Numerical solution of the Ericksen-Leslie model for liquid crystalline polymers free surface flows

Pedro A. Cruz, Murilo F. Tomé, Sean McKee, Iain W. Stewart

Research output: Contribution to journalArticle

Abstract

In this paper we present a finite difference method on a staggered grid for solving two-dimensional free surface flows of liquid crystalline polymers governed by the Ericksen–Leslie dynamic equations. The numerical technique is based on a projection method and employs Cartesian coordinates. The technique solves the governing equations using primitive variables for velocity, pressure, extra-stress tensor and the director. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. Code verification and convergence estimates are effected by solving a flow problem on 5 different meshes. Two free surface problems are tackled: A jet impinging on a flat surface and injection molding. In the first case the buckling phenomenon is examined and shown to be highly dependent on the elasticity of the fluid. In the second case, injection molding of two differently shaped containers is carried out and the director is shown to be strongly dependent on its orientation at the boundaries.
LanguageEnglish
Pages30-45
Number of pages16
JournalJournal of Non-Newtonian Fluid Mechanics
Volume268
Early online date18 Apr 2019
DOIs
Publication statusPublished - 30 Jun 2019

Fingerprint

Leslie model
Liquid Crystalline Polymer
Injection Molding
injection molding
Free Surface Flow
Liquid crystal polymers
Numerical Solution
primitive equations
Impinging Jet
Injection molding
Staggered Grid
Convergence Estimates
Balance Laws
Mass Conservation
Cartesian coordinates
Dependent
conservation equations
polymers
Stress Tensor
stress tensors

Keywords

  • Ericksen–Leslie model
  • liquid crystalline polymers
  • free-surface flows
  • injection molding process
  • finite difference

Cite this

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title = "Numerical solution of the Ericksen-Leslie model for liquid crystalline polymers free surface flows",
abstract = "In this paper we present a finite difference method on a staggered grid for solving two-dimensional free surface flows of liquid crystalline polymers governed by the Ericksen–Leslie dynamic equations. The numerical technique is based on a projection method and employs Cartesian coordinates. The technique solves the governing equations using primitive variables for velocity, pressure, extra-stress tensor and the director. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. Code verification and convergence estimates are effected by solving a flow problem on 5 different meshes. Two free surface problems are tackled: A jet impinging on a flat surface and injection molding. In the first case the buckling phenomenon is examined and shown to be highly dependent on the elasticity of the fluid. In the second case, injection molding of two differently shaped containers is carried out and the director is shown to be strongly dependent on its orientation at the boundaries.",
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Numerical solution of the Ericksen-Leslie model for liquid crystalline polymers free surface flows. / Cruz, Pedro A.; Tomé, Murilo F.; McKee, Sean; Stewart, Iain W.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 268, 30.06.2019, p. 30-45.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical solution of the Ericksen-Leslie model for liquid crystalline polymers free surface flows

AU - Cruz, Pedro A.

AU - Tomé, Murilo F.

AU - McKee, Sean

AU - Stewart, Iain W.

PY - 2019/6/30

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AB - In this paper we present a finite difference method on a staggered grid for solving two-dimensional free surface flows of liquid crystalline polymers governed by the Ericksen–Leslie dynamic equations. The numerical technique is based on a projection method and employs Cartesian coordinates. The technique solves the governing equations using primitive variables for velocity, pressure, extra-stress tensor and the director. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. Code verification and convergence estimates are effected by solving a flow problem on 5 different meshes. Two free surface problems are tackled: A jet impinging on a flat surface and injection molding. In the first case the buckling phenomenon is examined and shown to be highly dependent on the elasticity of the fluid. In the second case, injection molding of two differently shaped containers is carried out and the director is shown to be strongly dependent on its orientation at the boundaries.

KW - Ericksen–Leslie model

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KW - free-surface flows

KW - injection molding process

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