A numerical method for solving the dynamic three-dimensional Ericksen–Leslie equations for nematic liquid crystals subject to a strong magnetic field

• Published in: Journal of non-Newtonian fluid mechanics Vol. 165; no. 3; pp. 143 - 157
• Main Authors: Cruz, Pedro A., Tomé, Murilo F., Stewart, Iain W., McKee, Sean
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 01.02.2010; Elsevier
• Subjects: Analytic solution; Cross-disciplinary physics: materials science; rheology; Ericksen–Leslie equations; Exact sciences and technology; Finite difference; Liquid crystals: nematic, cholesteric, smectic, discotic, etc; Material form; Nematic liquid crystal; Physics; Rheology; Three-dimensional flow; Finite difference; Analytic solution; Nematic liquid crystal; Three-dimensional flow; Ericksen–Leslie equations; Ericksen-Leslie equations; Fluid flow; Magnetic field effects; Boundary conditions; Numerical method; Nematic crystals; Three dimensional model; Analytical method; High field; Parallel flow; Channel flow; Dynamic model; Finite difference method
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2009.10.007

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen–Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tomé and McKee [32]; Tomé et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution.