Skip to main content
Log in

Giant enhancement of hydrodynamically enforced entropic trapping in thin channels

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Using our generalized Fick-Jacobs approach [1, 2] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coefficient on the channel height. In particular, we observe a giant suppression of the effective diffusivity in thin channels; four orders of magnitude compared to the bulk value.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Martens, A.V. Straube, G. Schmid, L. Schimansky-Geier, P. Hänggi, Phys. Rev. Lett. 110, 010601 (2013)

    Article  ADS  Google Scholar 

  2. S. Martens, G. Schmid, A.V. Straube, L. Schimansky-Geier, P. Hänggi, Eur. Phys. J. Special Topics 222, 2453 (2013)

    Article  ADS  Google Scholar 

  3. P.S. Dittrich, A. Manz, Nat. Rev. Drug. Discov. 5, 210 (2006)

    Article  Google Scholar 

  4. F.J. Keil, R. Krishna, M.-O. Coppens, Rev. Chem. Eng. 16, 71 (2000)

    Article  Google Scholar 

  5. A.M. Berezhkovskii, S.M. Bezrukov, Biophys. J. 88, L17 (2005)

    Article  Google Scholar 

  6. A.M. Berezhkovskii, S.M. Bezrukov, Phys. Rev. Lett. 100, 038104 (2008)

    Article  ADS  Google Scholar 

  7. M. Firnkes, D. Pedone, J. Knezevic, M. Döblinger, U. Rant, Nano Lett. 10, 2162 (2010)

    Article  ADS  Google Scholar 

  8. J. Voldman, Annu. Rev. Biomed. Eng. 8, 425 (2006)

    Article  Google Scholar 

  9. P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  10. D. Reguera, A. Luque, P.S. Burada, G. Schmid, J.M. Rubí, P. Hänggi, Phys. Rev. Lett. 108, 020604 (2012)

    Article  ADS  Google Scholar 

  11. R. Harrison, P. Todd, S. Rudge, D. Petrides, Bioseparations Science and Engineering (Oxford University Press, USA, 2002)

  12. K.D. Dorfman, Rev. Mod. Phys. 82, 2903 (2010)

    Article  ADS  Google Scholar 

  13. G. Giupponi, I. Pagonabarraga, Phys. Rev. Lett. 106, 248304 (2011)

    Article  ADS  Google Scholar 

  14. M. MacDonald, G. Spalding, K. Dholakia, Nature 426, 421 (2003)

    Article  ADS  Google Scholar 

  15. L. Bogunovic, R. Eichhorn, J. Regtmeier, D. Anselmetti, P. Reimann, Soft Matter 8, 3900 (2012)

    Article  ADS  Google Scholar 

  16. C. Kettner, P. Reimann, P. Hänggi, F. Müller, Phys. Rev. E 61, 312 (2000)

    Article  ADS  Google Scholar 

  17. X.T. Zheng, J.C. Wu, B.Q. Ai, F.G. Li, Eur. Phys. J. B 86, 479 (2013)

    Article  ADS  Google Scholar 

  18. V.Y. Zitserman, A.M. Berezhkovskii, A.E. Antipov, Y.A. Makhnovskii, J. Chem. Phys. 135, 121102 (2011)

    Article  ADS  Google Scholar 

  19. L. Dagdug, I. Pineda, J. Chem. Phys. 137, 024107 (2012)

    Article  ADS  Google Scholar 

  20. T. Motz, G. Schmid, P. Hänggi, D. Reguera, J.M. Rubí, J. Chem. Phys. 141, 074104 (2014)

    Article  ADS  Google Scholar 

  21. D. Reguera, G. Schmid, P.S. Burada, J.M. Rubí, P. Reimann, P. Hänggi, Phys. Rev. Lett. 96, 130603 (2006)

    Article  ADS  Google Scholar 

  22. P. Burada, P. Hänggi, F. Marchesoni, G. Schmid, P. Talkner, Chem. Phys. Chem. 10, 45 (2009)

    Google Scholar 

  23. J.M. Rubí, D. Reguera, Chem. Phys. 375, 518 (2010)

    Article  ADS  Google Scholar 

  24. P.K. Ghosh, P. Hänggi, F. Marchesoni, S. Martens, F. Nori, L. Schimansky-Geier, G. Schmid, Phys. Rev. E 85, 011101 (2012)

    Article  ADS  Google Scholar 

  25. S.L. Dettmer, S. Pagliara, K. Misiunas, U.F. Keyser, Rev. Sci. Instrum. 85, 023708 (2014)

    Article  ADS  Google Scholar 

  26. S.L. Dettmer, S. Pagliara, K. Misiunas, U.F. Keyser, Phys. Rev. E 98, 062305 (2014)

    Article  ADS  Google Scholar 

  27. M. Jacobs, Diffusion Processes, 2nd edn. (Springer, New York, 1967)

  28. R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)

    Article  Google Scholar 

  29. D. Reguera, J.M. Rubí, Phys. Rev. E 64, 061106 (2001)

    Article  ADS  Google Scholar 

  30. P. Kalinay, J.K. Percus, Phys. Rev. E 74, 041203 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  31. P. Kalinay, Phys. Rev. E 84, 011118 (2011)

    Article  ADS  Google Scholar 

  32. S. Martens, G. Schmid, L. Schimansky-Geier, P. Hänggi, Phys. Rev. E 83, 051135 (2011)

    Article  ADS  Google Scholar 

  33. S. Martens, G. Schmid, L. Schimansky-Geier, P. Hänggi, Chaos 21, 047518 (2011)

    Article  ADS  Google Scholar 

  34. S. Martens, I.M. Sokolov, L. Schimansky-Geier, J. Chem. Phys. 136, 111102 (2012)

    Article  ADS  Google Scholar 

  35. P.K. Ghosh, P. Hänggi, F. Marchesoni, F. Nori, G. Schmid, Phys. Rev. E 86, 021112 (2012)

    Article  ADS  Google Scholar 

  36. P.K. Ghosh, P. Hänggi, F. Marchesoni, F. Nori, G. Schmid, Europhys. Lett. 98, 50002 (2012)

    Article  ADS  Google Scholar 

  37. M. Schindler, P. Talkner, M. Kostur, P. Hänggi, Physica A 385, 46 (2007)

    Article  ADS  Google Scholar 

  38. G. Volpe, I. Buttinoni, D. Vogt, H.-J. Kummerer, C. Bechinger, Soft Matter 7, 8810 (2011)

    Article  ADS  Google Scholar 

  39. C. Scholz, F. Wirner, J. Götz, U. Rüde, G.E. Schröder-Turk, K. Mecke, C. Bechinger, Phys. Rev. Lett. 109, 264504 (2012)

    Article  ADS  Google Scholar 

  40. C. Scholz, F. Wirner, Y. Li, C. Bechinger, Exp. Fluids 53, 1327 (2012b)

    Article  Google Scholar 

  41. B.Q. Ai, Y.F. He, F.G. Li, W.R. Zhong, J. Chem. Phys. 138, 154107 (2013)

    Article  ADS  Google Scholar 

  42. F.G. Li, B.Q. Ai, J. Stat. Mech. Theor. Exp. 2014, P04027 (2014)

    Article  MathSciNet  Google Scholar 

  43. M. Tarama, A.M. Menzel, H. Löwen, Phys. Rev. E 90, 032907 (2014)

    Article  ADS  Google Scholar 

  44. J.C.T. Eijkel, A. van den Berg, Microfluid. Nanofluid. 1, 249 (2005)

    Article  Google Scholar 

  45. J. Happel, H. Brenner, Low Reynolds number hydrodynamics: with special applications to particulate media (Prentice-Hall, Inc., Engelwood Cliffs, N.J., 1965)

  46. M.R. Maxey, J.J. Riley, Phys. Fluids 26, 883 (1983)

    Article  ADS  MATH  Google Scholar 

  47. H. Bhatia, G. Norgard, V. Pascucci, P.-T. Bremer, IEEE Trans. Visual. Comput. Graphics 19, 1386 (2013)

    Article  Google Scholar 

  48. A.V. Straube, J. Phys. Condens. Matter 23, 184122 (2011)

    Article  ADS  Google Scholar 

  49. N. Laachi, M. Kenward, E. Yariv, K.D. Dorfman, Europhys. Lett. 80, 50009 (2007)

    Article  ADS  Google Scholar 

  50. P.S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, J.M. Rubí, BioSystems 93, 16 (2008)

    Article  Google Scholar 

  51. I.M. Sokolov, Eur. Phys. J. 31, 1353 (2010)

    Article  MATH  Google Scholar 

  52. H. Bruus, Theoretical Microfluidics (Oxford University Press, 2008)

  53. E. Lauga, A.D. Stroock, H.A. Stone, Phys. Fluids 16, 3051 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  54. G. Taylor, Phil. Trans. R. Soc. Lond. A 219, 186 (1953)

    Google Scholar 

  55. R. Aris, Phil. Trans. R. Soc. Lond. A 235, 67 (1956)

    Google Scholar 

  56. A. Zöttl, H. Stark, Eur. Phys. J. E 36, 4 (2013)

    Article  ADS  Google Scholar 

  57. D. Di Carlo, D. Irimia, R.G. Tompkins, M. Toner, Proc. Nat. Ac. Sc. USA 104, 18892 (2007)

    Article  ADS  Google Scholar 

  58. N. Liron, S. Mochon, J. Eng. Math. 10, 287 (1976)

    Article  MATH  Google Scholar 

  59. S. Reddig, H. Stark, J. Chem. Phys. 138, 234902 (2013)

    Article  ADS  Google Scholar 

  60. P. Hänggi, H. Thomas, Phys. Rep. 88, 207 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  61. H. Risken, The Fokker-Planck Equation, 2nd edn. (Springer, Berlin, 1989)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Martens.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martens, S., Straube, A.V., Schmid, G. et al. Giant enhancement of hydrodynamically enforced entropic trapping in thin channels. Eur. Phys. J. Spec. Top. 223, 3095–3111 (2014). https://doi.org/10.1140/epjst/e2014-02321-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2014-02321-9

Keywords

Navigation