Mô hình số cho dòng chảy đa pha trong vi lưu và kỹ thuật quy trình vi mô: tổng quan về các phương pháp và ứng dụng

Microfluidics and Nanofluidics - Tập 12 - Trang 841-886 - 2012
Martin Wörner1
1Karlsruhe Institute of Technology (KIT), Institute for Nuclear and Energy Technologies, Eggenstein-Leopoldshafen, Germany

Tóm tắt

Bài báo này trình bày một cái nhìn tổng quát về các phương pháp và mô hình số cho các mô phỏng phân giải giao diện của dòng chảy đa pha trong lĩnh vực vi lưu và kỹ thuật quy trình vi mô. Trọng tâm của bài báo là về các phương pháp tiếp tuyến, bao gồm ba phương pháp phổ biến trong giới hạn giao diện sắc nét, đó là phương pháp thể tích dịch lỏng với tái cấu trúc giao diện, phương pháp mức độ và phương pháp theo dõi mặt trước, cùng với các phương pháp có chiều dày giao diện hữu hạn như các phương pháp dựa trên chức năng màu và phương pháp trường pha. Các biến thể của phương pháp Boltzmann lưới vi mô cho các dòng chảy hai chất lỏng cũng được thảo luận, cùng với các phương pháp kết hợp khác nhau. Cơ sở toán học của mỗi phương pháp được trình bày và những lợi ích cũng như hạn chế cụ thể của nó được nhấn mạnh. Đối với các phương pháp tiếp tuyến, vấn đề liên kết phương trình tiến hóa giao diện với các phương trình Navier-Stokes một trường và các vấn đề liên quan được thảo luận. Các phương pháp và mô hình cho lực căng bề mặt, các đường tiếp xúc, truyền nhiệt và khối lượng cũng như sự chuyển pha được giới thiệu. Trong phần thứ hai của bài báo này, các ứng dụng của các phương pháp trong lĩnh vực vi lưu và kỹ thuật quy trình vi mô được xem xét, bao gồm động lực học dòng chảy (dòng chảy tách rời và phân đoạn, hình thành bọt và giọt, vỡ và kết hợp), truyền nhiệt và khối lượng (có và không có phản ứng hóa học), trộn và phân tán, dòng chảy Marangoni và chất hoạt động bề mặt, cũng như sự sôi.

Từ khóa

#mô hình số #dòng chảy đa pha #vi lưu #kỹ thuật quy trình vi mô #phương pháp tiếp tuyến #năng lượng bề mặt #truyền nhiệt và khối lượng

Tài liệu tham khảo

Abdallah R, Magnico P, Fumey B, de Bellefon C (2006) CFD and kinetic methods for mass transfer determination in a mesh microreactor. AIChE J 52(6):2230–2237 Abiev RS (2009) Circulation and bypass modes of the slug flow of a gas–liquid mixture in capillaries. Theor Found Chem Eng 43(3):298–306 Abou-Hassan A, Sandre O, Cabuil V (2010) Microfluidics in inorganic chemistry. Angew Chem Int Edit 49(36):6268–6286 Adalsteinsson D, Sethian JA (1995) A fast level set method for propagating interfaces. J Comput Phys 118(2):269–277 Afkhami S, Bussmann M (2009) Height functions for applying contact angles to 3D VOF simulations. Int J Numer Methods Fluids 61(8):827–847 Afkhami S, Zaleski S, Bussmann M (2009) A mesh-dependent model for applying dynamic contact angles to VOF simulations. J Comput Phys 228(15):5370–5389 Ahn HT, Shashkov M (2007) Multi-material interface reconstruction on generalized polyhedral meshes. J Comput Phys 226(2):2096–2132 Ahn HT, Shashkov M (2009) Adaptive moment-of-fluid method. J Comput Phys 228(8):2792–2821 Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439–472 Alke A, Bothe D (2009) 3D Numerical modeling of soluble surfactant at fluidic interfaces based on the volume-of-fluid method. FDMP 5(4):345–372 Alke A, Bothe D, Kröger M, Weigand B, Weirich D, Weking H (2010) Direct numerical simulation of high Schmidt number mass transfer from air bubbles rising in liquids using the volume-of-fluid-method. Ercoftac Bull 82:5–10 Amaya-Bower L, Lee T (2010) Single bubble rising dynamics for moderate Reynolds number using lattice Boltzmann method. Comput Fluids 39(7):1191–1207 Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse-interface methods in fluid mechanics. Annu Rev Fluid Mech 30:139–165 Angeli P, Gavriilidis A (2008) Hydrodynamics of Taylor flow in small channels: a review. P I Mech Eng C-J Mec 222(5):737–751 Aota A, Nonaka M, Hibara A, Kitamori T (2007) Countercurrent laminar microflow for highly efficient solvent extraction. Angew Chem Int Edit 46(6):878–880 Aota A, Mawatari K, Kitamori T (2009) Parallel multiphase microflows: fundamental physics, stabilization methods and applications. Lab Chip 9(17):2470–2476 Atencia J, Beebe DJ (2005) Controlled microfluidic interfaces. Nature 437(7059):648–655 Aubin J, Ferrando M, Jiricny V (2010) Current methods for characterising mixing and flow in microchannels. Chem Eng Sci 65(6):2065–2093 Aulisa E, Manservisi S, Scardovelli R (2003) A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows. J Comput Phys 188(2):611–639 Aulisa E, ManserviSi S, Scardovelli R (2006) A novel representation of the surface tension force for two-phase flow with reduced spurious currents. Comput Method Appl M 195(44–47):6239–6257 Aulisa E, Manservisi S, Scardovelli R, Zaleski S (2007) Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry. J Comput Phys 225(2):2301–2319 Ausas RF, Dari EA, Buscaglia GC (2011) A geometric mass-preserving redistancing scheme for the level set function. Int J Numer Methods Fluids 65(8):989–1010 Badalassi VE, Ceniceros HD, Banerjee S (2003) Computation of multiphase systems with phase field models. J Comput Phys 190(2):371–397 Bänsch E (2001) Finite element discretization of the Navier–Stokes equations with a free capillary surface. Numer Math 88(2):203–235 Bao J, Yuan P, Schaefer L (2008) A mass conserving boundary condition for the lattice Boltzmann equation method. J Comput Phys 227(18):8472–8487 Baroud CN, Okkels F, Menetrier L, Tabeling P (2003) Reaction–diffusion dynamics: confrontation between theory and experiment in a microfluidic reactor. Phys Rev E 67(6):060104 Benson DJ (2002) Volume of fluid interface reconstruction methods for multi-material problems. Appl Mech Rev 55(2):151–165 Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases 1. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94(3):511–525 Bird RB, Stewart WE, Lightfoot EN (2007) Transport phenomena. 2nd rev. edn. Wiley, New York Blanchette F (2009) Flow lines and mixing within drops in microcapillaries. Phys Rev E 80(6):066316 Blanchette F (2010) Simulation of mixing within drops due to surface tension variations. Phys Rev Lett 105(7):074501 Bonn D, Eggers J, Indekeu J, Meunier J, Rolley E (2009) Wetting and spreading. Rev Mod Phys 81(2):739–805 Bonometti T, Magnaudet J (2007) An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics. Int J Multiph Flow 33 (2):109–133 Booty MR, Siegel M (2010) A hybrid numerical method for interfacial fluid flow with soluble surfactant. J Comput Phys 229(10):3864–3883 Bothe D (2009) Calculations and simulations. In: Dietrich TR (ed) Microchemical engineering in practice. Wiley, Oxford, pp 165–184 Bothe D, Warnecke HJ (2007) Berechnung und Beurteilung strömungsbasierter komplex-laminarer Mischprozesse. Chem-Ing-Tech 79(7):1001–1014 Bothe D, Koebe M, Wielage K, Prüss J, Warnecke HJ (2004) Direct numerical simulation of mass transfer between rising gas bubbles and water. In: Sommerfeld M (ed) Bubbly flows. Analysis, modelling and calculation. Springer, Berlin, pp 159–174 Bothe D, Kröger M, Alke A, Warnecke H-J (2009a) VOF-based simulation of conjugate mass transfer from freely moving fluid particles. In: Mammoli AA, Brebbia CA (eds) Computational methods in multiphase flow V. WIT Press, Southampton, pp 157–168 Bothe D, Kröger M, Alke A, Warnecke HJ (2009b) VOF-based simulation of reactive mass transfer across deformable interfaces. Prog Comput Fluid Dyn 9(6–7):325–331 Bothe D, Kröger M, Warnecke HJ (2011) A VOF-based conservative method for the simulation of reactive mass transfer from rising bubbles. FDMP 7(3):303–316 Boyer F (2002) A theoretical and numerical model for the study of incompressible mixture flows. Comput Fluids 31(1):41–68 Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100(2):335–354 Bringer MR, Gerdts CJ, Song H, Tice JD, Ismagilov RF (2004) Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets. Philos T Roy Soc A 362(1818):1087–1104 Bruus H (2008) Theoretical microfluidics. Oxford master series in physics, vol 18. Oxford University Press, Oxford Carlson A, Do-Quang M, Amberg G (2010) Droplet dynamics in a bifurcating channel. Int J Multiph Flow 36(5):397–405 Casey M, Wintergerste T (2000) Best practice guidelines for industrial computational fluid dynamics of single-phase flows. ERCOFTAC Ceniceros HD (2003) The effects of surfactants on the formation and evolution of capillary waves. Phys Fluids 15(1):245–256 Ceniceros HD, Roma AM (2007) A nonstiff, adaptive mesh refinement-based method for the Cahn–Hilliard equation. J Comput Phys 225(2):1849–1862 Ceniceros HD, Roma AM, Silveira-Neto A, Villar MM (2010) A robust, fully adaptive hybrid level-set/front-tracking method for two-phase flows with an accurate surface tension computation. Commun Comput Phys 8(1):51–94 Cervone A, Manservisi S, Scardovelli R, Zaleski S (2009) A geometrical predictor–corrector advection scheme and its application to the volume fraction function. J Comput Phys 228(2):406–419 Chang QM, Alexander JID (2006) Analysis of single droplet dynamics on striped surface domains using a lattice Boltzmann method. Microfluid Nanofluid 2(4):309–326 Chang YC, Hou TY, Merriman B, Osher S (1996) A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J Comput Phys 124(2):449–464 Chao J, Mei R, Singh R, Shyy W (2011) A filter-based, mass-conserving lattice Boltzmann method for immiscible multiphase flows. Int J Numer Methods Fluids 66(5):622–647 Chasanis P, Lautenschleger A, Kenig EY (2010) Numerical investigation of carbon dioxide absorption in a falling-film micro-contactor. Chem Eng Sci 65(3):1125–1133 Chatzikyriakou D, Walker SP, Hewitt GF, Narayanan C, Lakehal D (2009) Comparison of measured and modelled droplet-hot wall interactions. Appl Therm Eng 29(7):1398–1405 Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329–364 Chen Y, Kulenovic R, Mertz R (2009a) Numerical study on the formation of Taylor bubbles in capillary tubes. Int J Therm Sci 48(2):234–242 Chen YP, Zhang CB, Shi MH, Peterson GP (2009b) Role of surface roughness characterized by fractal geometry on laminar flow in microchannels. Phys Rev E 80(2):026301 Cheng M, Hua J, Lou J (2010) Simulation of bubble–bubble interaction using a lattice Boltzmann method. Comput Fluids 39(2):260–270 Chung TJ (2002) Computational fluid dynamics. Cambridge University Press, Cambridge Chung C, Hulsen MA, Kim JM, Ahn KH, Lee SJ (2008) Numerical study on the effect of viscoelasticity on drop deformation in simple shear and 5:1:5 planar contraction/expansion microchannel. J Non-Newton Fluid Mech 155(1–2):80–93 Chung C, Kim JM, Hulsen MA, Ahn KH, Lee SJ (2009) Effect of viscoelasticity on drop dynamics in 5:1:5 contraction/expansion microchannel flow. Chem Eng Sci 64(22):4515–4524 Compère G, Marchandise E, Remacle J-F (2008) Transient adaptivity applied to two-phase incompressible flows. J Comput Phys 227(3):1923–1942 Constantinou A, Gavriilidis A (2010) CO2 absorption in a microstructured mesh reactor. Ind Eng Chem Res 49(3):1041–1049 Cox RG (1986) The dynamics of the spreading of liquids on a solid-surface. 1. Viscous-flow. J Fluid Mech 168:169–194 Coyajee E, Boersma BJ (2009) Numerical simulation of drop impact on a liquid–liquid interface with a multiple marker front-capturing method. J Comput Phys 228(12):4444–4467 Cristini V, Tan Y-C (2004) Theory and numerical simulation of droplet dynamics in complex flows-a review. Lab Chip 4(4):257–264 Croce G, D’Agaro P (2005) Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow. J Phys D Appl Phys 38(10):1518–1530 Crowe CT, Sommerfeld M, Tsuji Y (1998) Multiphase flows with droplets and particles. CRC Press, Boca Raton Cubaud T, Tatineni M, Zhong XL, Ho CM (2005) Bubble dispenser in microfluidic devices. Phys Rev E 72(3):037302 Cummins SJ, Francois MM, Kothe DB (2005) Estimating curvature from volume fractions. Comput Struct 83(6–7):425–434 Dai L, Cai WF, Xin F (2009) Numerical study on bubble formation of a gas–liquid flow in a T-junction microchannel. Chem Eng Technol 32(12):1984–1991 Davidson MR, Harvie DJE (2007) Predicting the effect of interfacial flow of insoluble surfactant on the deformation of drops rising in a liquid. ANZIAM J 48:C661–C676 Davidson MR, Rudman M (2002) Volume-of-fluid calculation of heat or mass transfer across deforming interfaces in two-fluid flow. Numer Heat Tr B-Fund 41(3–4):291–308 Davidson MR, Harvie DJE, Cooper-White JJ (2005) Flow focusing in microchannels. ANZIAM J 46 (E):C47–C58 Davis RH, Schonberg JA, Rallison JM (1989) The lubrication force between two viscous drops. Phys Fluids A 1(1):77–81 De Menech M (2006) Modeling of droplet breakup in a microfluidic T-shaped junction with a phase-field model. Phys Rev E 73(3):031505 De Menech M, Garstecki P, Jousse F, Stone HA (2008) Transition from squeezing to dripping in a microfluidic T-shaped junction. J Fluid Mech 595:141–161 de Sousa FS, Mangiavacchi N, Nonato LG, Castelo A, Tomé MF, Ferreira VG, Cuminato JA, McKee S (2004) A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces. J Comput Phys 198(2):469–499 Di Carlo D (2009) Inertial microfluidics. Lab Chip 9(21):3038–3046 Di Carlo D, Irimia D, Tompkins RG, Toner M (2007) Continuous inertial focusing, ordering, and separation of particles in microchannels. P Natl Acad Sci USA 104(48):18892–18897 Di Y, Wang X-P (2009) Precursor simulations in spreading using a multi-mesh adaptive finite element method. J Comput Phys 228(5):1380–1390 Dietrich TR (2009) Microchemical engineering in practice. Wiley, Oxford Dijkhuizen W, Roghair I, Annaland MVS, Kuipers JAM (2010) DNS of gas bubbles behaviour using an improved 3D front tracking model—model development. Chem Eng Sci 65(4):1427–1437 Ding H, Spelt PDM (2007) Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations. J Fluid Mech 576:287–296 Ding H, Spelt PDM, Shu C (2007) Diffuse interface model for incompressible two-phase flows with large density ratios. J Comput Phys 226(2):2078–2095 Ding L, Shu C, Ding H, Zhao N (2010) Stencil adaptive diffuse interface method for simulation of two-dimensional incompressible multiphase flows. Comput Fluids 39(6):936–944 Diwakar SV, Das SK, Sundararajan T (2009) A quadratic spline based interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows. J Comput Phys 228(24):9107–9130 Doku GN, Verboom W, Reinhoudt DN, van den Berg A (2005) On-microchip multiphase chemistry—a review of microreactor design principles and reagent contacting modes. Tetrahedron 61(11):2733–2742 Drew DA (1983) Mathematical-modeling of two-phase flow. Annu Rev Fluid Mech 15:261–291 Drew DA, Passman SL (1999) Theory of multicomponent fluids. Springer, New York Dreyfus R, Tabeling P, Willaime H (2003) Ordered and disordered patterns in two-phase flows in microchannels. Phys Rev Lett 90(14):144505 Drumright-Clarke MA, Renardy Y (2004) The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia. Phys Fluids 16(1):14–21 Dupin MM, Halliday I, Care CM (2006) Simulation of a microfluidic flow-focusing device. Phys Rev E 73(5):055701 Dupont J-B, Legendre D (2010) Numerical simulation of static and sliding drop with contact angle hysteresis. J Comput Phys 229(7):2453–2478 Dupuis A, Yeomans JM (2004) Lattice Boltzmann modelling of droplets on chemically heterogeneous surfaces. Future Gener Comp Syst 20(6):993–1001 Dussan EB (1979) Spreading of liquids on solid-surfaces—static and dynamic contact lines. Annu Rev Fluid Mech 11:371–400 Dziuk G (1991) An algorithm for evolutionary surfaces. Numer Math 58(6):603–611 Ehrfeld W, Hessel V, Löwe H (2000) Microreactors: new technology for modern chemistry. Wiley, Chichester Enright D, Fedkiw R, Ferziger J, Mitchell I (2002) A hybrid particle level set method for improved interface capturing. J Comput Phys 183(1):83–116 Enright D, Losasso F, Fedkiw R (2005) A fast and accurate semi-Lagrangian particle level set method. Comput Struct 83(6–7):479–490 Erickson D (2005) Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices. Microfluid Nanofluid 1(4):301–318 Erickson D, Li D, Park CB (2002) Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries. J Colloid Interf Sci 250(2):422–430 Fair RB (2007) Digital microfluidics: is a true lab-on-a-chip possible? Microfluid Nanofluid 3(3):245–281 Fang C, Hidrovo C, Wang F-M, Eaton J, Goodson K (2008) 3-D numerical simulation of contact angle hysteresis for microscale two phase flow. Int J Multiph Flow 34(7):690–705 Farhat H, Choi W, Lee JS (2010) Migrating multi-block lattice Boltzmann model for immiscible mixtures: 3D algorithm development and validation. Comput Fluids 39(8):1284–1295 Fedkiw RP, Aslam T, Merriman B, Osher S (1999) A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J Comput Phys 152(2):457–492 Fei K, Hong CW (2007) All-angle removal of CO2 bubbles from the anode microchannels of a micro fuel cell by lattice-Boltzmann simulation. Microfluid Nanofluid 3(1):77–88 Fei K, Cheng CH, Hong CW (2006) Lattice Boltzmann simulations of CO2 bubble dynamics at the anode of a μDMFC. J Fuel Cell Sci Tech 3(2):180–187 Fei K, Chen WH, Hong CW (2008) Microfluidic analysis of CO2 bubble dynamics using thermal lattice-Boltzmann method. Microfluid Nanofluid 5(1):119–129 Feigl K, Megias-Alguacil D, Fischer P, Windhab EJ (2007) Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants. Chem Eng Sci 62(12):3242–3258 Ferziger JH, Peric M (2002) Computational methods for fluid dynamics, 3rd edn. Springer, Berlin Fletcher DF, Haynes BS, Aubin J, Xuereb C (2009) Modelling of microfluidic devices. In: Hessel V, Renken A, Schouten JC, Yoshida J (eds) Micro process engineering, vol 1., Fundamentals, operations and catalysts. Wiley, Weinheim, pp 117–144 Francois M, Shyy W (2003) Computations of drop dynamics with the immersed boundary method, Part 2: drop impact and heat transfer. Numer Heat Tr B-Fund 44(2):119–143 Francois MM, Swartz BK (2010) Interface curvature via volume fractions, heights, and mean values on nonuniform rectangular grids. J Comput Phys 229(3):527–540 Francois MM, Cummins SJ, Dendy ED, Kothe DB, Sicilian JM, Williams MW (2006) A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J Comput Phys 213(1):141–173 Fujioka H, Grotberg JB (2005) The steady propagation of a surfactant-laden liquid plug in a two-dimensional channel. Phys Fluids 17(8):082102 Fukagata K, Kasagi N, Ua-arayaporn P, Himeno T (2007) Numerical simulation of gas–liquid two-phase flow and convective heat transfer in a micro tube. Int J Heat Fluid Flow 28(1):72–82 Fukai J, Shiiba Y, Yamamoto T, Miyatake O, Poulikakos D, Megaridis CM, Zhao Z (1995) Wetting effects on the spreading of a liquid droplet colliding with a flat surface—experiment and modeling. Phys Fluids 7(2):236–247 Fuster D, Agbaglah G, Josserand C, Popinet S, Zaleski S (2009) Numerical simulation of droplets, bubbles and waves: state of the art. Fluid Dyn Res 41(6):065001 Gada VH, Sharma A (2009) On derivation and physical interpretation of level set method-based equations for two-phase flow simulations. Numer Heat Tr B-Fund 56(4):307–322 Gad-el-Hak M (1999) The fluid mechanics of microdevices—the Freeman scholar lecture. J Fluids Eng 121(1):5–33 Galusinski C, Vigneaux P (2008) On stability condition for bifluid flows with surface tension: Application to microfluidics. J Comput Phys 227(12):6140–6164 Ganesan S, Tobiska L (2008) An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flows. Int J Numer Methods Fluids 57(2):119–138 Ganesan S, Tobiska L (2009a) A coupled arbitrary Lagrangian–Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants. J Comput Phys 228(8):2859–2873 Ganesan S, Tobiska L (2009b) Modelling and simulation of moving contact line problems with wetting effects. Comput Visual Sci 12(7):329–336 Garstecki P, Fuerstman MJ, Stone HA, Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. Lab Chip 6(3):437–446 Gerlach D, Tomar G, Biswas G, Durst F (2006) Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows. Int J Heat Mass Transfer 49(3–4):740–754 Germann TC, Kadau K (2008) Trillion-atom molecular dynamics becomes a reality. Int J Mod Phys C 19(9):1315–1319 Geschke O, Klank H, Telleman P (2008) Microsystem engineering of lab-on-a-chip devices, 2nd edn. Wiley, Weinheim Ghidersa BE, Wörner M, Cacuci DG (2004) Exploring the flow of immiscible fluids in a square vertical mini-channel by direct numerical simulation. Chem Eng J 101(1–3):285–294 Gibou F, Chen L, Nguyen D, Banerjee S (2007) A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change. J Comput Phys 222(2):536–555 Ginzburg I, Wittum G (2001) Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants. J Comput Phys 166(2):302–335 Glatzel T, Litterst C, Cupelli C, Lindemann T, Moosmann C, Niekrawietz R, Streule W, Zengerle R, Koltay P (2008) Computational fluid dynamics (CFD) software tools for microfluidic applications—a case study. Comput Fluids 37(3):218–235 Gleichmann N, Malsch D, Kielpinski M, Rossak W, Mayer G, Henkel T (2008) Toolkit for computational fluidic simulation and interactive parametrization of segmented flow based fluidic networks. Chem Eng J 135:S210–S218 Gomez FA (2008) Biological applications of microfluidics. Wiley, Hoboken Gomez P, Hernandez J, Lopez J (2005) On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows. Int J Numer Methods Eng 63(10):1478–1512 Greaves D (2004) A quadtree adaptive method for simulating fluid flows with moving interfaces. J Comput Phys 194(1):35–56 Groß S, Reusken A (2007) An extended pressure finite element space for two-phase incompressible flows with surface tension. J Comput Phys 224(1):40–58 Groß S, Reusken A (2011) Numerical methods for two-phase incompressible flows. Springer, Heidelberg Groß S, Reichelt V, Reusken A (2006) A finite element based level set method for two-phase incompressible flows. Comput Visual Sci 9(4):239–257 Gu H, Duits MHG, Mugele F (2011) Droplets formation and merging in two-phase flow microfluidics. Int J Mol Sci 12(4):2572–2597 Gubbins KE, Moore JD (2010) Molecular modeling of matter: impact and prospects in engineering. Ind Eng Chem Res 49(7):3026–3046 Guettel R, Knochen J, Kunz U, Kassing M, Turek T (2008) Preparation and catalytic evaluation of cobalt-based monolithic and powder catalysts for Fischer–Tropsch synthesis. Ind Eng Chem Res 47(17):6589–6597 Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S (1999) Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J Comput Phys 152(2):423–456 Gunstensen AK, Rothman DH, Zaleski S, Zanetti G (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43(8):4320–4327 Günther A, Jensen KF (2006) Multiphase microfluidics: from flow characteristics to chemical and materials synthesis. Lab Chip 6(12):1487–1503 Günther A, Kreutzer MT (2009) Multiphase flow. In: Hessel V, Renken A, Schouten JC, Yoshida J (eds) Micro process engineering, vol 1., Fundamentals, operations and catalystsWiley, Weinheim, pp 3–40 Günther A, Khan SA, Thalmann M, Trachsel F, Jensen KF (2004) Transport and reaction in microscale segmented gas–liquid flow. Lab Chip 4(4):278–286 Guo F, Chen B (2009) Numerical study on Taylor bubble formation in a micro-channel T-junction using VOF method. Microgravity Sci Technol 21:51–58 Gupta A, Murshed SMS, Kumar R (2009a) Droplet formation and stability of flows in a microfluidic T-junction. Appl Phys Lett 94(16):164107 Gupta R, Fletcher DF, Haynes BS (2009b) On the CFD modelling of Taylor flow in microchannels. Chem Eng Sci 64(12):2941–2950 Gupta R, Fletcher DF, Haynes BS (2010) CFD modelling of flow and heat transfer in the Taylor flow regime. Chem Eng Sci 65(6):2094–2107 Hagedorn JG, Martys NS, Douglas JF (2004) Breakup of a fluid thread in a confined geometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization with confinement. Phys Rev E 69(5):056312 Haj-Hariri H, Shi Q, Borhan A (1997) Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers. Phys Fluids 9(4):845–855 Hao L, Cheng P (2009) Lattice Boltzmann simulations of liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel. J Power Sources 190(2):435–446 Hao Y, Prosperetti A (2004) A numerical method for three-dimensional gas–liquid flow computations. J Comput Phys 196(1):126–144 Hardt S (2005) An extended volume-of-fluid method for micro flows with short-range interactions between fluid interfaces. Phys Fluids 17(10):100601 Hardt S, Wondra F (2008) Evaporation model for interfacial flows based on a continuum-field representation of the source terms. J Comput Phys 227(11):5871–5895 Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8(12):2182–2189 Haroun Y, Legendre D, Raynal L (2010a) Direct numerical simulation of reactive absorption in gas–liquid flow on structured packing using interface capturing method. Chem Eng Sci 65(1):351–356 Haroun Y, Legendre D, Raynal L (2010b) Volume of fluid method for interfacial reactive mass transfer: application to stable liquid film. Chem Eng Sci 65(10):2896–2909 Hartman RL, Jensen KF (2009) Microchemical systems for continuous-flow synthesis. Lab Chip 9(17):2495–2507 Hartmann D, Meinke M, Schröder W (2008) Differential equation based constrained reinitialization for level set methods. J Comput Phys 227(14):6821–6845 Hartmann D, Meinke M, Schröder W (2010a) The constrained reinitialization equation for level set methods. J Comput Phys 229(5):1514–1535 Hartmann D, Meinke M, Schröder W (2010b) On accuracy and efficiency of constrained reinitialization. Int J Numer Methods Fluids 63(11):1347–1358 Harvie DJE, Fletcher DF (2000) A new volume of fluid advection algorithm: the stream scheme. J Comput Phys 162(1):1–32 Harvie DJE, Fletcher DF (2001) A new volume of fluid advection algorithm: the defined donating region scheme. Int J Numer Methods Fluids 35(2):151–172 Harvie DJE, Davidson MR, Cooper-White JJ, Rudman M (2006a) A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets. Chem Eng Sci 61(15):5149–5158 Harvie DJE, Davidson MR, Rudman M (2006b) An analysis of parasitic current generation in volume of fluid simulations. Appl Math Model 30(10):1056–1066 Harvie DJE, Davidson MR, Cooper-White JJ, Rudman M (2007) A parametric study of droplet deformation through a microfluidic contraction: shear thinning liquids. Int J Multiph Flow 33(5):545–556 Harvie DJE, Cooper-White JJ, Davidson MR (2008) Deformation of a viscoelastic droplet passing through a microfluidic contraction. J Non-Newton Fluid Mech 155(1–2):67–79 Haverkamp V, Hessel V, Löwe H, Menges G, Warnier MJF, Rebrov EV, de Croon MHJM, Schouten JC, Liauw MA (2006) Hydrodynamics and mixer-induced bubble formation in micro bubble columns with single and multiple-channels. Chem Eng Technol 29(9):1015–1026 Hayashi K, Sou A, Tomiyama A (2006) A volume tracking method based on non-uniform subcells and continuum surface force model using a local level set function. Comput Fluid Dyn J 15(2):225–232 He QW, Kasagi N (2008) Phase-Field simulation of small capillary-number two-phase flow in a microtube. Fluid Dyn Res 40(7–8):497–509 He QW, Hasegawa Y, Kasagi N (2010) Heat transfer modelling of gas–liquid slug flow without phase change in a micro tube. Int J Heat Fluid Flow 31(1):126–136 Herrmann M (2008) A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids. J Comput Phys 227(4):2674–2706 Herwig H, Gloss D, Wenterodt T (2010) Flow in channels with rough walls—old and new concepts. Heat Transfer Eng 31(8):658–665 Hessel V, Hardt S, Löwe H (2004) Chemical micro process engineering: fundamentals, modelling and reactions. Wiley, Weinheim Hessel V, Angeli P, Gavriilidis A, Löwe H (2005) Gas–liquid and gas–liquid–solid microstructured reactors: contacting principles and applications. Ind Eng Chem Res 44(25):9750–9769 Hessel V, Renken A, Schouten JC, Yoshida J (2009) Micro process engineering: a comprehensive handbook. Wiley, Weinheim Heyes DM, Baxter J, Tuzun U, Qin RS (2004) Discrete-element method simulations: from micro to macro scales. Philos T Roy Soc A 362(1822):1853–1865 Hirsch C (2007) Numerical computation of internal and external flows: fundamentals of computational fluid dynamics, 2nd edn. Butterworth-Heinemann, Amsterdam Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225 Hirt CW, Amsden AA, Cook JL (1974) Arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253 Hu HH, Patankar NA, Zhu MY (2001) Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. J Comput Phys 169(2):427–462 Huang W, Russell RD (2011) Adaptive moving mesh methods. Springer, New York Huang H, Liang D, Wetton B (2004) Computation of a moving drop/bubble on a solid surface using a front-tracking method. Commun Math Sci 2(4):535–552 Huang WF, Liu QS, Li Y (2006) Capillary filling flows inside patterned-surface microchannels. Chem Eng Technol 29(6):716–723 Huang JJ, Shu C, Chew YT (2008) Numerical investigation of transporting droplets by spatiotemporally controlling substrate wettability. J Colloid Interf Sci 328(1):124–133 Huebner A, Sharma S, Srisa-Art M, Hollfelder F, Edel JB, deMello AJ (2008) Microdroplets: a sea of applications? Lab Chip 8(8):1244–1254 Huh C, Scriven LE (1971) Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J Colloid Interf Sci 35(1):85–101 Hysing S (2006) A new implicit surface tension implementation for interfacial flows. Int J Numer Methods Fluids 51(6):659–672 Hysing S, Turek S, Kuzmin D, Parolini N, Burman E, Ganesan S, Tobiska L (2009) Quantitative benchmark computations of two-dimensional bubble dynamics. Int J Numer Methods Fluids 60(11):1259–1288 Imke U (2004) Porous media simplified simulation of single- and two-phase flow heat transfer in micro-channel heat exchangers. Chem Eng J 101(1–3):295–302 Inamuro T, Ogata T, Tajima S, Konishi N (2004) A lattice Boltzmann method for incompressible two-phase flows with large density differences. J Comput Phys 198(2):628–644 Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow. Eyrolles, Paris Ishii M, Hibiki T (2006) Thermo-fluid dynamics of two-phase flow. Springer, New York Jacqmin D (1999) Calculation of two-phase Navier–Stokes flows using phase-field modeling. J Comput Phys 155(1):96–127 Jacqmin D (2000) Contact-line dynamics of a diffuse fluid interface. J Fluid Mech 402:57–88 James AJ, Lowengrub J (2004) A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J Comput Phys 201(2):685–722 Jamet D, Lebaigue O, Coutris N, Delhaye JM (2001) The second gradient method for the direct numerical simulation of liquid–vapor flows with phase change. J Comput Phys 169(2):624–651 Jamet D, Torres D, Brackbill JU (2002) On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method. J Comput Phys 182(1):262–276 Jang W, Jilesen J, Lien FS, Ji H (2008) A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system. Int J Comput Fluid Dyn 22(4):241–257 Jia XL, McLaughlin JB, Kontomaris K (2008) Lattice Boltzmann simulations of flows with fluid–fluid interfaces. Asia-Pac J Chem Eng 3(2):124–143 Johnson RA, Borhan A (2003) Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility. J Colloid Interf Sci 261(2):529–541 Jousse F, Farr R, Link DR, Fuerstman MJ, Garstecki P (2006) Bifurcation of droplet flows within capillaries. Phys Rev E 74(3):036311 Junk M, Klar A, Luo L-S (2005) Asymptotic analysis of the lattice Boltzmann equation. J Comput Phys 210(2):676–704 Juric D, Tryggvason G (1998) Computations of boiling flows. Int J Multiph Flow 24(3):387–410 Kadau K, Barber JL, Germann TC, Holian BL, Alder BJ (2010) Atomistic methods in fluid simulation. Philos T R Soc A 368(1916):1547–1560 Kadioglu SY, Sussman M (2008) Adaptive solution techniques for simulating underwater explosions and implosions. J Comput Phys 227(3):2083–2104 Kandlikar SG (2008) Exploring roughness effect on laminar internal flow-are we ready for change? Nanosc Microsc Therm Eng 12(1):61–82 Kandlikar SG (2010) Scale effects on flow boiling heat transfer in microchannels: a fundamental perspective. Int J Therm Sci 49(7):1073–1085 Kang M, Fedkiw RP, Liu X-D (2000) A boundary condition capturing method for multiphase incompressible flow. J Sci Comput 15(3):323–360 Karniadakis G, Beskok A, Aluru NR (2005) Microflows and nanoflows: fundamentals and simulation. Springer, New York Kashid MN, Kiwi-Minsker L (2009) Microstructured reactors for multiphase reactions: state of the art. Ind Eng Chem Res 48(14):6465–6485 Kececi S, Wörner M, Onea A, Soyhan HS (2009) Recirculation time and liquid slug mass transfer in co-current upward and downward Taylor flow. Catal Today 147(Supplement 1):S125–S131 Kenig EY, Ganguli AA, Atmakidis T, Chasanis P (2011) A novel method to capture mass transfer phenomena at free fluid–fluid interfaces. Chem Eng Process 50(1):68–76 Keskin O, Wörner M, Soyhan HS, Bauer T, Deutschmann O, Lange R (2010) Viscous co-current downward Taylor flow in a square mini-channel. AIChE J 56(7):1693–1702 Khenner M (2004) Computation of the material indicator function near the contact line (in Tryggvason’s method). J Comput Phys 200(1):1–7 Kim J (2005) A continuous surface tension force formulation for diffuse-interface models. J Comput Phys 204(2):784–804 Kim J, Lowengrub J (2005) Phase field modeling and simulation of three-phase flows. Interface Free Bound 7(4):435–466 Kobayashi I, Mukataka S, Nakajima M (2004) CFD simulation and analysis of emulsion droplet formation from straight-through microchannels. Langmuir 20(22):9868–9877 Kockmann N (2008) Transport phenomena in micro process engineering. Springer, Berlin Kreutzer MT, Bakker JJW, Kapteijn F, Moulijn JA, Verheijen PJT (2005a) Scaling-up multiphase monolith reactors: linking residence time distribution and feed maldistribution. Ind Eng Chem Res 44(14):4898–4913 Kreutzer MT, Kapteijn F, Moulijn JA, Heiszwolf JJ (2005b) Multiphase monolith reactors: chemical reaction engineering of segmented flow in microchannels. Chem Eng Sci 60(22):5895–5916 Kuksenok O, Jasnow D, Yeomans J, Balazs AC (2003) Periodic droplet formation in chemically patterned microchannels. Phys Rev Lett 91(10):108303 Kunkelmann C, Stephan P (2009) CFD simulation of boiling flows using the volume-of-fluid method within OpenFOAM. Numer Heat Tr A-Appl 56(8):631–646 Lafaurie B, Nardone C, Scardovelli R, Zaleski S, Zanetti G (1994) Modelling merging and fragmentation in multiphase flows with SURFER. J Comput Phys 113(1):134–147 Lai JM, Huang CY, Chen CH, Kung LL, Lin JD (2010) Influence of liquid hydrophobicity and nozzle passage curvature on microfluidic dynamics in a drop ejection process. J Micromech Microeng 20(1):015033 Lakehal D (2002) On the modelling of multiphase turbulent flows for environmental and hydrodynamic applications. Int J Multiphase Flow 28(5):823–863 Lakehal D, Labois M (2011) A new modelling strategy for phase-change heat transfer in turbulent interfacial two-phase flow. Int J Multiphase Flow 37(6):627–639 Lakehal D, Meier M, Fulgosi M (2002) Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows. Int J Heat Fluid Flow 23(3):242–257 Lakehal D, Larrignon G, Narayanan C (2008) Computational heat transfer and two-phase flow topology in miniature tubes. Microfluid Nanofluid 4(4):261–271 Lakshmanan P, Ehrhard P (2010) Marangoni effects caused by contaminants adsorbed on bubble surfaces. J Fluid Mech 647:143–161 Lallemand P, Luo L-S, Peng Y (2007) A lattice Boltzmann front-tracking method for interface dynamics with surface tension in two dimensions. J Comput Phys 226(2):1367–1384 Lauga E, Brenner MP, Stone HA (2007) Microfluidics: the no-slip boundary condition. In: Tropea C, Yarin A, Foss JF (eds) Handbook of experimental fluid dynamics. Springer, New York, pp 1219–1240 Lee T (2009) Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids. Comput Math Appl 58(5):987–994 Lee T, Lin C-L (2005) A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio. J Comput Phys 206(1):16–47 Lee J, Pozrikidis C (2006) Effect of surfactants on the deformation of drops and bubbles in Navier–Stokes flow. Comput Fluids 35(1):43–60 Lee W, Son G (2008) Bubble dynamics and heat transfer during nucleate boiling in a microchannel. Numer Heat Tr A-Appl 53(10):1074–1090 Lion N, Rossier JS, Girault HH (2006) Microfluidic applications in biology: from technologies to systems biology. Wiley, Weinheim Liovic P, Lakehal D (2007) Multi-physics treatment in the vicinity of arbitrarily deformable gas–liquid interfaces. J Comput Phys 222(2):504–535 Liovic P, Rudman M, Liow JL, Lakehal D, Kothe D (2006) A 3D unsplit-advection volume tracking algorithm with planarity-preserving interface reconstruction. Comput Fluids 35(10):1011–1032 Lishchuk SV, Care CM, Halliday I (2003) Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents. Phys Rev E 67(3):036701 Liu DS, Wang SD (2008) Hydrodynamics of Taylor flow in noncircular capillaries. Chem Eng Process 47(12):2098–2106 Liu X-D, Fedkiw RP, Kang M (2000) A boundary condition capturing method for Poisson’s equation on irregular domains. J Comput Phys 160(1):151–178 Liu H, Krishnan S, Marella S, Udaykumar HS (2005) Sharp interface Cartesian grid method II: a technique for simulating droplet interactions with surfaces of arbitrary shape. J Comput Phys 210(1):32–54 Liu J, Yap YF, Nguyen NT (2009a) Behavior of microdroplets in diffuser/nozzle structures. Microfluid Nanofluid 6(6):835–846 Liu J, Yap YF, Nguyen NT (2009b) Motion of a droplet through microfluidic ratchets. Phys Rev E 80(4):046319 Lopez J, Hernandez J (2010) On reducing interface curvature computation errors in the height function technique. J Comput Phys 229(13):4855–4868 López J, Hernández J, Gómez P, Faura F (2004) A volume of fluid method based on multidimensional advection and spline interface reconstruction. J Comput Phys 195(2):718–742 López J, Hernández J, Gómez P, Faura F (2005) An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows. J Comput Phys 208(1):51–74 Losasso F, Fedkiw R, Osher S (2006) Spatially adaptive techniques for level set methods and incompressible flow. Comput Fluids 35(10):995–1010 Lowengrub J, Truskinovsky L (1998) Quasi-incompressible Cahn–Hilliard fluids and topological transitions. P R Soc Lond a Mat 454(1978):2617–2654 Luo LS, Girimaji SS (2003) Theory of the lattice Boltzmann method: two-fluid model for binary mixtures. Phys Rev E 67(3):036302 Lv X, Zou QP, Zhao Y, Reeve D (2010) A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids. J Comput Phys 229(7):2573–2604 Lyklema J (1991) Fundamentals of interface and colloid science, vol III: liquid–fluid interfaces. Academic Press, London Ma C, Bothe D (2011) Direct numerical simulation of thermocapillary flow based on the volume of fluid method. Int J Multiphase Flow 37(9):1045–1058 Macklin P, Lowengrub J (2006) An improved geometry-aware curvature discretization for level set methods: application to tumor growth. J Comput Phys 215(2):392–401 Malik M, Fan ES-C, Bussmann M (2007) Adaptive VOF with curvature-based refinement. Int J Numer Methods Fluids 55(7):693–712 Marchandise E, Remacle J-F (2006) A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. J Comput Phys 219(2):780–800 Marchandise E, Remacle J-F, Chevaugeon N (2006) A quadrature-free discontinuous Galerkin method for the level set equation. J Comput Phys 212(1):338–357 Mary P, Studer V, Tabeling P (2008) Microfluidic droplet-based liquid–liquid extraction. Anal Chem 80(8):2680–2687 Mehravaran M, Hannani SK (2008) Simulation of incompressible two-phase flows with large density differences employing lattice Boltzmann and level set methods. Comput Method Appl M 198(2):223–233 Min C (2010) On reinitializing level set functions. J Comput Phys 229(8):2764–2772 Min C, Gibou F (2007) A second order accurate level set method on non-graded adaptive Cartesian grids. J Comput Phys 225(1):300–321 Mognetti BM, Yeomans JM (2009) Capillary filling in microchannels patterned by posts. Phys Rev E 80(5):056309 Mognetti BM, Yeomans JM (2010) Modeling receding contact lines on superhydrophobic surfaces. Langmuir 26(23):18162–18168 Mohammadi A, Floryan JM, Kaloni PN (2011) Spectrally accurate method for analysis of stationary flows of second-order fluids in rough micro-channels. Int J Numer Methods Fluids 66(4):509–536 Mukherjee A (2009) Contribution of thin-film evaporation during flow boiling inside microchannels. Int J Therm Sci 48(11):2025–2035 Mukherjee A, Dhir VK (2004) Study of lateral merger of vapor bubbles during nucleate pool boiling. J Heat Transfer 126(6):1023–1039 Mukherjee A, Kandlikar SG (2005) Numerical simulation of growth of a vapor bubble during flow boiling of water in a microchannel. Microfluid Nanofluid 1(2):137–145 Mukherjee A, Kandlikar SG (2009) The effect of inlet constriction on bubble growth during flow boiling in microchannels. Int J Heat Mass Transf 52(21–22):5204–5212 Muradoglu M (2010) Axial dispersion in segmented gas–liquid flow: effects of alternating channel curvature. Phys Fluids 22(12):122106 Muradoglu M, Gokaltun S (2004) Implicit multigrid computations of buoyant drops through sinusoidal constrictions. J Appl Mech 71(6):857–865 Muradoglu M, Kayaalp AD (2006) An auxiliary grid method for computations of multiphase flows in complex geometries. J Comput Phys 214(2):858–877 Muradoglu M, Stone HA (2005) Mixing in a drop moving through a serpentine channel: a computational study. Phys Fluids 17(7):073305 Muradoglu M, Tasoglu S (2010) A front-tracking method for computational modeling of impact and spreading of viscous droplets on solid walls. Comput Fluids 39(4):615–625 Muradoglu M, Tryggvason G (2008) A front-tracking method for computation of interfacial flows with soluble surfactants. J Comput Phys 227(4):2238–2262 Muradoglu M, Günther A, Stone HA (2007) A computational study of axial dispersion in segmented gas–liquid flow. Phys Fluids 19(7):072109 Muzaferija S, Peric M (1999) Computation of flows using interface-tracking and interface-capturing methods. In: Mahrenholtz O, Markiewicz M (eds) Nonlinear water wave interaction. WIT Press, Southampton, pp 59–100 Narayanan C, Lakehal D (2008) Two-phase convective heat transfer in miniature pipes under normal and microgravity conditions. J Heat Transf 130(7):074502 Naraynan C, Lakehal D (2006) Simulation of filling of microfluidic devices using a coarse-grained continuum contact angle model. In: Paper presented at the NSTI Nanotechnology Conference and Trade Show, Boston, May 7–11 Nas S, Tryggvason G (2003) Thermocapillary interaction of two bubbles or drops. Int J Multiphase Flow 29(7):1117–1135 Ndinisa NV, Wiley DE, Fletcher DF (2005) Computational fluid dynamics simulations of Taylor bubbles in tubular membranes—model validation and application to laminar flow systems. Chem Eng Res Des 83 (A1):40–49 Nguyen N-T, Wereley ST (2006) Fundamentals and applications of microfluidics, 2nd edn. Artech House, Boston Nie XB, Chen SY, Weinan E, Robbins MO (2004) A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J Fluid Mech 500:55–64 Nikolopoulos N, Nikas KS, Bergeles G (2009) A numerical investigation of central binary collision of droplets. Comput Fluids 38(6):1191–1202 Nobari M, Tryggvason G (1996) Numerical simulations of three-dimensional drop collisions. AIAA J 34(4):750–755 Nobari MR, Jan Y-J, Tryggvason G (1996) Head-on collision of drops—a numerical investigation. Phys Fluids 8(1):29–42 Noh WF, Woodward P (1976) SLIC (simple line interface calculation). In: Lecture notes in physics, vol 59. Springer, New York, pp 330–340 Nourgaliev RR, Dinh TN, Theofanous TG, Joseph D (2003) The lattice Boltzmann equation method: theoretical interpretation, numerics and implications. Int J Multiphase Flow 29(1):117–169 Ohta M, Suzuki M (1996) Numerical analysis of mass transfer from a free motion drop in a solvent extraction process. Solvent Extr Res Dev 3:138–149 Olgac U, Kayaalp AD, Muradoglu M (2006) Buoyancy-driven motion and breakup of viscous drops in constricted capillaries. Int J Multiphase Flow 32(9):1055–1071 Olsson E, Kreiss G (2005) A conservative level set method for two phase flow. J Comput Phys 210(1):225–246 Olsson E, Kreiss G, Zahedi S (2007) A conservative level set method for two phase flow II. J Comput Phys 225(1):785–807 Onea A, Wörner M, Cacuci DG (2009) A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels. Chem Eng Sci 64(7):1416–1435 Osher S, Fedkiw RP (2003) Level set methods and dynamic implicit surfaces. Springer, Berlin Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49 Özkan F, Wörner M, Wenka A, Soyhan HS (2007) Critical evaluation of CFD codes for interfacial simulation of bubble-train flow in a narrow channel. Int J Numer Methods Fluids 55(6):537–564 Öztaskin MC, Wörner M, Soyhan HS (2009) Numerical investigation of the stability of bubble train flow in a square minichannel. Phys Fluids 21(4):042108 Peskin CS (1977) Numerical analysis of blood flow in the heart. J Comput Phys 25(3):220–252 Peskin CS (2002) The immersed boundary method. Acta Numerica 11:479–517 Petera J, Weatherley LR (2001) Modelling of mass transfer from falling droplets. Chem Eng Sci 56(16):4929–4947 Pilliod JE, Puckett EG (2004) Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J Comput Phys 199(2):465–502 Pooley CM, Furtado K (2008) Eliminating spurious velocities in the free-energy lattice Boltzmann method. Phys Rev E 77(4):046702 Pooley CM, Kusumaatmaja H, Yeomans JM (2008) Contact line dynamics in binary lattice Boltzmann simulations. Phys Rev E 78(5):056709 Popinet S (2009) An accurate adaptive solver for surface-tension-driven interfacial flows. J Comput Phys 228(16):5838–5866 Popinet S, Zaleski S (1999) A front-tracking algorithm for accurate representation of surface tension. Int J Numer Methods Fluids 30(6):775–793 Pozrikidis C (2001) Interfacial dynamics for stokes flow. J Comput Phys 169(2):250–301 Price G, Reader G, Rowe R, Bugg J (1998) A piecewise parabolic interface calculation for volume-tracking. In: Paper presented at the 6th Annual conference of the computational fluid dynamics society of Canada, Quebec, June 7–9 2001 Prosperetti A, Tryggvason G (2007) Computational methods for multiphase flow. Cambridge University Press, Cambridge Qian DY, Lawal A (2006) Numerical study on gas and liquid slugs for Taylor flow in a T-junction microchannel. Chem Eng Sci 61(23):7609–7625 Qian TZ, Wang XP, Sheng P (2006) A variational approach to moving contact line hydrodynamics. J Fluid Mech 564:333–360 Quan S, Schmidt DP (2007) A moving mesh interface tracking method for 3D incompressible two-phase flows. J Comput Phys 221(2):761–780 Quan S, Lou J, Schmidt DP (2009) Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations. J Comput Phys 228(7):2660–2675 Raessi M, Mostaghimi J, Bussmann M (2007) Advecting normal vectors: a new method for calculating interface normals and curvatures when modeling two-phase flows. J Comput Phys 226(1):774–797 Raessi M, Bussmann M, Mostaghimi J (2009) A semi-implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows. Int J Numer Methods Fluids 59(10):1093–1110 Raessi M, Mostaghimi J, Bussmann M (2010) A volume-of-fluid interfacial flow solver with advected normals. Comput Fluids 39(8):1401–1410 Raimondi ND, Prat L, Gourdon C, Cognet P (2008) Direct numerical simulations of mass transfer in square microchannels for liquid–liquid slug flow. Chem Eng Sci 63(22):5522–5530 Ralston J, Popescu M, Sedev R (2008) Dynamics of wetting from an experimental point of view. Annu Rev Mater Res 38:23–43 Rannou G (2008) Lattice-Boltzmann method and immiscible two-phase flow, Master Thesis. Georgia Institute of Technology, Atlanta Renardy Y, Renardy M (2002) PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J Comput Phys 183(2):400–421 Renardy M, Renardy Y, Li J (2001) Numerical simulation of moving contact line problems using a volume-of-fluid method. J Comput Phys 171(1):243–263 Renardy YY, Renardy M, Cristini V (2002) A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio. Eur J Mech B-Fluid 21(1):49–59 Rider WJ, Kothe DB (1998) Reconstructing volume tracking. J Comput Phys 141(2):112–152 Rohde M, Kandhai D, Derksen JJ, van den Akker HEA (2006) A generic, mass conservative local grid refinement technique for lattice-Boltzmann schemes. Int J Numer Methods Fluids 51(4):439–468 Rosengarten G, Harvie DJE, Cooper-White J (2006) Contact angle effects on microdroplet deformation using CFD. Appl Math Model 30(10):1033–1042 Rudman M (1997) Volume-tracking methods for interfacial flow calculations. Int J Numer Methods Fluids 24(7):671–691 Rudman M (1998) A volume-tracking method for incompressible multifluid flows with large density variations. Int J Numer Methods Fluids 28(2):357–378 Russo G, Smereka P (2000) A remark on computing distance functions. J Comput Phys 163(1):51–67 Sabisch W (2000) Dreidimensionale numerische Simulation der Dynamik von aufsteigenden Einzelblasen und Blasenschwärmen mit einer Volume-of-Fluid-Methode. Forschungszentrum Karlsruhe Wissenschaftliche Berichte, FZKA 6478 Sabisch W, Wörner M, Grötzbach G, Cacuci DG (2001) Dreidimensionale numerische Simulation von aufsteigenden Einzelblasen und Blasenschwärmen mit einer Volume-of-Fluid Methode. Chem-Ing-Tech 73(4):368–373 Saha AA, Mitra SK (2009a) Effect of dynamic contact angle in a volume of fluid (VOF) model for a microfluidic capillary flow. J Colloid Interf Sci 339(2):461–480 Saha AA, Mitra SK (2009b) Numerical study of capillary flow in microchannels with alternate hydrophilic–hydrophobic bottom wall. J Fluids Eng 131(6):061202 Saliterman S (2006) Fundamentals of bioMEMS and medical microdevices. SPIE, Bellingham Santos RM, Kawaji M (2010) Numerical modeling and experimental investigation of gas–liquid slug formation in a microchannel T-junction. Int J Multiphase Flow 36(4):314–323 Sarrazin F, Loubiere K, Prat L, Gourdon C, Bonometti T, Magnaudet J (2006) Experimental and numerical study of droplets hydrodynamics in microchannels. AIChE J 52(12):4061–4070 Sarrazin F, Bonometti T, Prat L, Gourdon C, Magnaudet J (2008) Hydrodynamic structures of droplets engineered in rectangular micro-channels. Microfluid Nanofluid 5(1):131–137 Sbragaglia M, Benzi R, Biferale L, Succi S, Toschi F (2006) Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows. Phys Rev Lett 97(20):204503 Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31:567–603 Scardovelli R, Zaleski S (2000) Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J Comput Phys 164(1):228–237 Schlottke J, Weigand B (2008) Direct numerical simulation of evaporating droplets. J Comput Phys 227(10):5215–5237 Schönfeld F, Hardt S (2009) Dynamic contact angles in CFD simulations. Comput Fluids 38(4):757–764 Schönfeld F, Rensink D (2003) Simulation of droplet generation by mixing nozzles. Chem Eng Technol 26(5):585–591 Schubert K, Brandner J, Fichtner M, Linder G, Schygulla U, Wenka A (2001) Microstructure devices for applications in thermal and chemical process engineering. Microscale Therm Eng 5(1):17–39 Schuster A, Lakshmanan R, Ponton J, Sefiane K (2003) Simulation and design of a non-adiabatic multiphase microreactor. Int J Chem React Eng 1:A45 Seppecher P (1996) Moving contact lines in the Cahn–Hilliard theory. Int J Eng Sci 34(9):977–992 Sessoms DA, Belloul M, Engl W, Roche M, Courbin L, Panizza P (2009) Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements. Phys Rev E 80(1):016317 Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. P Natl Acad Sci USA 93(4):1591–1595 Sethian JA (1999a) Fast marching methods. Siam Rev 41(2):199–235 Sethian JA (1999b) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 2nd edn. Cambridge University Press, New York Sethian JA, Smereka P (2003) Level set methods for fluid interfaces. Annu Rev Fluid Mech 35:341–372 Shan XW, Chen HD (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47(3):1815–1819 Shao N, Salman W, Gavriilidis A, Angeli P (2008) CFD simulations of the effect of inlet conditions on Taylor flow formation. Int J Heat Fluid Flow 29(6):1603–1611 Shen J, Yang X (2009) An efficient moving mesh spectral method for the phase-field model of two-phase flows. J Comput Phys 228(8):2978–2992 Shepel SV, Smith BL (2009) On surface tension modelling using the level set method. Int J Numer Methods Fluids 59(2):147–171 Shin S, Juric D (2002) Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J Comput Phys 180(2):427–470 Shin S, Juric D (2009) A hybrid interface method for three-dimensional multiphase flows based on front tracking and level set techniques. Int J Numer Methods Fluids 60(7):753–778 Shirani E, Ashgriz N, Mostaghimi J (2005) Interface pressure calculation based on conservation of momentum for front capturing methods. J Comput Phys 203(1):154–175 Shui LL, Eijkel JCT, van den Berg A (2007) Multiphase flow in micro- and nanochannels. Sensor Actuat B Chem 121(1):263–276 Sikalo S, Wilhelm HD, Roisman IV, Jakirlic S, Tropea C (2005) Dynamic contact angle of spreading droplets: experiments and simulations. Phys Fluids 17(6):062103 Silva G, Leal N, Semiao V (2008) Micro-PIV and CFD characterization of flows in a microchannel: velocity profiles, surface roughness and Poiseuille numbers. Int J Heat Fluid Flow 29(4):1211–1220 Smith KA, Ottino JM, Warren PB (2005) Simple representation of contact-line dynamics in a level-set model of an immiscible fluid interface. Ind Eng Chem Res 44(5):1194–1198 Smolianski A (2005) Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces. Int J Numer Methods Fluids 48(3):231–269 Sommerfeld M, van Wachem B, Oliemans R (2008) Best practice guidelines for computational fluid dynamics of dispersed multiphase flows. ERCOFTAC, SIAMUF Swedish Industrial Association for Multiphase Flows Son G, Dhir VK (1998) Numerical simulation of film boiling near critical pressures with a level set method. J Heat Transf 120(1):183–192 Son G, Dhir VK (2007) A level set method for analysis of film boiling on an immersed solid surface. Numer Heat Tr B-Fund 52(2):153–177 Son G, Hur N (2002) A coupled level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles. Numer Heat Tr B-Fund 42(6):523–542 Son G, Dhir VK, Ramanujapu N (1999) Dynamics and heat transfer associated with a single bubble during nucleate boiling on a horizontal surface. J Heat Transfer 121(3):623–631 Spelt PDM (2005) A level-set approach for simulations of flows with multiple moving contact lines with hysteresis. J Comput Phys 207(2):389–404 Squires TM, Quake SR (2005) Microfluidics: fluid physics at the nanoliter scale. Rev Mod Phys 77(3):977–1026 Stone HA (1990) A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys Fluids A 2(1):111–112 Stone HA, Kim S (2001) Microfluidics: basic issues, applications, and challenges. AIChE J 47(6):1250–1254 Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices. Annu Rev Fluid Mech 36(1):381–411 Strain J (1999) Tree methods for moving interfaces. J Comput Phys 151(2):616–648 Strubelj L, Tiselj I, Mavko B (2009) Simulations of free surface flows with implementation of surface tension and interface sharpening in the two-fluid model. Int J Heat Fluid Flow 30(4):741–750 Succi S (2001) The Lattice Boltzmann equation for fluid dynamics and beyond. Clarendon, Oxford Sun Y, Beckermann C (2007) Sharp interface tracking using the phase-field equation. J Comput Phys 220(2):626–653 Sun DL, Tao WQ (2010) A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows. Int J Heat Mass Transf 53(4):645–655 Sussman M (2003) A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J Comput Phys 187(1):110–136 Sussman M, Fatemi E (1999) An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. Siam J Sci Comput 20(4):1165–1191 Sussman M, Puckett EG (2000) A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J Comput Phys 162(2):301–337 Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159 Sussman M, Almgren AS, Bell JB, Colella P, Howell LH, Welcome ML (1999) An adaptive level set approach for incompressible two-phase flows. J Comput Phys 148(1):81–124 Sussman M, Smith KM, Hussaini MY, Ohta M, Zhi-Wei R (2007) A sharp interface method for incompressible two-phase flows. J Comput Phys 221(2):469–505 Swift MR, Orlandini E, Osborn WR, Yeomans JM (1996) Lattice Boltzmann simulations of liquid–gas and binary fluid systems. Phys Rev E 54(5):5041–5052 Tabeling P (2005) Introduction to microfluidics. Oxford University Press, New York Tabeling P (2009) A brief introduction to slippage, droplets and mixing in microfluidic systems. Lab Chip 9(17):2428–2436 Tabeling P (2010) Investigating slippage, droplet breakup, and synthesizing microcapsules in microfluidic systems. Phys Fluids 22(2):021302 Taha T, Cui ZF (2006a) CFD modelling of slug flow in vertical tubes. Chem Eng Sci 61(2):676–687 Taha T, Cui ZF (2006b) CFD modelling of slug flow inside square capillaries. Chem Eng Sci 61(2):665–675 Takada N, Misawa M, Tomiyama A (2006) A phase-field method for interface-tracking simulation of two-phase flows. Math Comput Simulat 72(2–6):220–226 Tanguy S, Ménard T, Berlemont A (2007) A level set method for vaporizing two-phase flows. J Comput Phys 221(2):837–853 Tanthapanichakoon W, Aoki N, Matsuyama K, Mae K (2006) Design of mixing in microfluidic liquid slugs based on a new dimensionless number for precise reaction and mixing operations. Chem Eng Sci 61(13):4220–4232 Taylor GI (1961) Deposition of a viscous fluid on the wall of a tube. J Fluid Mech 10(2):161–165 Terashima H, Tryggvason G (2009) A front-tracking/ghost-fluid method for fluid interfaces in compressible flows. J Comput Phys 228(11):4012–4037 Theberge AB, Courtois F, Schaerli Y, Fischlechner M, Abell C, Hollfelder F, Huck WTS (2010) Microdroplets in microfluidics: an evolving platform for discoveries in chemistry and biology. Angew Chem Int Edit 49(34):5846–5868 Theodorakakos A, Bergeles G (2004) Simulation of sharp gas–liquid interface using VOF method and adaptive grid local refinement around the interface. Int J Numer Methods Fluids 45(4):421–439 Thomas S, Esmaeeli A, Tryggvason G (2010) Multiscale computations of thin films in multiphase flows. Int J Multiph Flow 36(1):71–77 Thome JR (2004) Boiling in microchannels: a review of experiment and theory. Int J Heat Fluid Flow 25(2):128–139 Thömmes G, Becker J, Junk M, Vaikuntam AK, Kehrwald D, Klar A, Steiner K, Wiegmann A (2009) A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. J Comput Phys 228(4):1139–1156 Thulasidas TC, Abraham MA, Cerro RL (1997) Flow patterns in liquid slugs during bubble-train flow inside capillaries. Chem Eng Sci 52(17):2947–2962 Tomar G, Biswas G, Sharma A, Agrawal A (2005) Numerical simulation of bubble growth in film boiling using a coupled level-set and volume-of-fluid method. Phys Fluids 17(11):112103 Tomar G, Fuster D, Zaleski S, Popinet S (2010) Multiscale simulations of primary atomization. Comput Fluids 39(10):1864–1874 Tong AY, Wang Z (2007) A numerical method for capillarity-dominant free surface flows. J Comput Phys 221(2):506–523 Tornberg A-K, Engquist B (2000) A finite element based level-set method for multiphase flow applications. Comput Visual Sci 3(1):93–101 Torres DJ, Brackbill JU (2000) The point-set method: front-tracking without connectivity. J Comput Phys 165(2):620–644 Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S, Jan YJ (2001) A front-tracking method for the computations of multiphase flow. J Comput Phys 169(2):708–759 Tryggvason G, Thomas S, Lu J, Aboulhasanzadeh B (2010) Multiscale issues in DNS of multiphase flows. Acta Math Sci 30(2):551–562 Tryggvason G, Scardovelli R, Zaleski S (2011) Direct numerical simulations of gas–liquid multiphase flows. Cambridge University Press, Cambridge Ubbink O, Issa RI (1999) A method for capturing sharp fluid interfaces on arbitrary meshes. J Comput Phys 153(1):26–50 Udaykumar HS, Krishnan S, Marella S (2009) Adaptively refined, parallelised sharp interface Cartesian grid method for three-dimensional moving boundary problems. Int J Comput Fluid Dyn 23(1):1–24 Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100(1):25–37 Urbant P, Leshansky A, Halupovich Y (2008) On the forced convective heat transport in a droplet-laden flow in microchannels. Microfluid Nanofluid 4(6):533–542 van der Graaf S, Nisisako T, Schroen CGPH, van der Sman RGM, Boom RM (2006) Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. Langmuir 22(9):4144–4152 van der Pijl SP, Segal A, Vuik C, Wesseling P (2005) A mass-conserving level-set method for modelling of multi-phase flows. Int J Numer Methods Fluids 47(4):339–361 van der Sman R, van der Graaf S (2006) Diffuse interface model of surfactant adsorption onto flat and droplet interfaces. Rheol Acta 46(1):3–11 van Steijn V, Kreutzer MT, Kleijn CR (2007) μ-PIV study of the formation of segmented flow in microfluidic T-junctions. Chem Eng Sci 62(24):7505–7514 van Steijn V, Kleijn CR, Kreutzer MT (2009) Flows around confined bubbles and their importance in triggering pinch-off. Phys Rev Lett 103(21):214501 Verhaeghe F, Luo L-S, Blanpain B (2009) Lattice Boltzmann modeling of microchannel flow in slip flow regime. J Comput Phys 228(1):147–157 Villanueva W, Amberg G (2006) Some generic capillary-driven flows. Int J Multiphase Flow 32(9):1072–1086 Wang ZY, Tong AY (2010) A sharp surface tension modeling method for two-phase incompressible interfacial flows. Int J Numer Methods Fluids 64(7):709–732 Wang Z, Yang J, Koo B, Stern F (2009a) A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves. Int J Multiphase Flow 35(3):227–246 Wang Z, Yang J, Stern F (2009b) An improved particle correction procedure for the particle level set method. J Comput Phys 228(16):5819–5837 Wang CW, Oskooei A, Sinton D, Moffitt MG (2010) Controlled self-assembly of quantum dot-block copolymer colloids in multiphase microfluidic reactors. Langmuir 26(2):716–723 Wegener M, Eppinger T, Bäumler K, Kraume M, Paschedag AR, Bänsch E (2009) Transient rise velocity and mass transfer of a single drop with interfacial instabilities—Numerical investigations. Chem Eng Sci 64(23):4835–4845 Welch SWJ (1995) Local simulation of two-phase flows including interface tracking with mass transfer. J Comput Phys 121(1):142–154 Welch SWJ, Wilson J (2000) A volume of fluid based method for fluid flows with phase change. J Comput Phys 160(2):662–682 Weller HG (2006) A new approach to VOF-based interface capturing methods for incompressible and compressible flow. Tech. Rep. TR/HGW/07, OpenCFD Ltd. Werder T, Walther JH, Koumoutsakos P (2005) Hybrid atomistic–continuum method for the simulation of dense fluid flows. J Comput Phys 205(1):373–390 Weymouth GD, Yue DKP (2010) Conservative volume-of-fluid method for free-surface simulations on Cartesian-grids. J Comput Phys 229(8):2853–2865 Whitesides GM (2006) The origins and the future of microfluidics. Nature 442(7101):368–373 Wolf FG, dos Santos LOE, Philippi PC (2010) Capillary rise between parallel plates under dynamic conditions. J Colloid Interf Sci 344(1):171–179 Wörner M, Sabisch W, Grötzbach G, Cacuci DG (2001) Volume-averaged conservation equations for volume-of-fluid interface tracking. In: Proceedings of the 4th International Conference on Multiphase Flow, New Orleans, Louisiana, USA, May 27–June 1 2001 Wörner M, Ghidersa BE, Ilic M, Cacuci DG (2005) Volume-of-fluid method based numerical simulations of gas–liquid two-phase flow in confined geometries. Houille Blanche 6:91–104 Wörner M, Ghidersa B, Onea A (2007) A model for the residence time distribution of bubble-train flow in a square mini-channel based on direct numerical simulation results. Int J Heat Fluid Flow 28(1):83–94 Wu L, Tsutahara M, Kim L, Ha M (2008a) Numerical simulations of droplet formation in a cross-junction microchannel by the lattice Boltzmann method. Int J Numer Methods Fluids 57(6):793–810 Wu L, Tsutahara M, Kim LS, Ha M (2008b) Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel. Int J Multiphase Flow 34(9):852–864 Xiao F, Honma Y, Kono T (2005) A simple algebraic interface capturing scheme using hyperbolic tangent function. Int J Numer Methods Fluids 48(9):1023–1040 Xiong RQ, Chung JN (2010) A new model for three-dimensional random roughness effect on friction factor and heat transfer in microtubes. Int J Heat Mass Transfer 53(15–16):3284–3291 Xu J-J, Li Z, Lowengrub J, Zhao H (2006) A level-set method for interfacial flows with surfactant. J Comput Phys 212(2):590–616 Yabe T, Xiao F, Utsumi T (2001) The constrained interpolation profile method for multiphase analysis. J Comput Phys 169(2):556–593 Yan YY, Zu YQ (2007) A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio. J Comput Phys 227(1):763–775 Yang C, Li DQ (1996) A method of determining the thickness of liquid–liquid interfaces. Colloid Surf A 113(1–2):51–59 Yang C, Mao Z-S (2005) Numerical simulation of interphase mass transfer with the level set approach. Chem Eng Sci 60(10):2643–2660 Yang X, James AJ, Lowengrub J, Zheng X, Cristini V (2006) An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. J Comput Phys 217(2):364–394 Yap YF, Chai JC, Wong TN, Toh KC, Zhang HY (2006) A global mass correction scheme for the level-set method. Numer Heat Tr B-Fund 50(5):455–472 Yap YF, Tan SH, Nguyen NT, Murshed SMS, Wong TN, Yobas L (2009) Thermally mediated control of liquid microdroplets at a bifurcation. J Phys D Appl Phys 42(6):065503 Yen BKH, Günther A, Schmidt MA, Jensen KF, Bawendi MG (2005) A microfabricated gas–liquid segmented flow reactor for high-temperature synthesis: the case of CdSe quantum dots. Angew Chem Int Edit 44(34):5447–5451 Yokoi K (2007) Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm. J Comput Phys 226(2):1985–2002 Youngs DL (1982) Time-dependent multi-material flow with large fluid distortion. In: Morton KW, Baines MJ (eds) Numerical methods for fluid dynamics, vol 24. Academic Press, New York, pp 273–285 Yu Z, Fan L-S (2009) An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation. J Comput Phys 228(17):6456–6478 Yu Z, Hemminger O, Fan L-S (2007) Experiment and lattice Boltzmann simulation of two-phase gas–liquid flows in microchannels. Chem Eng Sci 62(24):7172–7183 Yue PT, Feng JJ, Liu C, Shen J (2004) A diffuse-interface method for simulating two-phase flows of complex fluids. J Fluid Mech 515:293–317 Yue P, Zhou C, Feng JJ, Ollivier-Gooch CF, Hu HH (2006) Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing. J Comput Phys 219(1):47–67 Yue P, Zhou C, Feng JJ (2007) Spontaneous shrinkage of drops and mass conservation in phase-field simulations. J Comput Phys 223(1):1–9 Zacharioudaki M, Kouris C, Dimakopoulos Y, Tsamopoulos J (2007) A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate transformation and third-order upwinding. J Comput Phys 227(2):1428–1469 Zagnoni M, Anderson J, Cooper JM (2010) Hysteresis in multiphase microfluidics at a T-Junction. Langmuir 26(12):9416–9422 Zahedi S, Gustavsson K, Kreiss G (2009) A conservative level set method for contact line dynamics. J Comput Phys 228(17):6361–6375 Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31(3):335–362 Zhang J, Eckmann DM, Ayyaswamy PS (2006) A front tracking method for a deformable intravascular bubble in a tube with soluble surfactant transport. J Comput Phys 214(1):366–396 Zhang YL, Zou QP, Greaves D (2010) Numerical simulation of free-surface flow using the level-set method with global mass correction. Int J Numer Methods Fluids 63(6):651–680 Zhao CX, Middelberg APJ (2011) Two-phase microfluidic flows. Chem Eng Sci 66(7):1394–1411 Zhao B, Moore JS, Beebe DJ (2001) Surface-directed liquid flow inside microchannels. Science 291(5506):1023–1026 Zhao J-F, Li Z-D, Li H-X, Li J (2010) Thermocapillary migration of deformable bubbles at moderate to large Marangoni number in microgravity. Microgravity Sci Tec 22(3):295–303 Zheng HW, Shu C, Chew YT (2005) Lattice Boltzmann interface capturing method for incompressible flows. Phys Rev E 72(5):056705 Zheng HW, Shu C, Chew YT (2006) A lattice Boltzmann model for multiphase flows with large density ratio. J Comput Phys 218(1):353–371 Zheng Y, Fujioka H, Grotberg JB (2007) Effects of gravity, inertia, and surfactant on steady plug propagation in a two-dimensional channel. Phys Fluids 19(8):082107 Zheng HW, Shu C, Chew YT, Sun JH (2008) Three-dimensional lattice Boltzmann interface capturing method for incompressible flows. Int J Numer Methods Fluids 56(9):1653–1671 Zhou CF, Yue PT, Feng JJ (2006) Formation of simple and compound drops in microfluidic devices. Phys Fluids 18(9):092105 Zhou C, Yue P, Feng JJ, Ollivier-Gooch CF, Hu HH (2010) 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids. J Comput Phys 229(2):498–511 Zhu X, Sui PC, Djilali N (2008) Numerical simulation of emergence of a water droplet from a pore into a microchannel gas stream. Microfluid Nanofluid 4(6):543–555