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

P.A. Cruz, Murilo F. Tome, Iain W. Stewart, Sean McKee

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 (Tomé and McKee, 1994; Tomé 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.
LanguageEnglish
Pages109-136
Number of pages28
JournalJournal of Computational Physics
Volume247
DOIs
Publication statusPublished - 15 Aug 2013

Fingerprint

Nematic liquid crystals
liquid crystals
Angular momentum
conservation equations
channel flow
Channel flow
Nonlinear equations
Finite difference method
partial differential equations
Partial differential equations
nonlinear equations
contraction
Conservation
Numerical methods
angular momentum
methodology
Magnetic fields
momentum
Geometry
geometry

Keywords

  • two-dimensional flow
  • Ericksen-Leslie equations
  • nematic liquid crystal
  • analytic solution
  • finite difference

Cite this

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title = "Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows",
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 (Tom{\'e} and McKee, 1994; Tom{\'e} 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.",
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Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows. / Cruz, P.A.; Tome, Murilo F.; Stewart, Iain W.; McKee, Sean.

In: Journal of Computational Physics, Vol. 247, 15.08.2013, p. 109-136.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows

AU - Cruz, P.A.

AU - Tome, Murilo F.

AU - Stewart, Iain W.

AU - McKee, Sean

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N2 - 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 (Tomé and McKee, 1994; Tomé 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.

AB - 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 (Tomé and McKee, 1994; Tomé 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.

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