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Motion of an elastic capsule in a constricted microchannel

  • Cecilia Rorai
  • Antoine Touchard
  • Lailai Zhu
  • Luca Brandt
Regular Article

Abstract

We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady-state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca , and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that best reproduces the behavior of the three-dimensional surface area. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation-correlated quantities grow linearly with Ca , while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca . The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

Graphical abstract

Keywords

Flowing Matter: Interfacial phenomena 

References

  1. 1.
    J. Freund, Annu. Rev. Fluid Mech. 46, 67 (2014).CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    X. Mao, T. Huang, Lab Chip 12, 4006 (2012).CrossRefGoogle Scholar
  3. 3.
    C. Lim, D. Hoon, Phys. Today 67, 26 (2014).CrossRefGoogle Scholar
  4. 4.
    S. Berger, L. Jou, Annu. Rev. Fluid Mech. 32, 347 (2000).CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    F. Mokken, M. Kedaria, C. Henny et al., Ann. Hematol. 64, 113 (1992).CrossRefGoogle Scholar
  6. 6.
    H. del Portillo, M. Ferrer, T. Brugat et al., Cellular Microbiol. 14, 343 (2012).CrossRefGoogle Scholar
  7. 7.
    B. Schnitzer, T. Sodeman, M. Mead et al., Science 177, 175 (1972).CrossRefADSGoogle Scholar
  8. 8.
    J. Shelby, J. White, K. Ganesan et al., Proc. Natl. Acad. Sci. U.S.A. 100, 14618 (2003).CrossRefADSGoogle Scholar
  9. 9.
    H. Bow, I.V. Pivkin, M. Diez-Silva et al., Lab Chip 11, 1065 (2011).CrossRefGoogle Scholar
  10. 10.
    D. Qi, D. Hoelzle, A. Rowat, Eur. Phys. J. ST 204, 85 (2012).CrossRefGoogle Scholar
  11. 11.
    L. Zhu, C. Rorai, D. Mitra et al., Soft Matter 10, 7705 (2014).Google Scholar
  12. 12.
    H. Wyss, T. Franke, E. Mele et al., Soft Matter 6, 4550 (2010).CrossRefADSGoogle Scholar
  13. 13.
    L. Huang, E. Cox, R. Austin et al., Scienze 304, 987 (2004).CrossRefADSGoogle Scholar
  14. 14.
    J.P. Beech, S.H. Holm, K. Adolfsson et al., Lab Chip 12, 1048 (2012).CrossRefGoogle Scholar
  15. 15.
    V.R. Muzykantov, Expert Opin. Drug Deliv. 7, 403 (2010).CrossRefGoogle Scholar
  16. 16.
    M. Favretto, J. Cluitmans, G. Bosman et al., J. Control. Release 170, 343 (2013).CrossRefGoogle Scholar
  17. 17.
    P. Prasad, Introduction to Biophotonics (John Wiley and Sons, 2003).Google Scholar
  18. 18.
    S.-Y. Park, P. Dimitrakopoulos, Soft Matter 9, 8844 (2013).CrossRefADSGoogle Scholar
  19. 19.
    R. Kusters, T. van der Heijden, B. Kaoui, J. Harting, C. Storm, Phys. Rev. E 90, 033006 (2014).CrossRefADSGoogle Scholar
  20. 20.
    H. Noguchi, G. Gompper, Proc. Natl. Acad. Sci. U.S.A. 102, 14159 (2005).CrossRefADSGoogle Scholar
  21. 21.
    G. Danker, P.M. Vlahovska, C. Misbah, Phys. Rev. Lett. 102, 148102 (2009).CrossRefADSGoogle Scholar
  22. 22.
    B. Kaoui, G. Biros, C. Misbah, Phys. Rev. Lett. 103, 188101 (2009).CrossRefADSGoogle Scholar
  23. 23.
    B. Kaoui, N. Tahiri, T. Biben et al., Phys. Rev. E 84, 041906 (2011).CrossRefADSGoogle Scholar
  24. 24.
    Y.W. Kim, J.Y. Yoo, Lab Chip 9, 1043 (2009).CrossRefGoogle Scholar
  25. 25.
    X. Xuan, J. Zhu, C. Church, Microfluid. Nanofluid. 9, 1 (2010).CrossRefGoogle Scholar
  26. 26.
    Z. Peng, A. Mashayekh, Q. Zhu, J. Fluid Mech. 742, 96 (2014).CrossRefADSGoogle Scholar
  27. 27.
    D. Cordasco, A. Yazdani, P. Bagchi, Phys. Fluids 26, 041902 (2014).CrossRefADSGoogle Scholar
  28. 28.
    H. Zhao, A.H.G. Isfahani, L.N. Olson et al., J. Comput. Phys. 229, 3726 (2010).CrossRefADSMATHMathSciNetGoogle Scholar
  29. 29.
    L. Zhu, L. Brandt, J. Fluid Mech. 770, 374 (2015).CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    R. Skalak, A. Tozeren, R.P. Zarda et al., Biophys. J. 13, 245 (1973).CrossRefADSGoogle Scholar
  31. 31.
    A. Kumar, M. Graham, J. Comput. Phys. 231, 6682 (2012).CrossRefADSMATHMathSciNetGoogle Scholar
  32. 32.
    J. Hernández-Ortiz, J. de Pablo, M. Graham, Phys. Rev. Lett. 98, 140602 (2007).CrossRefADSGoogle Scholar
  33. 33.
    A. Kumar, M. Graham, Phys. Rev. E 84, 066316 (2011).CrossRefADSGoogle Scholar
  34. 34.
    P. Pranay, S.G. Anekal, J.P. Hernandez-Ortiz et al., Phys. Fluids 22, 123103 (2010).CrossRefADSGoogle Scholar
  35. 35.
    P. Pranay, R.G. Henríquez-Rivera, M.D. Graham, Phys. Fluids 24, 061902 (2012).CrossRefADSGoogle Scholar
  36. 36.
    P. Fischer, J. Lottes, S. Kerkemeier, nek5000 Web page (2008) http://nek5000.mcs.anl.gov.
  37. 37.
    L. Zhu, Simulation of individual cells in flow, Phd dissertation, Royal Institute of Technology, Stockholm (2014) URL http://www.diva-portal.org/smash/record.jsf?pid=diva2:703338.
  38. 38.
    M. Spiga, G. Morino, Int. Commun. Heat Mass Transfer 21, 469 (1994).CrossRefGoogle Scholar
  39. 39.
    S.K. Doddi, P. Bagchi, Int. J. Multiphase Flow 34, 966 (2008).CrossRefGoogle Scholar
  40. 40.
    C. Rorai, F. Nason, L. Zhu, Proceedings of the IUTAM Symposium on Dynamics of Capsules, Vesicles and Cells in Flow (to appear).Google Scholar
  41. 41.
    A. Farutin, C. Misbah, Phys. Rev. E 89, 042709 (2014).CrossRefADSGoogle Scholar
  42. 42.
    S. Kuriakose, P. Dimitrakopoulos, Soft Matter 9, 4284 (2013).CrossRefADSGoogle Scholar
  43. 43.
    S. Kuriakose, P. Dimitrakopoulos, Phys. Rev. E 84, 011906 (2011).CrossRefADSGoogle Scholar
  44. 44.
    G. Coupier, A. Farutin, C. Minetti et al., Phys. Rev. Lett. 108, 178106 (2012).CrossRefADSGoogle Scholar
  45. 45.
    X.-Q. Hu, A.-V. Salsac, D. Barthes-Biesel, J. Fluid Mech. 705, 176 (2012).CrossRefADSMATHMathSciNetGoogle Scholar
  46. 46.
    B. Kaoui, A. Farutin, C. Misbah, Phys. Rev. E 80, 061905 (2009).CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Cecilia Rorai
    • 1
    • 2
  • Antoine Touchard
    • 1
    • 3
  • Lailai Zhu
    • 1
    • 4
  • Luca Brandt
    • 1
  1. 1.Linné Flow Centre and Swedish e-Science Research Centre (SeRC)KTH MechanicsStockholmSweden
  2. 2.NorditaStockholmSweden
  3. 3.ENSTA ParisTechPalaiseauFrance
  4. 4.Laboratory of Fluid Mechanics and InstabilitiesLausanneSwitzerland

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