Gay-Balmaz, Francois
Tronci, Cesare
The helicity and vorticity of liquid-crystal flows
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
467
nematic liquid crystal
helicity
vorticity
Spin-Glasses
Hamiltonian-Dynamics
Hydrodynamics
Orientation
Stability
Equations
Systems
Fluids
2011
2011
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 two dimensions. We extend all these results to particles of arbitrary shape by considering systems with fully broken rotational symmetry.
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Journal Articles
10.1098/rspa.2010.0309