Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring

Cousins, J. R. L. , Wilson, S.K., Mottram, N. J. , Wilkes, D. and Weegels, L. (2020) Transient flow-driven distortion of a nematic liquid crystal in channel flow with dissipative weak planar anchoring. Physical Review E, 102(6), 062703. (doi: 10.1103/PhysRevE.102.062703)

Abstract

Motivated by the One-Drop-Filling (ODF) method for the industrial manufacturing of Liquid Crystal Displays (LCDs), we analyse pressure driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasi-steady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number the solution for the director angle is dominated by elastic effects with viscous effects appearing at first order. As the Ericksen number varies there is a continuous transition between these asymptotic behaviours and, in fact, the two asymptotic solutions capture the behaviour rather well for all values of the Ericksen number. The steady state value of the director angle at the boundaries and the timescale of the evolution towards this steady state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mottram, Professor Nigel and Cousins, Dr Joseph
• Authors: Cousins, J. R. L., Wilson, S.K., Mottram, N. J., Wilkes, D., and Weegels, L.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Physical Review E
• Publisher: American Physical Society
• ISSN: 1539-3755
• ISSN (Online): 1550-2376
• Published Online: 18 December 2020
• Copyright Holders: Copyright © 2020 American Physical Society
• First Published: First published in Physical Review E 102:062703
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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