Frame hydrodynamics of biaxial nematics from molecular-theory-based tensor models

TL;DR

This paper derives a frame hydrodynamics model for biaxial nematics from a molecular tensor model, ensuring energy dissipation and connecting it to classical Ericksen--Leslie theory.

Contribution

It introduces a novel derivation of biaxial nematic hydrodynamics from a molecular tensor framework using Hilbert expansion.

Findings

Derived frame model coefficients from tensor model

Maintains energy dissipation in the derived model

Reduces to Ericksen--Leslie model under uniaxial conditions

Abstract

Starting from a dynamic tensor model about two second-order tensors, we derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert expansion. The coefficients in the frame model are derived from those in the tensor model. The energy dissipation of the tensor model is maintained in the frame model. The model is reduced to the Ericksen--Leslie model if the biaxial bulk energy minimum of the tensor model is reduced to a uniaxial one.