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Activity Induced Nematic Order in Isotropic Liquid Crystals

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Abstract

We use linear stability analysis to show that an isotropic phase of elongated particles with dipolar flow fields can develop nematic order as a result of their activity. We argue that ordering is favoured if the particles are flow-aligning and is strongest if the wavevector of the order perturbation is neither parallel nor perpendicular to the nematic director. Numerical solutions of the hydrodynamic equations of motion of an active nematic confirm the results. The instability is contrasted to the well-known hydrodynamic instability of an ordered active nematic.

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References

  1. Sanchez, T., Chen, D.T., DeCamp, S.J., Heymann, M., Dogic, Z.: Spontaneous motion in hierarchically assembled active matter. Nature 491(7424), 431 (2012)

    ADS  Google Scholar 

  2. Hardoüin, J., Hughes, R., Doostmohammadi, A., Laurent, J., Lopez-Leon, T., Yeomans, J.M., Ignés-Mullol, J., Sagués, F.: Reconfigurable flows and defect landscape of confined active nematics. Commun. Phys. 2(1), 1–9 (2019)

    Google Scholar 

  3. Weirich, K.L., Dasbiswas, K., Witten, T.A., Vaikuntanathan, S., Gardel, M.L.: Self-organizing motors divide active liquid droplets. Proc. Natl. Acad. Sci. USA 116(23), 11125 (2019)

    ADS  Google Scholar 

  4. Duclos, G., Blanch-Mercader, C., Yashunsky, V., Salbreux, G., Joanny, J.F., Prost, J., Silberzan, P.: Spontaneous shear flow in confined cellular nematics. Nat. Phys. 14(7), 728 (2018)

    Google Scholar 

  5. Saw, T.B., Doostmohammadi, A., Nier, V., Kocgozlu, L., Thampi, S., Toyama, Y., Marcq, P., Lim, C.T., Yeomans, J.M., Ladoux, B.: Topological defects in epithelia govern cell death and extrusion. Nature 544(7649), 212 (2017)

    ADS  Google Scholar 

  6. Di Leonardo, R., Angelani, L., Dell’Arciprete, D., Ruocco, G., Iebba, V., Schippa, S., Conte, M., Mecarini, F., De Angelis, F., Di Fabrizio, E.: Bacterial ratchet motors. Proc. Natl. Acad. Sci. USA 107(21), 9541 (2010)

    ADS  Google Scholar 

  7. Ramaswamy, S.: The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1(1), 323 (2010)

    ADS  Google Scholar 

  8. Bechinger, C., Di Leonardo, R., Löwen, H., Reichhardt, C., Volpe, G., Volpe, G.: Active particles in complex and crowded environments. Rev. Mod. Phys. 88(4), 045006 (2016)

    ADS  MathSciNet  Google Scholar 

  9. Illien, P., Golestanian, R., Sen, A.: ‘Fuelled’motion: phoretic motility and collective behaviour of active colloids. Chem. Soc. Rev. 46(18), 5508 (2017)

    Google Scholar 

  10. Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M., Simha, R.A.: Hydrodynamics of soft active matter. Rev. Mod. Phys. 85(3), 1143 (2013)

    ADS  Google Scholar 

  11. Koch, D.L., Subramanian, G.: Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  12. Thampi, S.P., Golestanian, R., Yeomans, J.M.: Vorticity, defects and correlations in active turbulence. Phil. Trans. R. Soc. A 372(2029), 20130366 (2014)

    ADS  Google Scholar 

  13. Giomi, L., Bowick, M.J., Ma, X., Marchetti, M.C.: Defect annihilation and proliferation in active nematics. Phys. Rev. Lett. 110(22), 228101 (2013)

    ADS  Google Scholar 

  14. Tjhung, E., Marenduzzo, D., Cates, M.E.: Spontaneous symmetry breaking in active droplets provides a generic route to motility. Proc. Natl. Acad. Sci. USA 109(31), 12381 (2012)

    ADS  Google Scholar 

  15. Shendruk, T.N., Doostmohammadi, A., Thijssen, K., Yeomans, J.M.: Dancing disclinations in confined active nematics. Soft Matter 13(21), 3853 (2017)

    ADS  Google Scholar 

  16. Wu, K.T., Hishamunda, J.B., Chen, D.T., DeCamp, S.J., Chang, Y.W., Fernández-Nieves, A., Fraden, S., Dogic, Z.: Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355(6331), eaal1979 (2017)

    MathSciNet  MATH  Google Scholar 

  17. Keber, F.C., Loiseau, E., Sanchez, T., DeCamp, S.J., Giomi, L., Bowick, M.J., Marchetti, M.C., Dogic, Z., Bausch, A.R.: Topology and dynamics of active nematic vesicles. Science 345(6201), 1135 (2014)

    ADS  Google Scholar 

  18. Metselaar, L., Yeomans, J.M., Doostmohammadi, A.: Topology and morphology of self-deforming active shells. Phys. Rev. Lett. 123, 208001 (2019)

    ADS  Google Scholar 

  19. Kawaguchi, K., Kageyama, R., Sano, M.: Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327 (2017)

    ADS  Google Scholar 

  20. Volfson, D., Cookson, S., Hasty, J., Tsimring, L.S.: Biomechanical ordering of dense cell populations. Proc. Natl. Acad. Sci. USA 105, 15346 (2008)

    ADS  Google Scholar 

  21. Nishiguchi, D., Nagai, K.H., Chaté, H., Sano, M.: Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria. Phys. Rev. E 95(2), 020601 (2017)

    ADS  Google Scholar 

  22. Mueller, R., Yeomans, J.M., Doostmohammadi, A.: Emergence of active nematic behavior in monolayers of isotropic cells. Phys. Rev. Lett. 122(4), 048004 (2019)

    ADS  Google Scholar 

  23. Simha, R.A., Ramaswamy, S.: Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89(5), 058101 (2002)

    ADS  MATH  Google Scholar 

  24. Voituriez, R., Joanny, J.F., Prost, J.: Spontaneous flow transition in active polar gels. Europhys. Lett. 70(3), 404 (2005)

    ADS  Google Scholar 

  25. Xi, W., Saw, T.B., Delacour, D., Lim, C.T., Ladoux, B.: Material approaches to active tissue mechanics. Nat. Rev. Mater. 4(1), 23 (2019)

    ADS  Google Scholar 

  26. Elgeti, J., Winkler, R.G., Gompper, G.: Physics of microswimmers-single particle motion and collective behavior: a review. Rep. Prog. Phys. 78(5), 056601 (2015)

    ADS  MathSciNet  Google Scholar 

  27. Thampi, S.P., Doostmohammadi, A., Golestanian, R., Yeomans, J.M.: Intrinsic free energy in active nematics. Europhys. Lett. 112(2), 28004 (2015)

    ADS  Google Scholar 

  28. de Gennes, P., Prost, J.: The Physics of Liquid Crystals. International series of monographs on physics. Clarendon Press, Oxford (1993)

    Google Scholar 

  29. Beris, A., Edwards, B.: Thermodynamics of Flowing Systems: with Internal Microstructure. Oxford Engineering Science Series. Oxford University Press, Oxford (1994)

    Google Scholar 

  30. Chaikin, P., Lubensky, T.: Principles of Condensed Matter Physics. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  31. Tóth, G., Denniston, C., Yeomans, J.M.: Hydrodynamics of topological defects in nematic liquid crystals. Phys. Rev. Lett. 88(10), 105504 (2002)

    ADS  Google Scholar 

  32. Edwards, S., Yeomans, J.: Spontaneous flow states in active nematics: a unified picture. Europhys. Lett. 85(1), 18008 (2009)

    ADS  Google Scholar 

  33. Giomi, L.: Geometry and topology of turbulence in active nematics. Phys. Rev. X 5, 031003 (2015)

    Google Scholar 

  34. Guillamat, P., Ignés-Mullol, J., Sagués, F.: Taming active turbulence with patterned soft interfaces. Nat. Commun. 8(1), 564 (2017)

    ADS  Google Scholar 

  35. Martínez-Prat, B., Ignés-Mullol, J., Casademunt, J., Sagués, F.: Selection mechanism at the onset of active turbulence. Nat. Phys. 15(4), 362 (2019)

    Google Scholar 

  36. Olmsted, P.D., Goldbart, P.M.: Isotropic-nematic transition in shear flow: state selection, coexistence, phase transitions, and critical behavior. Phys. Rev. A 46(8), 4966 (1992)

    ADS  Google Scholar 

  37. Lauga, E., Powers, T.R.: The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72(9), 096601 (2009)

    ADS  MathSciNet  Google Scholar 

  38. Saintillan, D.: Rheology of active fluids. Annu. Rev. Fluid Mech. 50, 563 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  39. Schiesser, W.: The Numerical Method of Lines: Integration of Partial Differential Equations. Elsevier Science, Amsterdam (2012)

    MATH  Google Scholar 

  40. Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., Viggen, E.: The Lattice Boltzmann Method: Principles and Practice. Graduate Texts in Physics. Springer, New York (2016)

    MATH  Google Scholar 

  41. Subramanian, G., Koch, D.L.: Critical bacterial concentration for the onset of collective swimming. J. Fluid Mech. 632, 359 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  42. Saintillan, D., Shelley, M.J.: Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100(17), 178103 (2008)

    ADS  Google Scholar 

  43. Saintillan, D., Shelley, M.J.: Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20(12), 123304 (2008)

    ADS  MATH  Google Scholar 

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Acknowledgements

We acknowledge Santhan Chandragiri for helpful discussions. A.D was supported by the Novo Nordisk Foundation (Grant agreement No. NNF18SA0035142)

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Correspondence to Sumesh P. Thampi.

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Communicated by Ivan Corwin.

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Santhosh, S., Nejad, M.R., Doostmohammadi, A. et al. Activity Induced Nematic Order in Isotropic Liquid Crystals. J Stat Phys 180, 699–709 (2020). https://doi.org/10.1007/s10955-020-02497-0

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  • DOI: https://doi.org/10.1007/s10955-020-02497-0

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