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Focusing and splitting streams of soft particles in microflows via viscosity gradients

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Abstract.

Microflows are intensively used for investigating and controlling the dynamics of particles, including soft particles such as biological cells and capsules. A classic result is the tank-treading motion of elliptically deformed soft particles in linear shear flows, which do not migrate across straight streamlines in the bulk. However, soft particles migrate across straight streamlines in Poiseuille flows. In this work we describe a new mechanism of cross-streamline migration by using soft capsules with a spherical equilibrium shape. If the viscosity varies perpendicular to the streamlines then the soft particles migrate across streamlines towards regions of a lower viscosity, even in linear shear flows. An interplay with the repulsive particle-boundary interaction causes then focusing of particles in linear shear flows with the attractor streamline closer to the wall in the low viscosity region. Viscosity variations perpendicular to the streamlines in Poiseuille flows leads either to a shift of the particle attractor or even to a splitting of particle attractors, which may give rise to interesting applications for particle separation. The location of attracting streamlines depend on the particle properties, like their size and elasticity. The cross-stream migration induced by viscosity variations is explained by analytical considerations, Stokesian dynamics simulations with a generalized Oseen tensor and lattice-Boltzmann simulations.

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References

  1. T.M. Squires, S.R. Quake, Rev. Mod. Phys. 77, 978 (2005)

    Article  ADS  Google Scholar 

  2. A.S. Popel, P.C. Johnson, Annu. Rev. Fluid Mech. 37, 43 (2005)

    Article  ADS  Google Scholar 

  3. A. Karimi, S. Yazdi, A.M. Ardekani, Biomicrofluidics 7, 021501 (2013)

    Article  Google Scholar 

  4. J.B. Dahl, J.-M.G. Lin, S.J. Muller, S. Kumar, Annu. Rev. Chem. Biomol. Eng. 6, 293 (2015)

    Article  Google Scholar 

  5. H. Amini, W. Lee, D.D. Carlo, Lap Chip 14, 2739 (2014)

    Article  Google Scholar 

  6. T.W. Secomb, Annu. Rev. Fluid Mech. 49, 443 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. I. Cantat, C. Misbah, Phys. Rev. Lett. 83, 880 (1999)

    Article  ADS  Google Scholar 

  8. U. Seifert, Phys. Rev. Lett. 83, 876 (1999)

    Article  ADS  Google Scholar 

  9. M. Abkarian, C. Lartigue, A. Viallat, Phys. Rev. Lett. 88, 068102 (2002)

    Article  ADS  Google Scholar 

  10. X. Grandchamp et al., Phys. Rev. Lett. 110, 108101 (2013)

    Article  ADS  Google Scholar 

  11. L.G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)

    Article  ADS  Google Scholar 

  12. S. Mandal, A. Bandopadhyay, S. Chakraborty, Phys. Rev. E 92, 023002 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Helmy, D. Barthès-Biesel, J. Mec. Theor. Appl. 1, 859 (1982)

    Google Scholar 

  14. B. Kaoui et al., Phys. Rev. E 77, 021903 (2008)

    Article  ADS  Google Scholar 

  15. G. Coupier, B. Kaoui, T. Podgorski, C. Misbah, Phys. Fluids 20, 111702 (2008)

    Article  ADS  Google Scholar 

  16. S.K. Doddi, P. Bagchi, Int. J. Multiphase Flow 34, 966 (2008)

    Article  Google Scholar 

  17. A. Förtsch, M. Laumann, D. Kienle, W. Zimmermann, EPL 119, 64003 (2017)

    Article  ADS  Google Scholar 

  18. M. Schlenk et al., Lab Chip 18, 3163 (2018)

    Article  Google Scholar 

  19. G. D’Avino et al., Comput. Fluids 39, 709 (2010)

    Article  MathSciNet  Google Scholar 

  20. D. Yuan et al., Lab Chip 18, 551 (2018)

    Article  Google Scholar 

  21. F. Del Giudice, S. Sathish, G. D’Avino, A.Q. Shen, Anal. Chem. 89, 13146 (2017)

    Article  Google Scholar 

  22. X. Lu, C. Liu, G. Hu, X. Xuan, J. Colloid Interf. Sci. 500, 182 (2017)

    Article  ADS  Google Scholar 

  23. M.A. Faridi et al., J. Nanobiotechnol. 15, 3 (2017)

    Article  Google Scholar 

  24. G. D’Avino, F. Greco, P.L. Maffettone, Annu. Rev. Fluid Mech. 49, 341 (2017)

    Article  ADS  Google Scholar 

  25. G. Segré, A. Silberberg, Nature 189, 209 (1961)

    Article  ADS  Google Scholar 

  26. G. Sekhon, R. Armstrong, M.S. Jhon, J. Polym. Sci., Polym. Phys. Ed. 20, 947 (1982)

    Article  ADS  Google Scholar 

  27. P.O. Brunn, Int. J. Multiphase Flow 187, 202 (1983)

    Google Scholar 

  28. M.S. Jhon, K.F. Freed, J. Polym. Sci.: Polym. Phys. 23, 255 (1985)

    Google Scholar 

  29. M. Laumann et al., EPL 117, 44001 (2017)

    Article  ADS  Google Scholar 

  30. I. Jo, Y. Huang, W. Zimmermann, E. Kanso, Phys. Rev. E 94, 063116 (2016)

    Article  ADS  Google Scholar 

  31. M. Laumann, A. Förtsch, E. Kanso, W. Zimmermann, New J. Phys. 21, 073012 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  32. V. Miralles, A. Huerre, F. Malloggi, M.-C. Jullien, Diagnostics 3, 33 (2013)

    Article  Google Scholar 

  33. J.K.G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996)

  34. T. Krüger, F. Varnik, D. Raabe, Comput. Math. Appl. 61, 3485 (2011)

    Article  MathSciNet  Google Scholar 

  35. S. Ramanujan, C. Pozrikidis, J. Fluid. Mech. 361, 117 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  36. D. Barthès-Biesel, Annu. Rev. Fluid Mech. 48, 25 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  37. G. Gompper, D.M. Kroll, J. Phys. I 6, 1305 (1996)

    Google Scholar 

  38. T. Krueger, M. Gross, D. Raabe, F. Varnik, Soft Matter 9, 9008 (2013)

    Article  ADS  Google Scholar 

  39. J. Kestin, J. Shankland, J. Non-Equilib. Thermodyn. 6, 241 (2009)

    ADS  Google Scholar 

  40. S. Gupta, Viscosity of Water, in Viscometry for Liquids, Springer Series in Materials Science (Springer, Cham, 2014).

  41. T. Krüger, The Lattice Boltzmann Method - Principles and Practice (Springer, Berlin, 2016)

  42. P.L. Bhatnagar, E.P. Gross, M. Krook, Phys. Rev. 94, 511 (1954)

    Article  ADS  Google Scholar 

  43. C.K. Aidun, J.R. Clausen, Annu. Rev. Fluid. Mech 42, 439 (2010)

    Article  ADS  Google Scholar 

  44. Z. Guo, C. Zheng, B. Shi, Phys. Rev. E 65, 046308 (2002)

    Article  ADS  Google Scholar 

  45. C.S. Peskin, Acta Numer. 11, 479 (2002)

    Article  MathSciNet  Google Scholar 

  46. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, England, 1992)

  47. J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)

    Article  ADS  Google Scholar 

  48. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)

  49. R. Milo, R. Phillips, Cell Biology by the Numbers (Garland Science, New York, NY, 2016)

  50. V. Telis, J. Telis-Romero, H. Mazzotti, A. Gabas, Int. J. Food Prop. 10, 185 (2007)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Theoretische Physik I, Universität Bayreuth, 95440, Bayreuth, Germany

    Matthias Laumann & Walter Zimmermann

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  1. Matthias Laumann
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  2. Walter Zimmermann
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Correspondence to Walter Zimmermann.

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Laumann, M., Zimmermann, W. Focusing and splitting streams of soft particles in microflows via viscosity gradients. Eur. Phys. J. E 42, 108 (2019). https://doi.org/10.1140/epje/i2019-11872-1

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