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Enhancement of mixing and adsorption in microfluidic devices by shear-induced diffusion and topography-induced secondary flow

Phys. Fluids 20, 053304 (2008); doi:10.1063/1.2912136

Published 7 May 2008

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Mauricio Lopez and Michael D. Graham
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA
Continuum simulations are used to assess the effects of shear-induced diffusion and secondary flow kinematics on the enhancement of mixing and adsorption during flow of suspensions in microfluidic channels. Unidirectional flow in rectangular channels is considered, as well as flow in channels with a topographically patterned wall that generates transverse flow. Patterns that lead both to chaotic and nonchaotic kinematics are considered. Effects of shear-induced diffusion due to the presence of suspended particles are incorporated via an empirical shear-rate dependent diffusivity. It is observed that for the bulk mixing case the most significant enhancement is due to convection. Channels with chaotic flow have the best mixing characteristics, followed by channels with swirling, nonchaotic flow. Only a small increase in mixing due to shear-induced diffusion is observed. For the case of adsorption from the bulk to a channel wall, on the other hand, it is observed that the most significant enhancement is due to shear-induced diffusion. Channels with secondary flows, both chaotic and nonchaotic, circulate solute-depleted fluid away from the adsorbing boundary but this is not sufficient to guarantee high fluxes toward the surface when the diffusivities are small. The most effective way to enhance adsorption is through the combination of both secondary flow and shear-induced diffusion. Secondary flow circulates fluid between bulk and boundary layer, while shear-induced diffusion enhances transport across the boundary layer. Nevertheless, under the large Peclet number conditions considered here, only a maximum of 30% of the solute is adsorbed to the surface for channels with length of 300 channel heights; for smooth channels without shear-induced diffusion this fraction is only 3%. ©2008 American Institute of Physics
History: Received 21 December 2007; accepted 24 March 2008; published 7 May 2008
Permalink: http://link.aip.org/link/?PHFLE6/20/053304/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.61.Fg
    Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
  • 47.85.Np
    Fluidics (applied)
  • 47.61.Ne
    Micromixing (flow phenomena)
  • 47.61.Jd
    Micro- and nano-scale multiphase flows
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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AIP is a member of CrossRef AIP

REFERENCES (66)
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  1. R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesides, and H. A. Stone, “Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels,” Appl. Phys. Lett. 76, 2376 (2000).
  2. A. E. Kamholz and P. Yager, “Theoretical analysis of molecular diffusion in pressure-driven laminar flow in microfluidic channels,” Biophys. J. 80, 155 (2001).
  3. A. E. Kamholz, E. A. Shilling, and P. Yager, “Optical measurement of transverse molecular diffusion in a microchannel,” Biophys. J. 80, 1967 (2001).
  4. J. Oak, D. V. Pence, and J. A. Liburdy, “Diffusion and flow development in co-flowing microchannel streams,” Microscale Thermophys. Eng. 5, 233 (2001).
  5. D. Gobby, P. Angeli, and A. Gavriilidis, “Mixing characteristics of T-type microfluidic mixers,” J. Micromech. Microeng. 11, 126 (2001).
  6. A. E. Kamholz and P. Yager, “Molecular diffusive scaling laws in pressure-driven microfluidic channels: deviation from one-dimensional Einstein approximations,” Sens. Actuators B 82, 117 (2002).
  7. J. M. MacInnes, X. Du, and R. W. K. Allen, “Prediction of electrokinetic and pressure flow in a microchannel T-junction,” Phys. Fluids 15, 1992 (2003).
  8. A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. Stone, and G. Whitesides, “Chaotic mixer for microchannels,” Science 295, 647 (2002).
  9. T. J. Johnson, D. Ross, and L. E. Locascio, “Rapid microfluidic mixing,” Anal. Chem. 74, 45 (2002).
  10. P. B. Howell, D. R. Mott, S. Fertig, C. R. Kaplan, J. P. Golden, E. S. Oran, and F. S. Ligler, “A microfluidic mixer with grooves placed on the top and bottom of the channel,” Lab Chip 5, 524 (2005).
  11. J. Ou, G. R. Moss, and J. P. Rothstein, “Enhanced mixing in laminar flows using ultrahydrophobic surfaces,” Phys. Rev. E 76, 016304 (2007).
  12. J. Kirtland, G. McGraw, and A. Stroock, “Mass transfer to reactive boundaries from steady three-dimensional flows in microchannels,” Phys. Fluids 18, 073602 (2006).
  13. H. A. Stone, A. D. Stroock, and A. Ajdari, “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid Mech. 36, 381 (2004).
  14. P. A. Auroux, D. Iossifidis, D. R. Reyes, and A. Manz, “Micro total analysis systems. 2. Analytical standard operations and applications,” Anal. Chem. 74, 2637 (2002).
  15. T. Vilkner, D. Janasek, and A. Manz, “Micro total analysis systems. Recent developments,” Anal. Chem. 76, 3373 (2004).
  16. M. Kakuta, F. G. Bessoth, and A. Manz, “Microfabricated devices for fluid mixing and their application for chemical synthesis,” Chem. Rec. 1, 395 (2001).
  17. M. A. Stremler, F. R. Haselton, and H. Aref, “Designing for chaos: Applications of chaotic advection at the microscale,” Philos. Trans. R. Soc. London, Ser. A 362, 1019 (2004).
  18. N. T. Nguyen and Z. Wu, “Micromixers—a review,” J. Micromech. Microeng. 15, R1 (2005).
  19. S. Wiggins and J. M. Ottino, “Foundations of chaotic mixing,” Philos. Trans. R. Soc. London, Ser. A 362, 937 (2004).
  20. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, 1989).
  21. J. Thiffeault, “Stretching and curvature of material lines in chaotic flows,” Physica D 198, 169 (2004).
  22. R. H. Liu, M. A. Tremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref, and D. Beebe, “Passive mixing in a three-dimensional serpentine microchannel,” J. Microelectromech. Syst. 9, 190 (2000).
  23. H. Chen and J. C. Meiners, “Topological mixing on a microfluidic chip,” Appl. Phys. Lett. 84, 2193 (2004).
  24. A. P. Sudarsan and V. M. Ugaz, “Fluid mixing in planar spiral microchannels,” Lab Chip 6, 74 (2006).
  25. A. Stroock and G. McGraw, “Investigation of the staggered herringbone mixer with a simple analytical method,” Philos. Trans. R. Soc. London, Ser. A 362, 971 (2004).
  26. T. J. Johnson and L. E. Locascio, “Characterization and optimization of slanted wall designs for microfluidic mixing under electroosmotic flow,” Lab Chip 2, 135 (2002).
  27. J. Aubin, D. Fletcher, and C. Xuereb, “Design of micromixers using CFD modelling,” Chem. Eng. Sci. 60, 2503 (2005).
  28. R. Glaser, “Antigen-antibody binding and mass transport by convection and diffusion to a surface: A two-dimensional computer model of binding and dissociation kinetics,” Anal. Biochem. 213, 152 (1993).
  29. D. G. Myszka, X. He, M. Dembo, T. A. Morton, and B. Goldstein, “Extending the range of rate constants available from BIACORE: Interpreting mass transport influenced binding data,” Biophys. J. 75, 583 (1998).
  30. S. Sjolander and C. Urbaniczky, “Integrated fluid handling system for biomolecular interaction analysis,” Anal. Chem. 63, 2338 (1991).
  31. M. Abrantes, M. T. Magone, L. F. Boyd, and P. Schuck, “Adaptation of a surface plasmon resonance biosensor with microfluidics for use with small sample volumes and long contact times,” Anal. Chem. 73, 2828 (2001).
  32. T. Gervais and K. Jensen, “Mass transport and surface reactions in microfluidic systems,” Chem. Eng. Sci. 61, 1102 (2006).
  33. O. Hofman, G. Voirin, P. Niedermann, and A. Manz, “Three-dimensional microfluidic confinement for efficient sample delivery to biosensor surfaces. Application to immunoassays on planar optical waveguides,” Anal. Chem. 74, 5243 (2002).
  34. R. A. Vijayendran, K. M. Motsegood, D. J. Beebe, and D. E. Leckband, “Evaluation of a three-dimensional micromixer in a surface-based biosensor,” Langmuir 19, 1824 (2003).
  35. S. K. Yoon, G. W. Fichtl, and P. J. A. Kenis, “Active control of the depletion boundary layers in microfluidic electrochemical reactors,” Lab Chip 6, 1516 (2006).
  36. D. L. Koch, “On hydrodynamic diffusion and drift in sheared suspensions,” Phys. Fluids A 1, 1742 (1989).
  37. V. Breedveld, D. van den Ende, A. Tripathi, and A. Acrivos, “The measurement of the shear-induced particle and fluid tracer diffusivities in concentrated suspensions by a novel method,” J. Fluid Mech. 375, 297 (1998).
  38. A. Acrivos, G. K. Batchelor, E. J. Hinch, D. L. Koch, and R. Mauri, “Longitudinal shear-induced diffusion of spheres in a dilute suspension,” J. Fluid Mech. 240, 651 (1992).
  39. I. E. Zarraga and D. T. Leighton, “Normal stress and diffusion in a dilute suspension of hard spheres undergoing shear flow,” Phys. Fluids 13, 565 (2001).
  40. S. Zeng, E. T. Kerns, and R. H. Davis, “The nature of particle contacts in sedimentation,” Phys. Fluids 8, 1389 (1996).
  41. Y. Wang, R. Mauri, and A. Acrivos, “The transverse shear-induced liquid and particle diffusivities of a dilute suspension of spheres undergoing a simple shear flow,” J. Fluid Mech. 327, 255 (1996).
  42. L. Durlofsky, J. F. Brady, and G. Bossis, “Dynamic simulation of hydrodynamically interacting particles,” J. Fluid Mech. 180, 21 (1987).
  43. M. Marchioro and A. Acrivos, “Shear-induced particle diffusivities from numerical simulations,” J. Fluid Mech. 443, 101 (2001).
  44. D. Drazer, J. Koplik, B. Khusid, and A. Acrivos, “Deterministic and stochastic behavior of non-Brownian spheres in sheared suspensions,” J. Fluid Mech. 460, 307 (2002).
  45. A. Sierou and J. F. Brady, “Shear-induced self-diffusion in non-colloidal suspensions,” J. Fluid Mech. 506, 285 (2004).
  46. E. Eckstein, D. Bayley, and A. Shapiro, “Self diffusion of particles in shear flow of a suspension,” J. Fluid Mech. 79, 191 (1977).
  47. D. T. Leighton and A. Acrivos, “Measurement of shear-induced self-diffusion in concentrated suspensions of spheres,” J. Fluid Mech. 177, 109 (1987).
  48. A. Nadim, “The Measurement of shear-induced diffusion in concentrated suspensions with a Couette Device,” Phys. Fluids 31, 2781 (1988).
  49. S. I. Madanshetty, A. Nadim, and H. A. Stone, “Experimental measurements of shear-induced diffusion in suspensions using long time data,” Phys. Fluids 8, 2011 (1996).
  50. M. Hoppenbrouwers and W. van de Water, “Dynamic light scattering in shear flow,” Phys. Fluids 10, 2128 (1998).
  51. V. Breedveld, D. van den Ende, M. Bosscher, R. J. J. Jongschaap, and J. Mellema, “Measuring shear-induced self-diffusion in a counterrotating geometry,” Phys. Rev. E 63, 021403 (2001).
  52. V. Breedveld, “Shear-induced self-diffusion in concentrated suspensions,” Ph.D. thesis, University of Twente, Enshede, 2000.
  53. I. E. Zarraga and D. T. Leighton, “Measuring of an unexpectedly large shear-induced self-diffusivity in a dilute suspension of spheres,” Phys. Fluids 14, 2194 (2002).
  54. M. Zurita-Gotor, J. Blawzdziewicz, and E. Wajnryb, “Swapping trajectories: A new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres,” J. Fluid Mech. 592, 447 (2007).
  55. M. Rahnama, D. L. Koch, Y. Iso, and C. Cohen, “Hydrodynamic, translational diffusion in fiber suspensions subject to simple shear flow,” Phys. Fluids A 5, 849 (1993).
  56. C. Pozrikidis, “Interception of two spheroidal particles in shear flow,” J. Non-Newtonian Fluid Mech. 136, 50 (2006).
  57. M. Lopez and M. D. Graham, “Shear-induced diffusion in dilute suspensions of spherical or non-spherical particles: effects of irreversibility and symmetry breaking,” Phys. Fluids 19, 073602 (2007).
  58. D. L. Koch, “Hydrodynamic diffusion near solid boundaries with application to heat and mass transport into sheared suspensions and fixed-fibre beds,” J. Fluid Mech. 318, 31 (1996).
  59. D. Kim, W. Cha, and R. L. Beissinger, “Mass transport of macromolecules in solution to surfaces,” J. Colloid Interface Sci. 159, 1 (1993).
  60. D. Kim and R. L. Beissinger, “Augmented mass transport of macromolecules in sheared suspensions to surfaces,” J. Colloid Interface Sci. 159, 9 (1993).
  61. C. Wang, “Flow over a surface with parallel grooves,” Phys. Fluids 15, 1114 (2003).
  62. W. Wang, L. Manas-Zloczower, and M. Kaufmann, “Entropic characterization of distributive mixing in polymer processing equipment,” AIChE J. 49, 1637 (2003).
  63. G. Mathew, I. Mezic, and L. Petzold, “A multiscale measure for mixing,” Physica D 211, 23 (2005).
  64. R. Bird, R. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley Interscience, New York, 1987), Vol. 1.
  65. D. Semwogerere, J. Morris, and E. Weeks, “Development of particle migration in pressure-driven flow of a Brownian suspension,” J. Fluid Mech. 581, 437 (2007).
  66. R. Miller and J. Morris, “Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions,” J. Non-Newtonian Fluid Mech. 135, 149 (2006).

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