Advertisement

Optimal control of particle separation in inertial microfluidics

  • Christopher ProhmEmail author
  • Fredi Tröltzsch
  • Holger Stark
Open Access
Regular Article

Abstract

Recently, inertial mircofluidics has emerged as a promising tool to manipulate complex liquids with possible biomedical applications, for example, to particle separation. Indeed, in experiments different particle types were separated based on their sizes (A.J. Mach, D. Di Carlo, Biotechnol. Bioeng. 107, 302 (2010)). In this article we use a theoretical study to demonstrate how concepts from optimal control theory help to design optimized profiles of control forces that allow to steer particles to almost any position at the outlet of a microfluidic channel. We also show that one specific control force profile is sufficient to guide two types of particles to different locations at the channel outlet, where they can be separated from each other. The particles just differ by their size which determines the strength of the inertial lift forces they experience. Our approach greatly enhances the efficiency of particle separation in the inertial regime.

Graphical abstract

Keywords

Soft Matter: Colloids and Nanoparticles 

References

  1. 1.
    M. Toner, D. Irimia, Annu. Rev. Biomed. Eng. 7, 77 (2005).CrossRefGoogle Scholar
  2. 2.
    N. Pamme, Lab Chip 7, 1644 (2007).CrossRefGoogle Scholar
  3. 3.
    H. Tsutsui, C.-M. Ho, Mech. Res. Commun. 36, 92 (2009).CrossRefzbMATHGoogle Scholar
  4. 4.
    T.M. Squires, S.R. Quake, Rev. Mod. Phys. 77, 977 (2005).CrossRefADSGoogle Scholar
  5. 5.
    F.P. Bretherton, J. Fluid Mech. 14, 284 (1962).CrossRefzbMATHMathSciNetADSGoogle Scholar
  6. 6.
    A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Microfluidics Nanofluidics 7, 217 (2009).CrossRefGoogle Scholar
  7. 7.
    A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Phys. Fluids 20, 101702 (2008).CrossRefADSGoogle Scholar
  8. 8.
    S.C. Hur, H.T.K. Tse, D. Di Carlo, Lab Chip 10, 274 (2010).CrossRefGoogle Scholar
  9. 9.
    S.S. Kuntaegowdanahalli, A.A.S. Bhagat, G. Kumar, I. Papautsky, Lab Chip 9, 2973 (2009).CrossRefGoogle Scholar
  10. 10.
    J. Seo, M.H. Lean, A. Kole, Appl. Phys. Lett. 91, 033901 (2007).CrossRefADSGoogle Scholar
  11. 11.
    D. Di Carlo, J.F. Edd, D. Irimia, R.G. Tompkins, M. Toner, Analyt. Chem. 80, 2204 (2008).CrossRefGoogle Scholar
  12. 12.
    Z. Wu, B. Willing, J. Bjerketorp, J.K. Jansson, K. Hjort, Lab Chip 9, 1193 (2009).CrossRefGoogle Scholar
  13. 13.
    A.J. Mach, D. Di Carlo, Biotechnol. Bioeng. 107, 302 (2010).CrossRefGoogle Scholar
  14. 14.
    F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, Graduate Studies in Mathematics (American Mathematical Society, 2010).Google Scholar
  15. 15.
    S.S. Sritharan, Optimal Control of Viscous Flow, Miscellaneous Titles in Applied Mathematics Series (Society for Industrial and Applied Mathematics, 1998).Google Scholar
  16. 16.
    M. Soner, Stochastic Optimal Control in Finance, Cattedra Galileiana (Edizioni della Normale, 2005).Google Scholar
  17. 17.
    G. Segré, A. Silberberg, Nature 189, 209 (1961).CrossRefADSGoogle Scholar
  18. 18.
    D. Di Carlo, J.F. Edd, K.J. Humphry, H.A. Stone, M. Toner, Phys. Rev. Lett. 102, 094503 (2009).CrossRefADSGoogle Scholar
  19. 19.
    J.P. Matas, J.F. Morris, E. Guazzelli, Oil Gas Sci. Technol. 59, 59 (2004).CrossRefGoogle Scholar
  20. 20.
    J. Zhou, P.V. Giridhar, S. Kasper, I. Papautsky, Lab Chip 13, 1919 (2013).CrossRefGoogle Scholar
  21. 21.
    S.C. Hur, A.J. Mach, D. Di Carlo, Biomicrofluidics 5, 022206 (2011).CrossRefGoogle Scholar
  22. 22.
    E.S. Asmolov, J. Fluid Mech. 381, 63 (1999).CrossRefzbMATHADSGoogle Scholar
  23. 23.
    B.P. Ho, L.G. Leal, J. Fluid Mech. 65, 365 (1974).CrossRefzbMATHADSGoogle Scholar
  24. 24.
    B. Chun, A.J.C. Ladd, Phys. Fluids 18, 031704 (2006).CrossRefADSGoogle Scholar
  25. 25.
    C. Prohm, M. Gierlak, H. Stark, Eur. Phys. J. E 35, 1 (2012).CrossRefGoogle Scholar
  26. 26.
    R. Merton, Continuous-Time Finance, Macroeconomics and Finance Series (Wiley, 1992).Google Scholar
  27. 27.
    R.C. Merton, Rev. Econ. Statistics 51, 247 (1969).CrossRefGoogle Scholar
  28. 28.
    R. Sutton, A. Barto, Reinforcement Learning: An Introduction, A Bradford book (MIT Press, 1998).Google Scholar
  29. 29.
    T. Schmiedl, U. Seifert, Phys. Rev. Lett. 98, 108301 (2007).CrossRefADSGoogle Scholar
  30. 30.
    H.J. Kushner, P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Applications of Mathematics, Vol. 24 (Springer, 2001).Google Scholar
  31. 31.
    M. Boué, P. Dupuis, SIAM J. Numer. Anal. 36, 667 (1999).CrossRefMathSciNetGoogle Scholar
  32. 32.
    Y. LeCun, L. Bottou, G. Orr, K. Muller, in Neural Networks: Tricks of the Trade, edited by G. Montavon, G.B. Orr, K.R. Müller (Springer, 1998).Google Scholar
  33. 33.
    H. Bruus, Theoretical Microfluidics (Oxford University Press, 2007).Google Scholar
  34. 34.
    G. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 2000).Google Scholar
  35. 35.
    A. Malevanets, R. Kapral, J. Chem. Phys. 110, 8605 (1999).CrossRefADSGoogle Scholar
  36. 36.
    A. Malevanets, R. Kapral, J. Chem. Phys. 112, 7260 (2000).CrossRefADSGoogle Scholar
  37. 37.
    G. Gompper, T. Ihle, D. Kroll, R. Winkler, in Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science (Springer Berlin Heidelberg, 2008) pp. 1--87.Google Scholar
  38. 38.
    S.B. Babu, H. Stark, Eur. Phys. J. E 34, 1 (2011).CrossRefGoogle Scholar
  39. 39.
    A. Zöttl, H. Stark, Phys. Rev. Lett. 108, 218104 (2012).CrossRefADSGoogle Scholar
  40. 40.
    M.T. Downton, H. Stark, J. Phys.: Condens. Matter 21, 204101 (2009).ADSGoogle Scholar
  41. 41.
    S.B. Babu, H. Stark, New J. Phys. 14, 085012 (2012).CrossRefADSGoogle Scholar
  42. 42.
    D. Babič, C. Bechinger, Phys. Rev. Lett. 94, 148303 (2005).CrossRefADSGoogle Scholar
  43. 43.
    S. Bleil, P. Reimann, C. Bechinger, Phys. Rev. E 75, 031117 (2007).CrossRefADSGoogle Scholar
  44. 44.
    N. Bruot, J. Kotar, F. de Lillo, M.C. Lagomarsino, P. Cicuta, Phys. Rev. Lett. 109, 164103 (2012).CrossRefADSGoogle Scholar
  45. 45.
    D.G. Grier, Nature 424, 810 (2003).CrossRefADSGoogle Scholar
  46. 46.
    K. Ladavac, K. Kasza, D.G. Grier, Phys. Rev. E 70, 010901 (2004).CrossRefADSGoogle Scholar
  47. 47.
    M. Padgett, R. Di Leonardo, Lab Chip 11, 1196 (2011).CrossRefGoogle Scholar
  48. 48.
    A. Ashkin, Biophys. J. 61, 569 (1992).CrossRefADSGoogle Scholar
  49. 49.
    A. Jannasch, A.F. Demirörs, P.D. van Oostrum, A. van Blaaderen, E. Schäffer, Nat. Photonics 6, 469 (2012).CrossRefADSGoogle Scholar
  50. 50.
    J. Dong, C.E. Castro, M.C. Boyce, M.J. Lang, S. Lindquist, Nat. Struct. Mol. Biol. 17, 1422 (2010).CrossRefGoogle Scholar
  51. 51.
    B. Maier, L. Potter, M. So, H.S. Seifert, M.P. Sheetz, Proc. Natl. Acad. Sci. U.S.A. 99, 16012 (2002).CrossRefADSGoogle Scholar
  52. 52.
    W.Y. Kim, J.Y. Yoo, Lab Chip 9, 1043 (2009).CrossRefGoogle Scholar
  53. 53.
    C. Prohm, H. Stark, unpublished results.Google Scholar
  54. 54.
    W. Lee, H. Amini, H.A. Stone, D. Di Carlo, Proc. Natl. Acad. Sci. U.S.A. 107, 22413 (2010).CrossRefADSGoogle Scholar
  55. 55.
    J.-P. Matas, V. Glezer, E. Guazzelli, J.F. Morris, Phys. Fluids 16, 4192 (2004).CrossRefADSGoogle Scholar
  56. 56.
    D. Di Carlo, D. Irimia, R.G. Tompkins, M. Toner, Proc. Natl. Acad. Sci. U.S.A. 104, 18892 (2007).CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Christopher Prohm
    • 1
    Email author
  • Fredi Tröltzsch
    • 2
  • Holger Stark
    • 1
  1. 1.Institute of Theoretical PhysicsTechnische Universität BerlinBerlinGermany
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany

Personalised recommendations