Generalized lattice Boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter

Area of Science:

• Computational physics
• Fluid dynamics
• Materials science

Background:

• Nematic liquid crystals exhibit complex hydrodynamic behaviors.
• Existing models often require significant computational resources.
• Accurate simulation of tensor order parameter dynamics is crucial.

Purpose of the Study:

• To develop a novel lattice Boltzmann (LB) scheme for simulating nematic liquid crystal hydrodynamics.
• To generalize the standard LB scalar density to a tensor quantity.
• To validate the scheme against analytical results and explore its applicability.

Main Methods:

• A generalized lattice Boltzmann equation with a direction-dependent Bhatnagar, Gross, and Krook (BGK) collision term was employed.
• Forcing terms were incorporated to account for antisymmetric stress tensor components.
• Chapman-Enskog analysis confirmed the recovery of Qian-Sheng equations with a sixth-order isotropic lattice.

Main Results:

• The LB scheme successfully recovered macroscopic properties like momentum, density, and tensor order parameter.
• The method accurately simulated flow alignment of the order tensor and Miesowicz viscosities.
• The algorithm demonstrated accurate prediction of order parameter changes under aligning flow and magnetic fields.

Conclusions:

• The developed lattice Boltzmann scheme provides an effective computational tool for nematic liquid crystal hydrodynamics.
• The generalization to a tensor order parameter enhances the scheme's capability to capture complex fluid behaviors.
• Preliminary results suggest potential for modeling interfaces between isotropic and nematic fluids.