The helicity and vorticity of liquid crystal flows

Abstract

We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation for a modified vorticity involving both velocity and structure fields (e.g. director and alignment tensor). This equation for the modified vorticity shares many relevant properties with ideal fluid dynamics and it allows for vortex filament configurations as well as point vortices in 2D. We extend all these results to particles of arbitrary shape by considering systems with fully broken rotational symmetry.

22 pages; no figures

References in corpus (2)

• Hydrodynamics of topological defects in nematic liquid crystals
• Reduction theory for symmetry breaking with applications to nematic systems

Cited by in corpus (7)

• Equivalent theories of liquid crystal dynamics
• Lagrangian averaged stochastic advection by Lie transport for fluids
• Vlasov moment flows and geodesics on the Jacobi group
• Euler-Poincaré approaches to nematodynamics
• On a Navier-Stokes-Allen-Cahn model with inertial effects
• Distortional Lifshitz Vectors and Helicity in Nematic Free Energy Density
• Equivalent variational approaches to biaxial liquid crystal dynamics