A finite volume method for computing flow induced orientation of nematic liquid crystals. (13th April 2017)

• Record Type: Journal Article
• Authors: Ryan, Shawn D.; Richards, Gregory; Zheng, Xiaoyu; Palffy-Muhoray, Peter
• Is Part Of: Molecular crystals and liquid crystals. Volume 647(2017)
• Page Start: 207
• Page End: 215
• Publication Date: 2017-04-13
• Subjects: Orientational order -- liquid crystals -- phase transitions -- finite volume method; Molecular crystals -- Periodicals; Liquid crystals -- Periodicals; Liquid crystals; Molecular crystals; Periodicals; 548
• DOI: 10.1080/15421406.2017.1289594
• Languages: English
• ISSNs: 1542-1406

Abstract

ABSTRACT: In this work, we propose a new method for studying dynamics in a liquid crystal arising from torques due to an externally imposed shear flow or other sources of torque. Here a spatially homogeneous liquid crystal system governed by a Smoluchowski equation for the orientational probability density function is investigated. To analyze the PDE model, we develop a novel direct computational algorithm based on a Voronoi cell-based finite volume scheme. This method has the capability of describing abrupt changes in the density function, using fluxes through cell boundaries. We first validate our approach by capturing prior results from Maier-Saupe theory illustrating a phase transition in the system due to nematic interactions as well as the effects of an externally imposed electric field. We then investigate the coupling of an external flow field with the Smoluchowski equation describing the full orientational dynamics of the system.