The helicity and vorticity of liquid crystal flows

Details The helicity and vorticity of liquid crystal flows The helicity and vorticity of liquid crystal flows

2010-06-15

arxiv.org/abs/1006.2984v2

Physics

Condensed Matter

Soft Condensed Matter

22 pages; no figures

Scientific paper

10.1098/rspa.2010.0309

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.

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