Microfluidics and Nanofluidics

, Volume 5, Issue 4, pp 493–505 | Cite as

Microfluidic mixing via transverse electrokinetic effects in a planar microchannel

  • N. Scott Lynn
  • Charles S. Henry
  • David S. Dandy
Research Paper

Abstract

A new micromixer incorporating integrated electrodes deposited on the bottom surface of a glass/PDMS microchannel is used to induce a localized, perpendicular electric field within pressure driven axial flow. The presence of the electric field drives electro-osmotic flow in the transverse direction along the channel walls, creating helical motion that serves to mix the fluid. A numerical model is used to describe the three-dimensional flow field, where characterization is performed via particle tracking of passive tracer particles, and the conditional entropy (Slc) is utilized to approximate the extent of mixing along cross-sectional planes. The geometrical parameters and operating conditions of the numerical model are used to fabricate an experimental device, and fluorescence microscopy measurements are used to verify mixing of rhodamine B across the width of the microchannel for a wide range of fluid flow rates. The results demonstrate that under certain operating conditions and selective placement of the electrode gaps along the width of the microchannel, efficient mixing can be achieved within 6 mm of the inlet.

Keywords

Micro-mixing Electro-osmosis Integrated electrodes PDMS 

List of symbols

Lmix

characteristic length for mixing

Tmix

characteristic time for mixing

ϕ

externally applied potential

λd

debye length

ε

dielectric constant of the fluid

εo

permittivity of vacuum

ζ

zeta-potential

\( \ifmmode\expandafter\vec\else\expandafter\vec\fi{E} \)

electric field vector

p

pressure

μ

viscosity

\( \ifmmode\expandafter\vec\else\expandafter\vec\fi{u} \)

linear velocity

φ

stream function

le

axial length of the electrode

wg

width of the electrode gap

wc

center position of the electrode gap

tcomp

computational time for particle advection

tn

average computational time for advection between planes

Slc

conditional mixing entropy

pj

probability that a particle is in bin j irrespective of species

pc,j

probability that a particle is of the type c whose position is in bin j

δa

adjusted extent of mixing

Ii

fluorescent intensity at pixel i during active mixing

Ii,o

fluorescent intensity at pixel i if no active mixing occurs

N

total number of pixels across the width of the micro-channel

w

width of micro-channel

h

height of micro-channel

n

total number of electrode cycles

F

mixing effectiveness

M

number of bins used to discretize channel cross-sections

wb

width of bin

li

axial position at the start of the i-th electrode cycle

References

  1. Altas I, Dym J, Gupta MM, Manohar RP (1998) Multigrid solution of automatically generated high-order discretizations for the biharmonic equation. SIAM J Sci Comput 19:1575–1585MATHCrossRefMathSciNetGoogle Scholar
  2. Anderson JL (1989) Colloid Transport by Interfacial Forces. Annu Rev Fluid Mech 21:61–99CrossRefGoogle Scholar
  3. Bhattacharya S, Datta A, Berg JM, Gangopadhyay S (2005) Studies on surface wettability of poly(dimethyl) siloxane (PDMS) and glass under oxygen-plasma treatment and correlation with bond strength. J Microelectromech Syst 14:590–597CrossRefGoogle Scholar
  4. Biddiss E, Erickson D, Li DQ (2004) Heterogeneous surface charge enhanced micromixing for electrokinetic flows. Anal Chem 76:3208–3213CrossRefGoogle Scholar
  5. Camesasca M, Manas-Zloczower I, Kaufman M (2005) Entropic characterization of mixing in microchannels. J Micromech Microeng 15:2038–2044CrossRefGoogle Scholar
  6. Camesasca M, Kaufman M, Manas-Zloczower I (2006) Quantifying fluid mixing with the Shannon entropy. Macromol Theory Simul 15:595–607CrossRefGoogle Scholar
  7. Cha J, Kim J, Ryu SK, Park J, Jeong Y, Park S, Park S, Kim HC, Chun K (2006) A highly efficient 3D micromixer using soft PDMS bonding. J Micromech Microeng 16:1778–1782CrossRefGoogle Scholar
  8. Chang CC, Yang RJ (2004) Computational analysis of electrokinetically driven flow mixing in microchannels with patterned blocks. J Micromech Microeng 14:550–558CrossRefGoogle Scholar
  9. Chang CC, Yang RJ (2006) A particle tracking method for analyzing chaotic electroosmotic flow mixing in 3D microchannels with patterned charged surfaces. J Micromech Microeng 16:1453–1462CrossRefGoogle Scholar
  10. Chang CC, Yang RJ (2007) Electrokinetic mixing in microfluidic systems. Microfluidics Nanofluidics 3:501–525CrossRefMathSciNetGoogle Scholar
  11. Chen H, Meiners JC (2004) Topologic mixing on a microfluidic chip. Appl Phys Lett 84:2193–2195CrossRefGoogle Scholar
  12. Dodge A, Jullien MC, Lee YK, Niu X, Okkels F, Tabeling P (2004) An example of a chaotic micromixer: the cross-channel micromixer. C R Phys 5:557–563CrossRefGoogle Scholar
  13. Gitlin I, Stroock AD, Whitesides GM, Ajdari A (2003) Pumping based on transverse electrokinetic effects. Appl Phys Lett 83:1486–1488CrossRefGoogle Scholar
  14. Hunter RJ (1981) Zeta potential in colloid science. Academic Press, New YorkGoogle Scholar
  15. Jiang F, Drese KS, Hardt S, Kupper M, Schonfeld F (2004) Helical flows and chaotic mixing in curved micro channels. Aiche J 50:2297–2305CrossRefGoogle Scholar
  16. Johnson TJ, Locascio LE (2002) Characterization and optimization of slanted well designs for microfluidic mixing under electroosmotic flow. Lab Chip 2:135–140CrossRefGoogle Scholar
  17. Kim DS, Lee SW, Kwon TH, Lee SS (2004) A barrier embedded chaotic micromixer. J Micromech Microeng 14:798–805CrossRefGoogle Scholar
  18. Lammertink RGH, Schlautmann S, Besselink GAJ, Schasfoort RBM (2004) Recirculation of nanoliter volumes within microfluidic channels. Anal Chem 76:3018–3022CrossRefGoogle Scholar
  19. Lee JN, Park C, Whitesides GM (2003) Solvent compatibility of poly(dimethylsiloxane)-based microfluidic devices. Anal Chem 75:6544–6554CrossRefGoogle Scholar
  20. Lee CY, Lee GB, Fu LM, Lee KH, Yang RJ (2004) Electrokinetically driven active micro-mixers utilizing zeta potential variation induced by field effect. J Micromech Microeng 14:1390–1398CrossRefGoogle Scholar
  21. Leu TS, Ma FC (2005) Novel EHD-pump driven micro mixers. J Mech 21:137–144Google Scholar
  22. Lin H, Storey BD, Oddy MH, Chen CH, Santiago JG (2004) Instability of electrokinetic microchannel flows with conductivity gradients. Phys Fluids 16:1922–1935CrossRefGoogle Scholar
  23. Lin JL, Lee KH, Lee GB (2005) Active mixing inside microchannels utilizing dynamic variation of gradient zeta potentials. Electrophoresis 26:4605–4615CrossRefGoogle Scholar
  24. McKnight TE, Culbertson CT, Jacobson SC, Ramsey JM (2001) Electroosmotically induced hydraulic pumping with integrated electrodes on microfluidic devices. Anal Chem 73:4045–4049CrossRefGoogle Scholar
  25. Meleshko VV (1998) Biharmonic problem in a rectangle. Appl Sci Res 58:217–249MATHCrossRefMathSciNetGoogle Scholar
  26. Munson MS, Yager P (2004) Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer. Analytica Chimica Acta 507:63–71CrossRefGoogle Scholar
  27. Neils C, Tyree Z, Finlayson B, Folch A (2004) Combinatorial mixing of microfluidic streams. Lab Chip 4:342–350CrossRefGoogle Scholar
  28. Niu XZ, Lee YK (2003) Efficient spatial-temporal chaotic mixing in microchannels. J Micromech Microeng 13:454–462CrossRefGoogle Scholar
  29. Niu XZ, Liu LY, Wen WJ and Sheng P (2006) Hybrid approach to high-frequency microfluidic mixing. Phys Rev Lett 97Google Scholar
  30. Oddy MH, Santiago JG, Mikkelsen JC (2001) Electrokinetic instability micromixing. Anal Chem 73:5822–5832CrossRefGoogle Scholar
  31. Pacheco JR, Chen KP, Hayes MA (2006) Rapid and efficient mixing in a slip-driven three-dimensional flow in a rectangular channel. Fluid Dyn Res 38:503–521MATHCrossRefGoogle Scholar
  32. Park J, Shin SM, Huh KY and Kang IS (2005) Application of electrokinetic instability for enhanced mixing in various micro-T-channel geometries. Phys Fluids 17Google Scholar
  33. Qian SZ, Bau HH (2002) A chaotic electroosmotic stirrer. Anal Chem 74:3616–3625CrossRefGoogle Scholar
  34. Qian SZ, Bau HH (2005) Theoretical investigation of electro-osmotic flows and chaotic stirring in rectangular cavities. Appl Math Model 29:726–753MATHCrossRefGoogle Scholar
  35. Sato H, Ito S, Tajima K, Orimoto N, Shoji S (2005) PDMS microchannels with slanted grooves embedded in three walls to realize efficient spiral flow. Sens Actuators A Phys 119:365–371CrossRefGoogle Scholar
  36. Schonfeld F, Hardt S (2004) Simulation of helical flows in microchannels. Aiche J 50:771–778CrossRefGoogle Scholar
  37. Selverov KP, Stone HA (2001) Peristaltically driven channel flows with applications toward micromixing. Physics of Fluids 13:1837–1859CrossRefGoogle Scholar
  38. Stone ZB, Stone HA (2005) Imaging and quantifying mixing in a model droplet micromixer. Phys Fluids 17Google Scholar
  39. Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:381–411CrossRefGoogle Scholar
  40. Stroock AD, Dertinger SK, Whitesides GM, Ajdari A (2002a) Patterning flows using grooved surfaces. Anal Chem 74:5306–5312CrossRefGoogle Scholar
  41. Stroock AD, Dertinger SKW, Ajdari A, Mezic I, Stone HA, Whitesides GM (2002b) Chaotic mixer for microchannels. Science 295:647–651CrossRefGoogle Scholar
  42. Sundaram N, Tafti DK (2004) Evaluation of microchamber geometries and surface conditions for electrokinetic driven mixing. Anal Chem 76:3785–3793CrossRefGoogle Scholar
  43. Sudarsan AP, Ugaz VM (2006) Fluid mixing in planar spiral microchannels. Lab Chip 6:74–82CrossRefGoogle Scholar
  44. Suzuki H, Ho CM, Kasagi N (2004) A chaotic mixer for magnetic bead-based micro cell sorter. J Microelectromech Syst 13:779–790CrossRefGoogle Scholar
  45. Sze A, Erickson D, Ren LQ, Li DQ (2003) Zeta-potential measurement using the Smoluchowski equation and the slope of the current-time relationship in electroosmotic flow. J Colloid Interface Sci 261:402–410CrossRefGoogle Scholar
  46. Therriault D, White SR, Lewis JA (2003) Chaotic mixing in three-dimensioned microvascular networks fabricated by direct-write assembly (vol 2, pg 265, 2002). Nat Mater 2:347–347CrossRefGoogle Scholar
  47. Vickers JA, Caulum MM, Henry CS (2006) Generation of hydrophilic poly(dimethylsiloxane) for high-performance microchip electrophoresis. Anal Chem 78:7446–7452CrossRefGoogle Scholar
  48. West J, Gleeson JP, Alderman J, Collins JK, Berney H (2003) Structuring laminar flows using annular magnetohydrodynamic actuation. Sens Actuators B Chem 96:190–199CrossRefGoogle Scholar
  49. Wu HY, Liu CH (2005) A novel electrokinetic micromixer. Sens Actuators A Phys 118:107–115CrossRefGoogle Scholar
  50. Xia YN, Whitesides GM (1998) Soft lithography. Annu Rev Mater Sci 28:153–184CrossRefGoogle Scholar
  51. Yamaguchi Y, Takagi F, Watari T, Yamashita K, Nakamura H, Shimizu H, Maeda H (2004a) Interface configuration of the two layered laminar flow in a curved microchannel. Chem Eng J 101:367–372CrossRefGoogle Scholar
  52. Yamaguchi Y, Takagi F, Yamashita K, Nakamura H, Maeda H, Sotowa K, Kusakabe K, Yamasaki Y, Morooka S (2004b) 3-D simulation and visualization of laminar flow in a microchannel with hair-pin curves. Aiche J 50:1530–1535CrossRefGoogle Scholar
  53. Yang JT, Huang KJ, Lin YC (2005) Geometric effects on fluid mixing in passive grooved micromixers. Lab Chip 5:1140–1147CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • N. Scott Lynn
    • 1
  • Charles S. Henry
    • 2
  • David S. Dandy
    • 1
  1. 1.Department of Chemical and Biological EngineeringColorado State UniversityFort CollinsUSA
  2. 2.Department of ChemistryColorado State UniversityFort CollinsUSA

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