Microrheology and Rheological Phenomena in Microfluidics

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Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 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 TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 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 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 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 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Model variables Orientational degree of freedom: rod-like disk-like alignment tensor symmetric traceless Flow: Flow velocity: Vorticity: Strain rate: Pressure tensor: (stress tensor) 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Model equations Dynamical equations for the alignment tensor: Alignment flux tensor: ... diffusion coefficient 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) 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Landau-de Gennes potential Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Landau-de Gennes potential (uniaxial) nematic phase isotropic phase 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Constitutive relation for the pressure tensor Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Constitutive relation for the pressure tensor momentum balance: Costitutive equations: C. Pereira Borgmeyer and S. Hess J. Non-Equilib. Thermodyn. 20, p. 359 (1995) 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Complete set of equations and boundary conditions: dynamical equation for the alignment tensor constitutive equation momentum balance equation Boundary conditions: strong anchoring alingment flux 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Plane Couette flow geoemtry Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Plane Couette flow geoemtry Effective one dimensional problem: Scaling: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Scaled model equations Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Scaled model equations Relaxation equation: Momentum balance equation: Pressure tensor: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Parameters Scaled second newtonian viscosity: Reynold number: Eriksen number : Deborah number : 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 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: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Apparent slip flow and hydrodyn. jets Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Apparent slip flow and hydrodyn. jets Parameters: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Apparent slip: Hydrodynamical jet: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Orientational dynamics Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Orientational dynamics Very low values of the order parameter. 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 The generation of jets inflection point The first jet starts at time 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Order parameter vs. hydrodynamical jet Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Order parameter vs. hydrodynamical jet Parameters: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Definition of different layers I III II 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Dynamics of the order parameter I II III I III II Orbits of the alignment tensor components. 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Angle between the main director and the x-Axes in the shear plane wagging tumbling I tumbling II 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Angle between the main director and the x-Axes in the shear plane wagging tumbling I tumbling II 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Angle between the main director and the x-Axes in the shear plane 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Time where the jet generates and decays. 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Jet generation Frank elasticity 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

Visualization of the alignment tensor Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Visualization of the alignment tensor The length of the edge are given by the eigenvalues. 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Shear band fluctuations Parameters: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

Shear band fluctuations Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Shear band fluctuations two four The transition between the bands is driven by the jets. three bands 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Shear band fluctuations Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Shear band fluctuations odinary Couette flow profile 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Stable shear bands Parameters: 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Stable shear band flow Shear band fluctuations Stable shear band flow 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

Orientational dynamics Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Orientational dynamics Shear band fluctuations Stable shear band flow 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.

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. 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers

Thank you for your attention! Microrheology and Rheological Phenomena in Microfluidics 08/12/2018 Slip Stream Thanks to: Siegfried Hess, Patrick Ilg, Stefan Grandner Russ Albright Thank you for your attention! 08/12/2018 Wall-effects on the flow of nematic liquid crystals and liquid crystal polymers TU Berlin Hess et. al.