Numerical solution of the Ericksen-Leslie dynamic equations for two-dimensional nematic liquid crystal flows

Author(s)

Cruz, Pedro A. ^[1] ; Tome, Murilo F. ^[1] ; Stewart, Iain W. ^[2] ; McKee, Sean ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Appl Math & Stat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark - Scotland

• Document type: Journal article
• Source: Journal of Computational Physics; v. 247, p. 109-136, AUG 15 2013.
• Web of Science Citations: 6

Abstract

A finite difference method for solving nematic liquid crystal flows under the effect of a magnetic field is developed. The dynamic equations of nematic liquid crystals, given by the Ericksen-Leslie dynamic theory, are employed. These are expressed in terms of primitive variables and solved employing the ideas behind the GENSMAC methodology (Tome and McKee, 1994; Tome et al., 2002) {[}38,41]. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. By employing fully developed flow assumptions an analytic solution for steady 2D-channel flow is found. The resulting numerical technique was then, in part, validated by comparing numerical solutions against this analytic solution. Convergence results are presented. To demonstrate the capabilities of the numerical method, the flow of a nematic liquid crystal through various complex geometries are then simulated. Results are obtained for L-shaped channels and planar 4:1 contraction for several values of Reynolds and Ericksen numbers. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 07/07038-2 - Numerical solution nematic liquid crystal
• Grantee: Pedro Alexandre da Cruz
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 04/16064-9 - Mechanics of non-stationary fluids: applications in aeronautics and rheology
• Grantee: José Alberto Cuminato
• Support Opportunities: Research Projects - Thematic Grants