Vol. 6, No. 7-8, 2011

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ISSN: 1559-3959
Numerical investigation of director orientation and flow of nematic liquid crystals in a planar 1:4 expansion

Pedro A. Cruz, Murilo F. Tomé, Iain W. Stewart and Sean McKee

Vol. 6 (2011), No. 7-8, 1017–1030
Abstract
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Numerical solutions to the equations describing Ericksen–Leslie dynamic theory for 2D nematic liquid crystal flows subject to a magnetic field are obtained. The governing equations are solved by a finite difference technique based on the GENSMAC methodology. The resulting numerical technique was verified by comparing numerical solutions for 2D-channel flow by means of mesh refinement. To demonstrate the capabilities of this method, the flow of a nematic liquid crystal in a planar 1:4 expansion was simulated. Calculations were performed for various Ericksen and Reynolds numbers. The results showed that an increase in the Ericksen number caused the appearance of lip and corner vortices.

Keywords
nematic liquid crystal, Ericksen–Leslie equations, two-dimensional flow, finite difference
Milestones
Received: 13 August 2010
Revised: 13 December 2010
Accepted: 10 January 2011
Published: 21 December 2011
Authors
Pedro A. Cruz
Department of Applied Mathematics and Statistics
University of São Paulo
Av. Trabalhador São-carlense, 400
13560-970 São Carlos, SP
Brazil
Murilo F. Tomé
Department of Applied Mathematics and Statistics
University of São Paulo
Av. Trabalhador São-carlense, 400
13560-970 São Carlos, SP
Brazil
Iain W. Stewart
Department Mathematics and Statistics
University of Strathclyde
Livingstone Tower
26 Richmond street
Glasgow
G1 1XH
United Kingdom
Sean McKee
Department Mathematics and Statistics
University of Strathclyde
Livingstone Tower
26 Richmond street
Glasgow
G1 1XH
United Kingdom