Published April 8, 2011
| public
Journal Article
The helicity and vorticity of liquid-crystal flows
- Creators
- Gay-Balmaz, François
- Tronci, Cesare
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 two dimensions. We extend all these results to particles of arbitrary shape by considering systems with fully broken rotational symmetry.
Additional Information
© 2011 The Royal Society. Received June 15, 2010. Accepted September 10, 2010. Published online before print October 6, 2010. We are indebted to Darryl Holm for his keen remarks about the relation between the modified vorticity and helicity conservation in the Ericksen–Leslie theory. Some of this work was carried out while visiting him at Imperial College London.Additional details
- Eprint ID
- 22863
- Resolver ID
- CaltechAUTHORS:20110314-133051902
- Created
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2011-03-15Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field