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Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers. Sebastian Heidenreich, Patrick Ilg, and Siegfried Hess; Institute for Theoretical Physics, TU Berlin; Institute for Polymer Physics, ETH Zuerich contact: sebastian@itp.physik.tu-berlin.de;

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Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

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  1. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers Sebastian Heidenreich, Patrick Ilg, and Siegfried Hess; Institute for Theoretical Physics, TU Berlin; Institute for Polymer Physics, ETH Zuerich contact: sebastian@itp.physik.tu-berlin.de; s.hess@physik.tu-berlin.de

  2. Overview • Model equations: • Relaxation equations for the alignment tensor • Hydrodynamic equations and constitutive equations for the pressure tensor • Scaled model equations • Flow effects of tumbling nematics: • Apparent slip flow; hydrodynamical jets • Shear band flow and fluctuations Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  3. For fluids consisting of • nano-rods the orientation • couples with the flow. Phases: The shape of molecules is modeled by hard rods orientation isotropic phase nematic phase Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  4. Orientational degree of freedom: disk-like rod-like Model variables alignment tensor symmetric traceless Flow: Flow velocity: Strain rate: Vorticity: (stress tensor) Pressure tensor: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  5. ... diffusion coefficient Model equations Dynamical equations for the alignment tensor: Alignment flux tensor: Derivative of the model potential: S. Hess, Z. Naturforsch. 30a, p. 728 (1975); C. Pereira Borgmeyer and S. Hess J. Non-Equilib. Thermodyn. 20, p. 359 (1995) Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  6. Landau-de Gennes potential (uniaxial) nematic phase isotropic phase Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  7. Constitutive relation for the pressure tensor momentum balance: Costitutive equations: C. Pereira Borgmeyer and S. Hess J. Non-Equilib. Thermodyn. 20, p. 359 (1995) Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  8. Complete set of equations and boundary conditions: dynamical equation for the alignment tensor constitutive equation momentum balance equation Boundary conditions: strong anchoring alingment flux Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  9. Plane Couette flow geoemtry Effective one dimensional problem: Scaling: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  10. Scaled model equations Relaxation equation: Momentum balance equation: Pressure tensor: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  11. Parameters Scaled second newtonian viscosity: Reynold number: Eriksen number : Deborah number : Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  12. Numerical results • Explicit finite difference scheme of 4th/3th order (400 grid points) • Time integration with a 4th order adaptive Runge Kutta algorithm • Nematic phase • No alignment flux • Low Reynold number • Boundary conditions: Strong anchoring: No slip condition: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  13. Parameters: Apparent slip flow and hydrodyn. jets Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  14. Apparent slip: Hydrodynamical jet: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  15. Orientational dynamics Very low values of the order parameter. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  16. inflection point The generation of jets The first jet starts at time Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  17. Order parameter vs. hydrodynamical jet Parameters: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  18. III II I Definition of different layers Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  19. III II I Dynamics of the order parameter I II III Orbits of the alignment tensor components. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  20. Angle between the main director and the x-Axes in the shear plane wagging tumbling I tumbling II Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  21. Angle between the main director and the x-Axes in the shear plane wagging tumbling I tumbling II Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  22. Angle between the main director and the x-Axes in the shear plane Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  23. Time where the jet generates and decays. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  24. Jet generation Frank elasticity Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  25. Visualization of the alignment tensor The length of the edge are given by the eigenvalues. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  26. Shear band fluctuations Parameters: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  27. Shear band fluctuations two four The transition between the bands is driven by the jets. three bands Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  28. Shear band fluctuations odinary Couette flow profile Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  29. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  30. Stable shear bands Parameters: Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  31. Stable shear band flow Stable shear band flow Shear band fluctuations Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  32. Orientational dynamics Stable shear band flow Shear band fluctuations Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  33. Conclusions • Hydrodynamic jets emerge as a consequence of the interplay of the Frank elasticity, Wall-effects and the flow coupling. • Shear band fluctuations are driven by hydrodynamic jets • For small Frank elasticity constant and high shear the shear bands are stable. Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

  34. Slip Stream Thank you for your attention! Thanks to:Siegfried Hess,Patrick Ilg,Stefan Grandner Russ Albright Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

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