Shear banding in nematogenic fluids with oscillating orientational dynamics

Abstract.

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic-nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear-banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non-monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical S-like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

Graphical abstract

References

  1. 1

    S.M. Fielding, Soft Matter 3, 1262 (2007)

    ADS  Article  Google Scholar 

  2. 2

    J.K. Dhont, W.J. Briels, Rheol. Acta 47, 257 (2008)

    Article  Google Scholar 

  3. 3

    M. Lopez-Gonzalez, W. Holmes, P. Callaghan, P. Photinos, Phys. Rev. Lett. 93, 268302 (2004)

    ADS  Article  Google Scholar 

  4. 4

    J. Decruppe, R. Cressely, R. Makhloufi, E. Cappelaere, Colloid Polym. Sci. 273, 346 (1995)

    Article  Google Scholar 

  5. 5

    L. Chen, C. Zukoski, B. Ackerson, H. Hanley, G. Straty, J. Barker, C. Glinka, Phys. Rev. Lett. 69, 688 (1992)

    ADS  Article  Google Scholar 

  6. 6

    V. Chikkadi, D. Miedema, M. Dang, B. Nienhuis, P. Schall, Phys. Rev. Lett. 113, 208301 (2014)

    ADS  Article  Google Scholar 

  7. 7

    J. Goveas, P. Olmsted, Eur. Phys. J. E 6, 79 (2001)

    Article  Google Scholar 

  8. 8

    N. Spenley, X. Yuan, M. Cates, J. Phys. II 6, 551 (1996)

    Google Scholar 

  9. 9

    P. Olmsted, O. Radulescu, C.Y. Lu, J. Rheol. 44, 257 (2000)

    ADS  Article  Google Scholar 

  10. 10

    Y.G. Tao, W. den Otter, W. Briels, Phys. Rev. Lett. 95, 237802 (2005)

    ADS  Article  Google Scholar 

  11. 11

    M. Ripoll, P. Holmqvist, R.G. Winkler, G. Gompper, J.K.G. Dhont, M.P. Lettinga, Phys. Rev. Lett. 101, 168302 (2008)

    ADS  Article  Google Scholar 

  12. 12

    P.D. Olmsted, C.Y.D. Lu, Phys. Rev. E 60, 4397 (1999)

    ADS  Article  Google Scholar 

  13. 13

    R. Larson, Macromolecules 23, 3983 (1990)

    ADS  Article  Google Scholar 

  14. 14

    O. Hess, S. Hess, Phys. A 207, 517 (1994)

    Article  Google Scholar 

  15. 15

    G. Rienäcker, M. Kröger, S. Hess, Phys. Rev. E 66, 040702 (2002)

    ADS  Article  Google Scholar 

  16. 16

    E.V. Alonso, A.A. Wheeler, T.J. Sluckin, Proc. R. Soc. A 459, 195 (2003)

    ADS  Article  Google Scholar 

  17. 17

    P.D. Olmsted, P. Goldbart, Phys. Rev. A 41, 4578 (1990)

    ADS  Article  Google Scholar 

  18. 18

    P.D. Olmsted, Ph.D. thesis, University of Illinois, Urbana-Champaign (1991)

  19. 19

    P.D. Olmsted, P.M. Goldbart, Phys. Rev. A 46, 4966 (1992)

    ADS  Article  Google Scholar 

  20. 20

    D.C. Roux, J.F. Berret, G. Porte, E. Peuvrel-Disdier, P. Lindner, Macromolecules 28, 1681 (1995)

    ADS  Article  Google Scholar 

  21. 21

    M. Lettinga, Z. Dogic, H. Wang, J. Vermant, Langmuir 21, 8048 (2005)

    Article  Google Scholar 

  22. 22

    B. Chakrabarti, M. Das, C. Dasgupta, S. Ramaswamy, A. Sood, Phys. Rev. Lett. 92, 055501 (2004)

    ADS  Article  Google Scholar 

  23. 23

    M.G. Forest, R. Zhou, Q. Wang, Multiscale Model. Simul. 6, 858 (2007)

    MathSciNet  Article  Google Scholar 

  24. 24

    D. Chakraborty, C. Dasgupta, A.K. Sood, Phys. Rev. E 82, 065301 (2010)

    ADS  Article  Google Scholar 

  25. 25

    M. Das, B. Chakrabarti, C. Dasgupta, S. Ramaswamy, A.K. Sood, Phys. Rev. E 71, 021707 (2005)

    ADS  Article  Google Scholar 

  26. 26

    D.A. Strehober, H. Engel, S.H.L. Klapp, Phys. Rev. E 88, 012505 (2013)

    ADS  Article  Google Scholar 

  27. 27

    H. Zhou, M.G. Forest, Q. Wang, Technical report, DTIC Document (2007)

  28. 28

    J.K.G. Dhont, M.P. Lettinga, Z. Dogic, T.A.J. Lenstra, H. Wang, S. Rathgeber, P. Carletto, L. Willner, H. Frielinghaus, P. Lindner, Farad. Discuss. 123, 157 (2003)

    ADS  Article  Google Scholar 

  29. 29

    P.G. de Gennes, The physics of liquid crystals (Clarendon Press, Oxford, 1993)

  30. 30

    S. Hess, Tensors for Physics (Springer Intl., Switzerland, 2015)

  31. 31

    R. Lugo-Frias, S.H.L. Klapp, J. Phys.: Condens. Matter (2016)

  32. 32

    C. Oseen, Trans. Faraday Soc. 29, 883 (1933)

    Article  Google Scholar 

  33. 33

    F.C. Frank, Discuss. Faraday Soc. 25, 19 (1958)

    Article  Google Scholar 

  34. 34

    Y. Singh, K. Singh, Phys. Rev. A 33, 3481 (1985)

    ADS  Article  Google Scholar 

  35. 35

    K. Singh, Y. Singh, Phys. Rev. A 34, 548 (1986)

    ADS  Article  Google Scholar 

  36. 36

    K. Singh, Y. Singh, Phys. Rev. A 35, 3535 (1987)

    ADS  Article  Google Scholar 

  37. 37

    G. Taylor, Proc. R. Soc. London. Ser. A, Math. Phys. Character 103, 58 (1923)

    ADS  Article  Google Scholar 

  38. 38

    S. Hess, Z. Naturforsch. 30a, 728 (1975)

    ADS  Google Scholar 

  39. 39

    I. Pardowitz, S. Hess, Phys. A 100, 540 (1980)

    Article  Google Scholar 

  40. 40

    S. Heidenreich, Ph.D. thesis, TU Berlin (2009)

  41. 41

    C. Pereira-Borgmeyer, S. Hess, J. Non-Equilib. Thermodyn. 20, 359 (1995)

    ADS  Article  Google Scholar 

  42. 42

    S. Hess, Z. Naturforsch. 31a, 1034 (1976)

    ADS  Google Scholar 

  43. 43

    S.R. De Groot, P. Mazur, Non-equilibrium thermodynamics (Dover, 1983)

  44. 44

    R. Ganapathy, S. Majumdar, A.K. Sood, Phys. Rev. E 78, 021504 (2008)

    ADS  Article  Google Scholar 

  45. 45

    S. Hess, M. Kröger, J. Phys.: Condens. Matter 16, S3835 (2004)

    ADS  Google Scholar 

  46. 46

    S. Hess, M. Kröger, in Computer Simulations of Liquid Crystals and Polymers (Springer Verlag, 2005) pp. 295--333

  47. 47

    P. Kaiser, W. Wiese, S. Hess, J. Non-Equilib. Thermodyn. 17, 153 (1992)

    ADS  Article  Google Scholar 

  48. 48

    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C, Vol. 2 (Cambridge University press, Cambridge, 1996)

  49. 49

    G. Rienäcker, Orientational dynamics of nematic liquid crystals in a shear flow (Shaker Verlag, Aachen, 2000)

  50. 50

    P. Sheng, Phys. Rev. A 26, 1610 (1982)

    ADS  Article  Google Scholar 

  51. 51

    B. Jerome, Rep. Prog. Phys. 54, 391 (1991)

    ADS  Article  Google Scholar 

  52. 52

    M. Ruths, S. Steinberg, J.N. Israelachvili, Langmuir 12, 6637 (1996)

    Article  Google Scholar 

  53. 53

    O. Manyuhina, A.M. Cazabat, M.B. Amar, EPL 92, 16005 (2010)

    ADS  Article  Google Scholar 

  54. 54

    O. Radulescu, P. Olmsted, J. Non-Newton. Fluid 91, 143 (2000)

    Article  Google Scholar 

  55. 55

    J. Adams, S. Fielding, P. Olmsted, J. Non-Newton. Fluid Mech. 151, 101 (2008)

    Article  Google Scholar 

  56. 56

    C.Y.D. Lu, P.D. Olmsted, R. Ball, Phys. Rev. Lett. 84, 642 (2000)

    ADS  Article  Google Scholar 

  57. 57

    P.D. Olmsted, Rheol. Acta 47, 283 (2008)

    Article  Google Scholar 

  58. 58

    K.R. Purdy, Z. Dogic, S. Fraden, A. Rühm, L. Lurio, S.G.J. Mochrie, Phys. Rev. E 67, 031708 (2003)

    ADS  Article  Google Scholar 

  59. 59

    Z. Dogic, S. Fraden, Langmuir 16, 7820 (2000)

    Article  Google Scholar 

  60. 60

    M. Fardin, T. Ober, V. Grenard, T. Divoux, S. Manneville, G. McKinley, S. Lerouge, Soft Matter 8, 10072 (2012)

    ADS  Article  Google Scholar 

  61. 61

    N. Herdegen, S. Hess, Physica A 115, 281 (1982)

    ADS  Article  Google Scholar 

  62. 62

    W. Loose, S. Hess, Phys. Rev. A 37, 2099 (1988)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to R. Lugo-Frias.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lugo-Frias, R., Reinken, H. & Klapp, S.H.L. Shear banding in nematogenic fluids with oscillating orientational dynamics. Eur. Phys. J. E 39, 88 (2016). https://doi.org/10.1140/epje/i2016-16088-3

Download citation

Keywords

  • Topical Issue: Nonequilibrium Collective Dynamics in Condensed and Biological Matter