统下的多相多组分流动问题。以格子Boltzmann方法为基础，重点介绍了气液及液液体系多相/多组分LBM模型的研究进展以及其在微流体系统中的应用。

关键词: 多相流, 微流体学, 微液滴, 模拟, 格子Boltzmann方法

CLC Number:

TQ018

FU Yuhang, ZHAO Shufang, WANG Wentan, JIN Yong, CHENG Yi. Application of lattice Boltzmann method for simulation of multiphase/multicomponent flow in microfluidics[J]. , 2014, 65(7): 2535-2543.

付宇航, 赵述芳, 王文坦, 金涌, 程易. 多相/多组分LBM模型及其在微流体领域的应用[J]. CIESC Journal, 2014, 65(7): 2535-2543.

References 53

[1]	Luo Guangsheng (骆广生), Wang Kai (王凯), Xu Jianhong (徐建鸿), Lü Yangcheng (吕阳成), Wang Yujun (王玉军). Multiphase flow, transport and reaction in micro-structured chemical systems [J]. CIESC Journal (化工学报), 2010, 61 (7): 1621-1626
[2]	Liu Zhe (刘喆). Experimental study and numerical simulation of liquid-liquid mixing intensification in mini-/micro-scale reactors [D]. Beijing: Tsinghua University, 2010
[3]	Zhang J F. Lattice Boltzmann method for microfluidics: models and applications [J]. Microfluid. Nanofluid., 2011, 10 (1): 1-28
[4]	Mcnamara G R, Zanetti G. Use of the Boltzmann-equation to simulate lattice-gas automata [J]. Phys. Rev. Lett., 1988, 61 (20): 2332-2335
[5]	Chen S Y, Chen H D, Martinez D, Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics [J]. Phys. Rev. Lett., 1991, 67 (27): 3776-3779
[6]	Koelman J M V A. A simple lattice Boltzmann scheme for Navier-Stokes fluid-flow [J]. Europhys. Lett., 1991, 15 (6): 603-607
[7]	Qian Y H, Dhumieres D, Lallemand P. Lattice BGK models for Navier-Stokes equation [J]. Europhys. Lett., 1992, 17 (6): 479-484
[8]	Guo Zhaoli (郭照立), Zheng Chuguang (郑楚光). Theory and Applications of Lattice Boltzmann Method (格子Boltzmann方法的原理与应用) [M]. Beijing: Science Press, 2009
[9]	Succi S, d'Humières D, Qian Y, Orszag S A. On the small-scale dynamical behavior of lattice BGK and lattice Boltzmann schemes [J]. J. Sci. Comput., 1993, 8: 219-230
[10]	Gunstensen A K, Rothman D H, Zaleski S, Zanetti G. Lattice Boltzmann model of immiscible fluids [J]. Phys. Rev. A, 1991, 43 (8): 4320-4327
[11]	Rothman D H, Keller J M. Immiscible cellular-automaton fluids [J]. J. Stat. Phys., 1988, 52 (3/4): 1119-1127
[12]	Lishchuk S V, Care C M, Halliday I. Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents [J]. Phys. Rev. E, 2003, 67 (3): 036701
[13]	Latva-Kokko M, Rothman D H. Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids [J]. Phys. Rev. E, 2005, 71 (5): 056702
[14]	Dortona U, Salin D, Cieplak M, Rybka R B, Banavar J R. 2-Color nonlinear Boltzmann cellular-automata-surface-tension and wetting [J]. Phys. Rev. E, 1995, 51 (4): 3718-3728
[15]	Leclaire S, Reggio M, Trepanier J Y. Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model [J]. Comput. Fluids., 2011, 48 (1): 98-112
[16]	Leclaire S, Reggio M, Trepanier J Y. Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model [J]. Appl. Math. Model., 2012, 36 (5): 2237-2252
[17]	Gunstensen A K. Lattice-Boltzmann studies of multiphase flow through porous media [D]. USA: MIT, 1992
[18]	Dupin M M, Halliday I, Care C M. Multi-component lattice Boltzmann equation for mesoscale blood flow [J]. J. Phys. A: Math. Gen., 2003, 36 (31): 8517-8534
[19]	Halliday I, Hollis A P, Care C M. Lattice Boltzmann algorithm for continuum multicomponent flow [J]. Phys. Rev. E, 2007, 76 (2): 026708
[20]	Leclaire S, Reggio M, Trepanier J Y. Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios [J]. J. Comput. Phys., 2013, 246: 318-342
[21]	Reis T, Phillips T N. Lattice Boltzmann model for simulating immiscible two-phase flows [J]. J. Phys. A: Math. Theor., 2007, 40: 4033-4053
[22]	Shan X W, Chen H D. Lattice Boltzmann model for simulating flows with multiple phases and components [J]. Phys. Rev. E, 1993, 47 (3): 1815-1819
[23]	Shan X W, Doolen G. Multicomponent lattice-Boltzmann model with interparticle interaction [J]. J. Stat. Phys., 1995, 81 (1/2): 379-393
[24]	Shan X W. Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models [J]. Phys. Rev. E, 2006, 73 (4): 047701
[25]	Sbragaglia M, Benzi R, Biferale L, Succi S, Sugiyama K, Toschi F. Generalized lattice Boltzmann method with multirange pseudopotential [J]. Phys. Rev. E, 2007, 75 (2): 026702
[26]	Shan X W, Chen H D. Simulation of nonideal gases and liquid-gas phase-transitions by the lattice Boltzmann-equation [J]. Phys. Rev. E, 1994, 49 (4): 2941-2948
[27]	Swift M R, Osborn W R, Yeomans J M. Lattice Boltzmann simulation of nonideal fluids [J]. Phys. Rev. Lett., 1995, 75 (5): 830-833
[28]	van der Graaf S, Nisisako T, Schroen C G P H, van der Sman R G M, Boom R M. Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel [J]. Langmuir, 2006, 22 (9): 4144-4152
[29]	Swift M R, Orlandini E, Osborn W R, Yeomans J M. Lattice Boltzmann simulations of liquid-gas and binary fluid systems [J]. Phys. Rev. E, 1996, 54 (5): 5041-5052
[30]	Inamuro T, Konishi N, Ogino F. A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach [J]. Comput. Phys. Commun., 2000, 129 (1/2/3): 32-45
[31]	Zhang J F, Kwok D Y. Apparent slip over a solid-liquid interface with a no-slip boundary condition [J]. Phys. Rev. E, 2004, 70 (5): 056701
[32]	Zhang J F, Kwok D Y. A mean-field free energy lattice Boltzmann model for multicomponent fluids [J]. European Physical Journal-Special Topics, 2009, 171: 45-53
[33]	Tölke J F. Implementation of a lattice Boltzmann kernel using the compute unified device architecture developed by nVIDIA [J]. Computing and Visualization in Science, 2010, 13 (1): 29-39
[34]	Dupin M M, Halliday I, Care C M. Simulation of a microfluidic flow-focusing device [J]. Phys. Rev. E, 2006, 73(5): 055701(R)
[35]	Anna S L, Bontoux N, Stone H A. Formation of dispersions using “flow focusing” in microchannels [J]. Appl. Phys. Lett., 2003, 82 (3): 364-366
[36]	Wang W T, Liu Z, Jin Y, Cheng Y. LBM simulation of droplet formation in micro-channels [J]. Chem. Eng. J., 2011, 173 (3): 828-836
[37]	Kim L S, Jeong H K, Ha M Y, Kim K C. Numerical simulation of droplet formation in a micro-channel using the lattice Boltzmann method [J]. Journal of Mechanical Science and Technology, 2008, 22(4): 770-779
[38]	Wu L, Tsutahara M, Kim L S, Ha M. Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel [J]. Int. J. Multiphas. Flow, 2008, 34 (9): 852-864
[39]	Gupta A, Murshed S M S, Kumar R. Droplet formation and stability of flows in a microfluidic T-junction [J]. Appl. Phys. Lett., 2009, 94 (16): 164107
[40]	Liu H H, Zhang Y H. Droplet formation in a T-shaped microfluidic junction [J]. J. Appl. Phys., 2009, 106 (3): 034906
[41]	Gupta A, Kumar R. Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction [J]. Microfluid. Nanofluid., 2010, 8 (6): 799-812.
[42]	Yang H, Zhou Q, Fan L S. Three-dimensional numerical study on droplet formation and cell encapsulation process in a micro T-junction [J]. Chem. Eng. Sci., 2013, 87: 100-110
[43]	Inamuro T, Tajima S, Ogino F. Lattice Boltzmann simulation of droplet collision dynamics [J]. Int. J. Heat Mass Tran., 2004, 47 (21): 4649-4657
[44]	Shardt O, Derksen J J, Mita S K. Simulations of droplet coalescence in simple shear flow [J]. Langmuir, 2013, 29 (21): 6201-6212
[45]	Yu Z, Heraminger O, Fan L S. Experiment and lattice Boltzmann simulation of two-phase gas-liquid flows in microchannels [J]. Chem. Eng. Sci., 2007, 62 (24): 7172-7183
[46]	Yu Z, Fan L S. An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation [J]. J. Comput. Phys., 2009, 228 (17): 6456-6478
[47]	Yu Z, Fan L S. Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow [J]. Phys. Rev. E, 2010, 82 (4): 046708.
[48]	Amaya-Bower L, Lee T. Numerical simulation of single bubble rising in vertical and inclined square channel using lattice Boltzmann method [J]. Chem. Eng. Sci., 2011, 66 (5): 935-952
[49]	Liu H H, Valocchi A J, Kang Q J. Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations [J]. Phys. Rev. E, 2012, 85 (4): 046309
[50]	Wang Wentan (王文坦), Liu Zhe (刘喆), Shao Ting (邵婷), Zhao Shufang (赵述芳), Jin Yong (金涌), Cheng Yi (程易). μ-LIF visualization and LBM simulation of mixing behavior inside droplets in microchannels [J]. CIESC Journal (化工学报), 2012, 63 (2): 375-381
[51]	Zhao S F, Wang W T, Zhang M X, Shao T, Jin Y, Cheng Y. Three-dimensional simulation of mixing performance inside droplets in micro-channels by lattice Boltzmann method [J]. Chem. Eng. J., 2012, 207: 267-277
[52]	Wang W T, Shao T, Zhao S F, Jin Y, Cheng Y. Experimental and numerical study of mixing behavior inside droplets in microchannels [J]. AIChE J., 2013, 59: 1801-1813
[53]	Zhao S F, Wang W T, Shao T, Jin Y, Cheng Y. Lattice Boltzmann simulation of mixing process inside micro-droplets in a gas - liquid Taylor flow// 2013 AIChE Annual Meeting[C]. San Francisco, CA, USA, 2013