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

P.A. Cruz, M.F. Tome, I.W. Stewart, S. McKee

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Abstract

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.
Original languageEnglish
Pages (from-to)143-157
Number of pages14
JournalJournal of Non-Newtonian Fluid Mechanics
Volume165
Issue number3-4
DOIs
Publication statusPublished - 2010

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Keywords

  • Three-dimensional flow
  • Ericksen–Leslie equations
  • Nematic liquid crystal
  • Finite difference
  • Analytic solution

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