Skip to main content
SpringerLink
Log in
Book cover

Micro- and Nanoflows pp 127–184Cite as

Modeling of Micromixers

  • Chapter
  • First Online:

  • 858 Accesses

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 118))

Abstract

Mixing of fluids is an extremely important process, widely used in various microfluidic devices (chemical microreactors, chemical and biological analyzers, drug delivery systems, etc.). Mixing in macroscopic flows usually occurs in the turbulent regime. However, microflows are mainly laminar, and mixing under standard conditions is caused only by molecular diffusion. Because of the extremely low values of the molecular diffusion coefficient, this manner of mixing is very ineffective. To increase the mixing velocity, it is necessary to use special devices: micromixers. For this reason, such devices are key elements of many microelectromechanical systems (MEMS). This chapter describes the results of CFD simulations of the simplest micromixers. The method used to solve the Navier-Stokes equations is described in the first two sections. Sections 4.3 and 4.4 are devoted to the study of the flow and mixing regimes in Y-type micromixers at low and moderate Reynolds numbers. In the next section, the flow in T-type micromixers is studied experimentally and the obtained data is compared with those from modeling. Modeling of two-phase flow and heat transfer in micromixers is considered in the two subsequent sections. One simple active method for mixing is discussed in the last section.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Aubina J, Fletcherb DF, Xuereb C (2005) Design of micromixers using CFD modeling. Chem Eng Sci 60:2503–2516

    Article  Google Scholar 

  • Bothe D, Stemich C, Warnecke H-J (2004) Theoretische und experimentelle Untersuchungen der Mischvorgänge in T-förmigen Microreaktoren. Teil 1. Numerische Simulation und Beurteilung des Strömungsmischens. CIT 76:1480–1484

    Google Scholar 

  • Bothe D, Stemich C, Warnecke H-J (2006) Fluid mixing in a T-shaped micro-mixer. Chem Eng Sci 61:2950–2958

    Article  Google Scholar 

  • Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335–354

    Article  ADS  MathSciNet  Google Scholar 

  • Cao J, Cheng P, Hong FJ (2008) A numerical study of an electrothermal votex enhanced micromixer. Microfluid Nanofluid 5:13–21

    Article  Google Scholar 

  • Dreher S, Kockmann N, Woias P (2009) Characterization of laminar transient flow regimes and mixing in T-shaped micromixers. Heat Transf Eng 30:91–100

    Article  ADS  Google Scholar 

  • Engler M, Kockmann N, Kiefer T, Woias P (2004) Numerical and experimental investigations on liquid mixing in static micromixers. Chem Eng J 101:315–322

    Article  Google Scholar 

  • Ferziger JH, Peric M (2006) Computational methods for fluid dynamics. Springer, Berlin

    MATH  Google Scholar 

  • Garstecki P (2006) Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of breakup. Lab Chip 6:437–446

    Article  Google Scholar 

  • Gavrilov AA, Minakov AV, Dekterev AA, Rudyak VY (2011) A numerical algorithm for modeling laminar flows in an annular channel with eccentricity. J Appl Ind Math 5(4):1–12

    Google Scholar 

  • Gobert C, Schwert F, Manhart M (2006) Lagrangian scalar tracking for laminar micromixing at high Schmidt numbers. In: Proceedings of ASME joint U.S.-European fluids engineering summer meeting, Miami, USA, Paper No. FEDSM2006-98035, pp 1053–1062

    Google Scholar 

  • Grigoriev IS, Meilikhova EZ (eds) (1991) Physical values. Handbook. Energoatomizdat, Moscow

    Google Scholar 

  • Hirt CW, Nichols BD (1981) Volume of Fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225

    Article  ADS  Google Scholar 

  • Hoffmann M, Schluter M, Rubiger N (2006) Experimental investigation of liquid–liquid mixing in T-shaped micro-mixers using µ-LIF and µ-PIV. Chem Eng Sci 61:2968–2976

    Article  Google Scholar 

  • Hong CC, Choi JW, Ahn CH (2004) A novel in-plain passive microfluidics mixer with modified Tesla structures. Lab Chip 4:109–113

    Article  Google Scholar 

  • Jiménez J (2005) The growth of a mixing layer in laminar channel. J Fluid Mech 535:245–254

    Article  ADS  MathSciNet  Google Scholar 

  • Karnidakis G, Beskok A, Aluru N (2005) Microflows and nanoflows. Interdisciplinary applied mathematics, vol 29. Springer, Berlin

    Google Scholar 

  • Karnik R (2008) Microfluidic mixing. In: Li D (ed) Encyclopedia of microfluidics and nanofluidics. Springer, Berlin, pp 1177–1186

    Google Scholar 

  • Kashinskii ON, Kurdyumov AS, Lobanov PD (2010) Perturbation of a downward liquid flow by a stationary gas slug. Fluid Dyn 45(4):591–598

    Article  ADS  Google Scholar 

  • Kelleher MD, Flentie DL, McKee RJ (1980) An experimental study of the secondary flow in a curved rectangular channel. Trans J Fluids Eng 102:92–96

    Article  Google Scholar 

  • Khandekar S, Agarwal G, Moharana MK (2010) Thermo-hydrodynamics of developing flow in a rectangular mini-channel array. In: Proceedings of 9th international and 20th national ISHMT-ASME heat and mass transfer conference, pp 1342–1349

    Google Scholar 

  • Kim BJ, Liu YZ, Sung HJ (2004) Micro PIV measurement of two-fluid flow with different refraction indices. Measur Sci Technol 15(6):1097–1103

    Google Scholar 

  • Koshizuka S, Nobe A, Oka Y (1998) Numerical analysis of breaking waves using the moving particle semi-implicit method. Int J Numer Methods Fluids 26(7):751–769

    Article  ADS  Google Scholar 

  • Kuznetzov VV, Shamirzaev AS, Ershov IN (2005) Motion of gas shells in small size rectangular channels. In: Proceedings of XXVIII Siberian thermophyasical seminar, IT SB RAS, Novosibirsk, pp 145–149

    Google Scholar 

  • Lauga E, Brenner MP, Stone HA (2005) Microfluidics: the no-slip boundary condition. In: Foss J, Tropea C, Yarin A (eds) Handbook of experimental fluid dynamics, Ch 15, Springer, New York

    Google Scholar 

  • Leonard BP (1979) A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Eng 19:59–98

    Article  ADS  Google Scholar 

  • Lin YC, Chung YC, Wu CY (2007) Mixing enhancement of the passive microfluidic mixer with J-shaped baffles in the tee channel. Biomed Microdevices 9:215–221

    Article  Google Scholar 

  • Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

    Google Scholar 

  • Mansur EA, Mingxing YE, Yundong W, Youyuan D (2008) A state-of-the-art review of mixing in microfluidic mixers. Chin J Chem Eng 16(4):503–516

    Article  Google Scholar 

  • Marchuk GI (1990) Splitting and alternating direction methods. Handbook of numerical analysis, vol 1. Elsevier, Amsterdam, pp 197–462

    Chapter  Google Scholar 

  • Martin JC, Moyce WJ (1952) An experimental study of the collapse of a liquid column on a rigid horizontal plane. Philos Trans Roy Soc Lond 244:312–324

    Article  ADS  Google Scholar 

  • Menter FR (1993) Zonal two equation k-w turbulence models for aerodynamic flows. AIAA Paper 93-2906-2917

    Google Scholar 

  • Minakov AV, Gavrilov AA, Dekterev AA (2008) Numerical algorithm for solving space hydrodynamical problems with moving hard bodies and free surface. Siberian J Ind Math 4(36):94–104

    MATH  Google Scholar 

  • Minakov AV, Rudyak VY, Gavrilov AA, Dekterev AA (2010) On optimization of mixing process of liquids in microchannels. J Siberian Fed Univ Math Phys 3(2):146–156

    Google Scholar 

  • Minakov AV, Rudyak VY, Gavrilov AA, Dekterev AA (2012) Mixing in a T-shaped micromixer at moderate Reynolds numbers. Thermophys Aeromech 19(3):385–395

    Article  ADS  Google Scholar 

  • Minakov A, Rudyak V, Yagodnitsina A, Bilsky A (2013a) Micro-LIF and numerical investigation of mixing in microchannel. J. Siberian Fed Univ Eng Technol 1(6):15–27

    Google Scholar 

  • Minakov A, Rudyak V, Dekterev A, Gavrilov A (2013b) Investigation of slip boundary conditions in the T-shaped microchannel. Int J Heat Fluid Flow 43:161–169

    Article  Google Scholar 

  • Minakov A, Yagodnitsina A, Lobasov A, Rudyak V, Bilsky A (2013c) Study of fluid flow in micromixer with symmetrical and asymmetrical inlet conditions. La Houille Blanche 5:12–21

    Article  Google Scholar 

  • Monaghan JJ (1994) Simulation of free surface flows with SPH. J Comput Phys 110:399–406

    Article  ADS  Google Scholar 

  • Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68:1703–1759

    Article  ADS  MathSciNet  Google Scholar 

  • Morris JP (1997) Modeling low Reynolds number incompressible flows using SPH. J Comput Phys 136:214–226

    Article  ADS  Google Scholar 

  • Ou J, Perot B, Rothstein P (2004) Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys Fluids 16:4635–4643

    Article  ADS  Google Scholar 

  • Podryabinkin EV, Rudyak VY (2011) Moment and forces exerted on the inner cylinder in eccentric annual flow. J Eng Thermophys 20(3):320–328

    Google Scholar 

  • Quin D, 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

    Article  Google Scholar 

  • Reid RC, Prausnitz JM, Sherwood TK (1977) The properties of gases and liquids. McGraw–Hill Company, New York

    Google Scholar 

  • Rudyak VY, Minakov AV, Gavrilov AA, Dekterev AA (2008) Application of new numerical algorithm of solving the Navier-Stokes equations for modeling the work of a viscometer of the physical pendulum type. Thermophys Aeromech 15(2):333–345

    Google Scholar 

  • Rudyak VY, Minakov AV, Gavrilov AA, Dekterev AA (2010) Modeling the flows in micromixers. Thermophys Aeromech 17(4):45–56

    Google Scholar 

  • Stroock AD, Dertinger SK, Whitesides GM, Ajdari A (2002) Patterning flows using grooved surfaces. Anal Chem 74(20):5306–5312

    Article  Google Scholar 

  • Tabeling P (2005) Introduction to mivrofluidics. Oxford University Press, Oxford

    Google Scholar 

  • Telib H, Manhart M, Iollo A (2004) Analysis and low-order modeling of the inhomogeneous transitional flow inside a T-mixer. Phys Fluids 16:2717–2731

    Article  ADS  Google Scholar 

  • Tzvetkov FF, Grigoriev BA (2005) Heat and mass transfer. MEI, Moskow

    Google Scholar 

  • Vanka SP, Luo G, Winkler CM (2004) Numerical study of scalar mixing in curved channels at low Reynolds number. AIChE J 50:2359–2368

    Article  Google Scholar 

  • Wang Y, Su T-C (1993) Computation of wave breaking on sloping beach by VOF method. In: Proceedings of the 3rd international offshore and polar engineering conference (ISOPE). Golden, CO, pp 96–101

    Google Scholar 

  • Wing TL, Rajan KM (2004) Flow measurements in microchannels using MicroPiIV system. In: Behnia M, Lin W, McBain GD (eds) Proceedings of the 15th Australasian fluid mechanics conference (CD-ROM), University of Sydney, Australia. Paper AFMC00150

    Google Scholar 

  • Wong SH, Ward MCL, Wharton CW (2004) Micro T-mixer as a rapid mixing micromixer. Sens Act B 100:359–379

    Article  Google Scholar 

  • Xu B, Wong TN, Nguyen N-T, Che Z, Chai JKC (2010) Thermal mixing of two miscible fluids in a T-shaped microchannel. Biomicrofluidics. https://doi.org/10.1063/1.3496359

  • Zaleski S, Li J, Succi S (1995) Two-dimensional Navier-Stokes simulation of deformation and breakup of liquid patches. Phys Rev Lett 75(2):244–247

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, Russian Federation

    Valery Ya. Rudyak

  2. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russian Federation

    Vladimir M. Aniskin, Anatoly A. Maslov & Sergey G. Mironov

  3. Siberian Federal University, Krasnoyarsk, Russian Federation

    Andrey V. Minakov

Authors
  1. Valery Ya. Rudyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir M. Aniskin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anatoly A. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrey V. Minakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sergey G. Mironov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valery Ya. Rudyak .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rudyak, V.Y., Aniskin, V.M., Maslov, A.A., Minakov, A.V., Mironov, S.G. (2018). Modeling of Micromixers. In: Micro- and Nanoflows. Fluid Mechanics and Its Applications, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-75523-6_4

Download citation

Publish with us

Policies and ethics

Search

Navigation