Chaotic Mixer for Microchannels
10.1126/science.1066238
Crossref journal-article
American Association for the Advancement of Science (AAAS)
Science (221)
Abstract

It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar—the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Péclet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.

Bibliography

Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezić, I., Stone, H. A., & Whitesides, G. M. (2002). Chaotic Mixer for Microchannels. Science, 295(5555), 647–651.

Authors 6
  1. Abraham D. Stroock (first)
  2. Stephan K. W. Dertinger (additional)
  3. Armand Ajdari (additional)
  4. Igor Mezić (additional)
  5. Howard A. Stone (additional)
  6. George M. Whitesides (additional)
References 30 Referenced 2,864
  1. 10.1126/science.282.5388.484
  2. 10.1073/pnas.96.1.11
  3. Dunn D. A., Feygin I., Drug Discovery Today 5, S84 (2000). (10.1016/S1359-6446(00)00064-7) / Drug Discovery Today by Dunn D. A. (2000)
  4. Losey M. W., Schmidt M. A., Jensen K. F., Ind. Eng. Chem. Res. 40, 2555 (2001). (10.1021/ie000523f) / Ind. Eng. Chem. Res. by Losey M. W. (2001)
  5. 10.1002/aic.690450215
  6. This condition is based on the following characteristic values: U < 100 cm/s l ∼ 0.01 cm ν = 0.01 g/cm·s. For channels l is typically taken to be the smallest cross-sectional dimension.
  7. Poiseuille flows are pressure-driven flows in channels and capillaries. Dispersion refers to the distribution of material by convection in flows in which the velocity is spatially nonuniform. In Poiseuille flows the speed varies from zero at the walls of the channel to its maximum value in the center. A band of miscible material that spans the cross section of the flow will be dispersed along the direction of the flow as the portions of the band near the center of the channel outpace those near the walls.
  8. Jones S. W., Young W. R., J. Fluid Mech. 280, 149 (1994). (10.1017/S0022112094002880) / J. Fluid Mech. by Jones S. W. (1994)
  9. The Péclet number Pe is a measure of the relative rate of convective transport to diffusive transport in a flow. Mixing becomes more difficult as Pe becomes larger. Typical numbers are as follows: U > 0.1 cm/s l ∼ 0.01 cm D < 10 −5 cm 2 /s.
  10. To estimate the mixing length we first estimate the time required for diffusion across the channel as l 2 / D then we multiply this time by the average flow speed.
  11. Jones S. W., Thomas O. M., Aref H., J. Fluid Mech. 209, 335 (1989). (10.1017/S0022112089003137) / J. Fluid Mech. by Jones S. W. (1989)
  12. J. M. Ottino The Kinematics of Mixing: Stretching Chaos and Transport (Cambridge Univ. Press Cambridge 1989).
  13. At high Péclet numbers we estimate the mixing length in a stirred flow by equating the residence time τ r = Δ y / U and the time for diffusion to act over the reduced width of the unmixed volumes τ D = Δ r 2 / D = ( l 2 / D )exp(−2Δ y /λ). We find that ln(Δ y m / l ) + 2Δ y m /λ ∼ ln( Pe ) or for large values of Pe Δ y m ∼ λln( Pe ). For flows that are nonchaotically stirred we expect a power-law dependence of Δ y m on Pe.
  14. Liu R. H., et al., J. Microelectromech. Syst. 9, 190 (2000). (10.1109/84.846699) / J. Microelectromech. Syst. by Liu R. H. (2000)
  15. M. Volpert I. Mezić C. D. Meinhart M. Dahleh Proceedings of the First International Conference on Heat Transfer Fluid Mechanics and Thermodynamics Kruger Park South Africa 2001.
  16. We made the master structures with two-step photolithography in SU-8 photoresist: The first layer of photolithography defined the channel structure; the second layer defined the pattern of ridges. The pattern of ridges was aligned to lie on top of the channel structure in the first layer. We measured the dimensions of the channel and the ridges using a profilometer. We made molds of the structure in PDMS. To close the channel we exposed the PDMS to a plasma for 1 min and sealed it to a glass cover slip.
  17. 10.1002/(SICI)1522-2683(20000101)21:1<27::AID-ELPS27>3.0.CO;2-C
  18. This difference in resistance can be understood as follows: For laminar flows the height of the channel determines the resistance to flow in the channel so in analogy to electronic circuits flowing over the ridges is like running current through resistors in series (higher total resistance) and flowing along the ridges is like running current through resistors in parallel (lower total resistance).
  19. A. Ajdari preprint Cond. Mat. 0101438; Phys. Rev. E 65 016301 (2002). (10.1103/PhysRevE.65.016301)
  20. dΔφdy = α 2 f ( q h w θ) with f ( q h w θ) =  34 qh 4qh−sinh(2qh)−2(qh)2 coth(qh)sinh2(qh)−(qh)2 sin θ cos θ π(h+w).  This equation is derived from the ratio of the typical transverse and axial flow speeds in an approximate-model Stokes flow for sinusoidal grooves that is valid for α « 1 and w » h. The maximum transverse flow is achieved for θ = 45° and α qh ∼ 2. A similar anisotropy is predicted for electroosmotic flows in channels with this geomtery. The details of this calculation will appear elsewhere.Such a sequence of manipulations leads to a baker's transformation of the volumes of fluid that are involved. See (12) for a more details.
  21. These parameters could equally well be defined with respect to the narrow side of the herringbone structure.
  22. We have evaluated the extent of the chaotic region in the cross section by numerically integrating an approximate two-dimensional representation of the transverse flow to generate a Poincaré map. The map is dense (no islands) everywhere in the cross section except in a narrow band (<10% of height) at the top of the channel. We have not systematically optimized the design of the mixer with respect to these Δφ m and p values.
  23. We qualify the mixing as thorough when the fluorescence appears uniform to within the resolution (∼2 μm) and sensitivity (down to variations of ∼5% of the maximum intensity) of our microscope.
  24. R. F. Probstein Physicochemical Hydrodynamics (Butterworths Boston 1989).
  25. Mezić I., Brady J. F., Wiggins S., SIAM J. Appl. Math. 56, 40 (1996). (10.1137/S0036139994270449) / SIAM J. Appl. Math. by Mezić I. (1996)
  26. Recent experimental results confirm that ridges in the floor of a channel do generate transverse components in electroosmotic flows (28).
  27. T. J. Johnson D. Ross L. E. Locascio Anal. Chem. 10.1021/ac010895d.
  28. We drove flow in the channels by applying a constant pressure at the inlet reservoir with compressed air. We imaged the evolution of fluorescent streams in the channels using a Leica TCS confocal microscope with a 40×/1.0 numerical aperture objective.
  29. Labeled polymers were prepared by allowing poly(ethylenimine) (molecular weight ∼500 000) to react with fluorocein isothiocyanate. The product was dialyzed for several days. Diffusivities were calculated based on the broadening of fluorescent streams of the dye in confocal images flows of known speed: D = 4 × 10 −6 cm 2 /s in water and D = 2 × 10 −8 cm 2 /s in 80% glycerol/20% water. Flow speeds were measured by weighing the fluid collected at the outlet of the channel. Viscosity of the glycerol/water solution was estimated to be 0.67 g/cm·s by comparing the flow rate to that of water through the same channel with the same applied pressure.
  30. Supported by Defense Advanced Research Projects Agency grants NSF ECS-9729405 and NSF DMR-9809363 Materials Research Science and Engineering Center (A.D.S. S.K.W.D. H.A.S. and G.M.W.); NIH grant GM51559 (A.D.S. S.K.W.D and G.M.W.); Army Research Office grant DAAG55-97-1-0114 (H.A.S.); and NSF-9875933 NSF DMS-9803555 and a Sloan Foundation Fellowship (I.M.). S.K.W.D. thanks the Deutsche Forschungsgemeinschaft for a research fellowship.
Dates
Type When
Created 23 years, 1 month ago (July 27, 2002, 5:47 a.m.)
Deposited 1 year, 7 months ago (Jan. 9, 2024, 6:06 p.m.)
Indexed 12 hours, 55 minutes ago (Aug. 31, 2025, 6:19 a.m.)
Issued 23 years, 7 months ago (Jan. 25, 2002)
Published 23 years, 7 months ago (Jan. 25, 2002)
Published Print 23 years, 7 months ago (Jan. 25, 2002)
Funders 0

None

@article{Stroock_2002, title={Chaotic Mixer for Microchannels}, volume={295}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1066238}, DOI={10.1126/science.1066238}, number={5555}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Stroock, Abraham D. and Dertinger, Stephan K. W. and Ajdari, Armand and Mezić, Igor and Stone, Howard A. and Whitesides, George M.}, year={2002}, month=jan, pages={647–651} }