- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Porous nematic microfluidics for generation of umbilic defects and umbilic defect lattices

Jure Aplinc1, Stephen Morris2, and Miha Ravnik1,3,*

  • 1Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
  • 2Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom
  • 3Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

  • *miha.ravnik@fmf.uni-lj.si
PDF

Phys. Rev. Fluids 1, 023303 – Published 28 June, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.023303

Abstract

We demonstrate that porous nematic microfluidics is a potential route for the generation of nematic umbilic defects and regular umbilic defect lattices. By using numerical modeling we show that the mutual (backflow) coupling between the flow velocity and the orientation director field of the nematic liquid crystal leads to the formation of positive umbilic defects at local peaks and to the formation of negative umbilic defects at the local saddles in the flow profile. The number of flow peaks and the index of the flow saddles (i.e., the number of the valleys) are shown to be directly related to the strength of the umbilic defect, effectively relating the two fields at the geometrical level. The regular arrangement of the barriers in the porous channels is demonstrated to lead to the formation of regular lattices of umbilic defects, including square, triangular, and even kagome lattices. Experimental realization of such systems is discussed, with particular focus on microfluidic-tunable birefringent photonic band structures and lattices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (61)

  1. H. Bruus, Theoretical Microfluidics (Oxford University Press, Oxford, 2011).
  2. C. A. Stan, L. Guglielmini, A. K. Ellerbee, D. Caviezel, H. A. Stone, and G. M. Whitesides, Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels, Phys. Rev. E. 84, 036302 (2011).
  3. J. de Jong, M. J. Geerken, R. G. H. Lammertink, and M. Wessling, Porous microfluidic devices – fabrication and applications, Chem. Eng. Technol. 30, 309 (2007).
  4. P. Tabeling, Introduction to Microfluidics (Oxford University Press, Oxford, 2010).
  5. B. F. B. Silva, M. Zepeda-Rosales, N. Venkateswaran, B. J. Fletcher, L. G. Carter, T. Matsui, T. M. Weiss, J. Han, Y. Li, U. Olsson, and C. R. Safinya, Nematic director reorientation at solid and liquid interfaces under flow: SAXS studies in a microfluidic device, Langmuir 31, 4361 (2015).
  6. A Sengupta, U. Tkalec, M. Ravnik, J. M. Yeomans, C. Bahr, and S. Herminghaus, Liquid Crystal Microfluidics for Tunable Flow Shaping, Phys. Rev. Lett. 110, 048303 (2013).
  7. M. Ravnik and J. M. Yeomans, Confined Active Nematic Flow in Cylindrical Capillaries, Phys. Rev. Lett. 110, 026001 (2013).
  8. J. S. Lintuvuori, K. Stratford, M. E. Cates, and D. Marenduzzo, Colloids in Cholesterics: Size-Dependent Defects and Non-Stokesian Microrheology, Phys. Rev. Lett. 105, 178302 (2010).
  9. A. Sengupta, S. Herminghaus, and C. Bahr, Liquid crystal microfluidics: Surface, elastic and viscous interactions at microscales, Liq. Cryst. 2, 73 (2014).
  10. K. Stratford, O. Henrich, J. S. Lintuvuori, M. E. Cates, and D. Marenduzzo, Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials, Nat. Commun. 5, 3954 (2014).
  11. D. A. Beller, M. A. Gharbi, A. Honglawan, K. J. Stebe, S. Yang, and R. D. Kamien, Focal Conic Flower Textures at Curved Interfaces, Phys. Rev. X 3, 041026 (2013).
  12. Y. Xia, F. Serra, R. D. Kamien, K. J. Stebe, and S. Yang, Direct mapping of local director field of nematic liquid crystals at the nanoscale, Proc. Natl. Acad. Sci. USA 112, 15291 (2015).
  13. A Mertelj, D Lisjak, M. Drofenik, and M. Čopič, Ferromagnetism in suspensions of magnetic platelets in liquid crystal, Nature (London) 504, 237 (2013).
  14. A Mertelj, A. Rešetič, S. Gyergyek, D. Makovec, and M. Čopič, Anisotropic microrheological properties of chain-forming magnetic fluids, Soft Matter 7, 125 (2011).
  15. I Muševič, U Škarabot, M. Tkalec, M. Ravnik, and S. Žumer, Two-dimensional nematic coloidal crystals self-assembled by topological defects, Science 313, 954 (2006).
  16. M. B. Pandey, T. Porenta, J. Brewer, A. Burkart, S. Čopar, S. Žumer, and I. I. Smalyukh, Self-assembly of Skyrmion-dressed chiral nematic colloids with tangential anchoring, Phys. Rev. E 89, 060502(R) (2014).
  17. P. J. Ackerman, J. van de Lagemaat, and I. I. Smalyukh, Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals, Nat. Commun. 6, 6012 (2015).
  18. F. E. Mackay and C. Denniston, Locally stable diamond colloidal crystal formed in a cholesteric liquid crystal, Soft Matter 10, 4430 (2014).
  19. A. Sengupta, Topological constraints in a microfluidic platform, Liq. Cryst. 41, 290 (2014).
  20. M. Humar, M Ravnik, S. Pajk, and I. Muševič, Electrically tunable liquid crystal optical microresonators, Nat. Photon. 3, 595 (2009).
  21. M. Čančula, M. Ravnik, and S. Žumer, Generation of vector beams with liquid crystal disclination lines, Phys. Rev. E 90, 022503 (2014).
  22. J. L. Ericksen, Anisotropic fluids, Arch. Ration. Mech. Anal. 4, 231 (1959).
  23. G. Rienäcker, M. Kröger, and S. Hess, Chaotic orientational behavior of a nematic liquid crystal subjected to a steady shear flow, Phys. Rev. E 66, 040702 (2002).
  24. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, Cambridge, 1992).
  25. M. Kleman and O. D. Lavrentovich, Soft Matter Physics: An Introduction (Springer, New York, 2003).
  26. P.-G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1993).
  27. T. Stieger, S. Püschel-Schlotthauer, M. Schoen, and M. G. Mazza, Flow-induced deformation of closed disclination lines near a spherical colloid immersed in a nematic host phase, Mol. Phys. 114, 259 (2015).
  28. H. Stark and D. Ventzki, Stokes drag of spherical particles in a nematic environment at low Ericksen numbers, Phys. Rev. E 64, 031711 (2001).
  29. M. Tasinkevych, M. G. Campbell, and I. I. Smalyukh, Splitting, linking, knotting, and solitonic escape of topological defects in nematic drops with handles, Proc. Natl. Acad. Sci. USA 111, 16268 (2014).
  30. P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities, Sci. Rep. 2, 414 (2012).
  31. G. P. Alexander, B. G. Chen, E. A. Matsumoto, and R. D. Kamien, Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals, Rev. Mod. Phys. 84, 497 (2012).
  32. O. Lehmann, Über fliessende krystalle, Z. Phys. Chem. 4, 462 (1889).
  33. L. M. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, 1999).
  34. M. G. Clerc, E. Vidal-Henriquez, J. D. Davila, and M. Kowalczyk, Symmetry breaking of nematic umbilical defects through an amplitude equation, Phys. Rev. E 90, 012507 (2014).
  35. I. S. Aranson and L. Kramer, The world of complex ginzburg-landau equation, Rev. Mod. Phys. 74, 99 (2002).
  36. G. P. Bewley, M. S. Paoletti, K. R. Sreenivasan, and D. P. Lathrop, Characterisation of reconnecting vortices in superfluid helium, Proc. Natl. Acad. Sci. USA 105, 13707 (2008).
  37. F. Flossmann, K. O'Holleran, M. R. Dennis, and M. J. Padgett, Polarization Singularities in 2D and 3D Speckle Fields, Phys. Rev. Lett. 100, 203902 (2008).
  38. F. Cardano, E. Karimi, L. Marucci, C. de Lisio, and E. Santamato, Generation and dynamics of optical beams with polarization singularities, Opt. Express 21, 8815 (2013).
  39. V. Kumar and N. K. Viswanathan, Topological structures in vector-vortex beam fields, J. Opt. Soc. Am. B 31, A40 (2014).
  40. V. Vitelli, B. Jain, and R. D. Kamien, Topological defects in gravitational lensing shear fields, J. Cosmol. Astropart. Phys. 2009, 034 (2009).
  41. M. J. Bowick, L. Chandar, E. A. Schiff, and A. M. Srivastava, The cosmological Kibble mechanism in the laboratory: String formation in liquid crystals, Science 263, 943 (1994).
  42. A. Rapini, Umbilics: Static properties and shear-induced displacements, J. Phys. 34, 629 (1973).
  43. T. Machon and G. P. Alexander, Umbilic Lines in Orientational Order, Phys. Rev. X 6, 011033 (2016).
  44. A. Rapini, L. Léger, and A. Marinet, Umbilics: Static and dynamical properties, J. Phys. (Paris) Colloq. 36, C1-189 (1975).
  45. T. A. Kumar, V. S. S. Sastry, K. Ishikawa, H. Takezoe, N. V. Madhusudana, and S. Dhara, Effect of an electric field on defects in a nematic liquid crystal with variable surface anchoring, Liq. Cryst. 38, 971 (2011).
  46. J. G. Wei and S. H. Chen, Electric-field-induced director-field transition of nematic liquid crystal in a closed conical cavity, Jpn. J. Appl. Phys. 33, 6249 (1994).
  47. J. G. Wei and S. H. Chen, Stability of an umbilical director field of nematic liquid crystal in a closed conical cavity, Jpn. J. Appl. Phys. 33, L660 (1994).
  48. P. Kumar, U. S. Hiremath, C. V. Yelamaggad, A. G. Rossberg, and K. S. Krishnamurthy, Electroconvection in a homeotropic bent-rod nematic liquid crystal beyond the dielectric inversion frequency, J. Phys. Chem. B 112, 9753 (2008).
  49. I. I. Smalyukh, B. I. Senyuk, P. Palffy-Muhoray, O. D. Lavrentovich, H. Huang, E. C. Gartland, Jr., V. H. Bodnar, T. Kosa, and B. Taheri, Electric-field-induced nematic-cholesteric transition and three-dimensional director structures in homeotropic cells, Phys. Rev. E 72, 061707 (2005).
  50. P. Pieranski, B. Yang, L. J. Burtz, A. Camu, and F. Simonetti, Generation of umbilics by magnets and flows, Liq. Cryst. 40, 1593 (2013).
  51. P. Pieranski, Generation of umbilics by poiseuille flows, Eur. Phys. J. E 37, 24 (2014).
  52. R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, Vortex Induction via Anisotropy Stabilized Light-Matter Interaction, Phys. Rev. Lett. 109, 143901 (2012).
  53. R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, Harnessing Optical Vortex Lattices in Nematic Liquid Crystals, Phys. Rev. Lett. 111, 093902 (2013).
  54. I. Dierking, M. Ravnik, E. Lark, J. Healey, G. P. Alexander, and J. M. Yeomans, Anisotropy in annihilation dynamics of umbilic defects in nematic liquid crystal, Phys. Rev. E 85, 021703 (2012).
  55. I. Dierking, O. Marshall, J. Wright, and N. Bulleid, Annihilation dynamics of umbilical defects in nematic liquid crystals under applied electric fields, Phys. Rev. E 71, 061709 (2005).
  56. A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems: With Internal Microstructure (Oxford University Press, New York, 1994).
  57. D. Marenduzzo, E. Orlandini, M. E. Cates, and J. M. Yeomans, Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations, Phys. Rev. E 76, 031921 (2007).
  58. C. Denniston, D. Marenduzzo, E. Orlandini, and J. M. Yeomans, Lattice Boltzmann algorithm for three-dimensional liquid-crystal hydrodynamics, Philos. Trans. R. Soc. London 362, 1745 (2004).
  59. S. A. Edwards and Y. M. Yeomans, Spontaneous flow states in active nematics: A unified picture, Europhys. Lett. 85, 18008 (2009).
  60. The Gaussian shape of the flow peak and saddle is used only for convenience in the calculations, as in realistic flow profiles the exact functional shape can be very different. However, as long as the general peak or saddle shape is retained, the mutual coupling between the flow and orientation generates the umbilic defects.
  61. M. Škarabot, Ž. Lokar, and I. Muševič, Transport of particles by a thermally induced gradient of the order parameter in nematic liquid crystals, Phys. Rev. E 87, 062501 (2013).

Outline

Information

Phys. Rev. Fluids 1, 023303– Published 28 June, 2016
  • Received 12 January 2016
  • Revised 29 March 2016

©2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation