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Convective–diffusive transport in parallel lamination micromixers

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Abstract

Effective mixing and a controllable concentration gradient are important in microfluidic applications. From the scaling law, decreasing the mixing length can shorten the mixing time and enhance the mixing quality. The small sizes lead to small Reynolds numbers and a laminar flow in microfluidic devices. Under these conditions, molecular diffusion is the main transport effect during the mixing process. In this paper, we present complete 2D analytical models of convective–diffusive transport in parallel lamination micromixers for a binary system. An arbitrary mixing ratio between solute and solvent is considered. The analytical solution indicates the two important parameters for convective–diffusive transport in microchannels: the Peclet number and the dimensionless mixing length. Furthermore, the model can also be extended to the mixing of multiple streams—a common and effective concept of parallel mixing in microchannels. Using laser machining and adhesive bonding, polymeric micromixers were fabricated and tested to verify the analytical results. The experimental results agree well with the analytical models.

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References

  1. Nguyen NT, Wereley ST (2003) Fundamentals and applications of microfluidics. Artech House, Boston, Massachusetts

    Google Scholar 

  2. Kamholz AE, Weigl BH, Finlayson BA, Yager P (1999) Quantitative analysis of molecular interaction in a microfluidic channel: the T-sensor. Anal Chem 71:5340–5347

    Article  CAS  PubMed  Google Scholar 

  3. Koch M, Chatelain D, Evans AGR, Brunnschweiler A (1998) Two simple micromixers based on silicon. J Micromech Microeng 8:123–126

    Article  CAS  Google Scholar 

  4. Gobby D, Angeli P, Gavriilidis A (2001) Mixing characteristics of T-type microfluidic mixers. J Micromech Microeng 11:126–132

    Article  Google Scholar 

  5. Ehrfeld W, Golbig K, Hessel V, Löwe H, Richter T (1999) Characterization of mixing in micromixers by a test reaction: single mixing units and mixing arrays. Ind Eng Chem Res 38:1075–1082

    Article  CAS  Google Scholar 

  6. Erbacher C, Bessoth FG, Busch M, Verpoorte E, Manz A (1999) Towards integrated continuous-flow chemical reactors. Mikrochim Acta 131:19–24

    CAS  Google Scholar 

  7. Schwesinger N, Frank T, Wurmus H (1996) A modular microfluid system with an integrated micromixer. J Micromech Microeng 6:99–102

    Article  CAS  Google Scholar 

  8. Koch M, Witt H, Evans G, Brunnschweiler A (1999) Improved characterization technique for micromixers. J Micromech Microeng 9:156–158

    Article  CAS  Google Scholar 

  9. Handique K, Burns MA (2001) Mathematical modeling of drop mixing in a slit-type microchannel. J Micromech Microeng 11:548–554

    Article  CAS  Google Scholar 

  10. Miyake R, Lammerink TSJ, Elwenspoek M, Fluitman JHJ (1993) Micro mixer with fast diffusion. In: Proceedings of the 6th IEEE international workshop on micro electro mechanical systems (MEMS’93), Fort Lauderdale, Florida, February 1993, pp 248–253

  11. He B, Burke BJ, Zhang X, Zhang R, Regnier FE (2001) A picoliter-volume mixer for microfluidic analytical systems. Anal Chem 73:1942–1947

    Article  CAS  PubMed  Google Scholar 

  12. Lin Y, Gerfen GJ, Rousseau DL, Yeh SR (2003) Ultrafast microfluidic mixer and freeze-quenching device. Anal Chem 75:5381–5386

    Article  CAS  PubMed  Google Scholar 

  13. Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Aref H, Beebe DJ (2000) Passive mixing in a three-dimensional serpentine microchannel. J Microelectromech Syst 9:190–197

    Article  Google Scholar 

  14. Stroock AD, Dertinger SK, Ajdari A, Mezic I, Stone HA, Whitesides GM (2002) Chaotic mixer for microchannels. Science 295:647–650

    Article  CAS  PubMed  Google Scholar 

  15. Wang H, Iovenitti P, Harvey E, Masood S (2003) Numerical investigation of mixing in microchannels with patterned grooves. J Micromech Microeng 13:801–808

    Article  Google Scholar 

  16. Bertsch A, Heimgartner S, Cousseau P, Renaud P (2001) Static micromixers based on large-scale industrial mixer geometry. Lab Chip 1:56–60

    Article  CAS  PubMed  Google Scholar 

  17. Park SJ, Kim JK, Park J, Chung S, Chung C, Chang JK (2004) Rapid three-dimensional passive rotation micromixer using the breakup process. J Micromech Microeng 14:6–14

    Article  Google Scholar 

  18. Evans J, Liepmann D, Pisano AP (1997) Planar laminar mixer. In: Proceeding of the 10th IEEE international workshop on micro electro mechanical systems (MEMS’97), Nagoya, Japan, January 1997, pp 96–101

  19. Liu H, Lenigk R, Druyor-Sanchez RL, Yang J, Grodzinski P (2003) Hybridization enhancement using cavitation microstreaming. Anal Chem 75:1911–1917

    Article  CAS  PubMed  Google Scholar 

  20. Yang Z, Goto H, Matsumoto M, Maeda R (2001) Ultrasonic micromixer for microfluidic systems. Sensor Actuat A–Phys 93:266–272

    Article  Google Scholar 

  21. Oddy MH, Santiago JG, Mikkelsen JC (2001) Electrokinetic instability micromixing. Anal Chem 73:5822–5832

    Article  CAS  PubMed  Google Scholar 

  22. Bao HH, Zhong J, Yi M (2001) A minute magneto hydro dynamic (MHD) mixer. Sensor Actuat B–Chem 79:207–215

    Article  Google Scholar 

  23. Lu LH, Ryu K, Liu C (2002) A magnetic microstirrer and array for microfluidic mixing. J Microelectromech Syst 11:462–469

    Article  CAS  Google Scholar 

  24. Tsai JH, Lin L (2002) Active microfluidic mixer and gas bubble filter driven by thermal bubble micropump. Sensor Actuat A–Phys 97–98:665–671

    Article  Google Scholar 

  25. Ismagilov RF, Stroock AD, Kenis PJA, Whitesides G, Stone HA (2000) Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels. Appl Phys Lett 76:2376–2378

    Article  CAS  Google Scholar 

  26. Kamholz AE, Yager P (2002) Molecular diffusive scaling laws in pressure-driven microfluidic channels: deviation from one-dimensional Einstein approximations. Sensor Actuat B–Chem 82:117–121

    Article  Google Scholar 

  27. Brenner H, Edwards DA (1993) Macrotransport processes. Butterworth-Heinemann, Boston, Massachusetts

    Google Scholar 

  28. Berad DA (2001) Taylor dispersion of a solute in a microfluidic channel. J Appl Phys 89:4467–4469

    Google Scholar 

  29. Dorfman KD, Brenner H (2001) Comment on “Taylor dispersion of a solute in a microfluidic channel.” J Appl Phys 90:6553–6554

    Article  CAS  Google Scholar 

  30. Beard DA (2001) Response to “Comment on “Taylor dispersion of a solute in a microfluidic channel” [J Appl Phys 90:6553]”. J Appl Phys 90:6555–6556

    Article  CAS  Google Scholar 

  31. Holden MA, Kumar S, Castellana E, Beskok A, Cremer PS (2003) Generating fixed concentration arrays in a microfluidic device. Sensor Actuat B–Chem 92:199–207

    Article  Google Scholar 

  32. Cussler EL (1984) Diffusion: mass transfer in fluid systems. Cambridge University Press, New York

    Google Scholar 

  33. Wu ZG, Nguyen NT, Huang XY (2004) Nonlinear diffusive mixing in microchannels: theory and experiments. J Micromech Microeng 14:604–611

    Article  CAS  Google Scholar 

  34. Galambos P, Forster F (1998) An optical micro-fluidic viscometer. In: Proceedings of the ASME international mechanical engineering congress and exposition, Anaheim, California, November 1988, pp 187–191

  35. Stiles PJ, Fletcher DF (2004) Hydrodynamic control of the interface between two liquids flowing through a horizontal or vertical microchannel. Lab Chip 4:121–124

    Article  CAS  PubMed  Google Scholar 

  36. Gaskell DR (1995) Introduction to thermodynamics of materials, 3rd edn. Taylor and Francis, London

    Google Scholar 

  37. Bassi FA, Arcovito G, D’Abramo G (1977) An improved optical method of obtaining the mutual diffusion coefficient from the refractive index gradient profile. J Phys E Sci Instrum 10:249–253

    Article  CAS  Google Scholar 

  38. Timmermans J (1960) The physio-chemical constants of binary systems in concentrated solution. Interscience, New York

    Google Scholar 

  39. Einstein A (1956) Investigation on the theory of the Brownian movement. Dover, New York

    Google Scholar 

Download references

Acknowledgements

This work was supported by the academic research fund of the Ministry of Education Singapore, contract number RG11/02. The first author wishes to gratefully acknowledge the PhD scholarship from Nanyang Technological University.

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  1. School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore

    Zhigang Wu & Nam-Trung Nguyen

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  1. Zhigang Wu
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  2. Nam-Trung Nguyen
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Correspondence to Nam-Trung Nguyen.

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Wu, Z., Nguyen, NT. Convective–diffusive transport in parallel lamination micromixers. Microfluid Nanofluid 1, 208–217 (2005). https://doi.org/10.1007/s10404-004-0011-x

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  • DOI: https://doi.org/10.1007/s10404-004-0011-x

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