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Hydrodynamic theory for nematic shells: The interplay among curvature, flow, and alignment
Gaetano Napoli1, Luigi Vergori2
1Dipartimento di Ingegneria dell'Innovazione, Università del Salento, via per Monteroni, Edificio "Corpo O", 73100 Lecce, Italy.
Physical Review. E
|September 15, 2016
Summary
We developed new hydrodynamic equations for 2D nematic liquid crystals on curved surfaces. These equations link fluid flow, molecular alignment, and substrate curvature, offering insights into material behavior.
Area of Science:
- Soft Matter Physics
- Materials Science
- Fluid Dynamics
Background:
- Nematic liquid crystals (NLCs) exhibit unique properties due to anisotropic molecular alignment.
- Understanding NLC behavior on curved surfaces is crucial for applications in flexible electronics and microfluidics.
- Existing theories often simplify substrate interactions or assume flat surfaces.
Purpose of the Study:
- To derive comprehensive hydrodynamic equations for 2D nematic liquid crystals on curved substrates.
- To incorporate degenerate anchoring conditions and the Frank potential into the theoretical framework.
- To analyze the interplay between fluid dynamics, director alignment, and substrate geometry.
Main Methods:
- Adaptation of the Ericksen-Leslie theory using the Lagrange-Rayleigh variational principle.
- Development of constitutive assumptions for free-energy density (2D Frank potential) and dissipation.
- Derivation of coupled equations of motion for velocity, director, and curvature.
Main Results:
- The derived equations successfully couple the velocity field, director alignment, and shell curvature.
- Demonstrated the model's applicability by analyzing shear flow effects on a nematic on a cylindrical shell.
- Provided a theoretical framework for predicting 2D NLC behavior on complex geometries.
Conclusions:
- The new hydrodynamic model accurately describes 2D nematic liquid crystals on curved substrates.
- The findings offer a foundation for designing and controlling NLC-based devices on non-planar surfaces.
- This work advances the understanding of soft matter physics in curved environments.
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