### Abstract

Language | English |
---|---|

Pages | 30-45 |

Number of pages | 16 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 268 |

Early online date | 18 Apr 2019 |

DOIs | |

Publication status | Published - 30 Jun 2019 |

### Fingerprint

### Keywords

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

### Cite this

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*Journal of Non-Newtonian Fluid Mechanics*, vol. 268, pp. 30-45. https://doi.org/10.1016/j.jnnfm.2019.04.004

**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.

Research output: Contribution to journal › Article

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

Y1 - 2019/6/30

N2 - 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.

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

KW - liquid crystalline polymers

KW - free-surface flows

KW - injection molding process

KW - finite difference

UR - https://www.journals.elsevier.com/journal-of-non-newtonian-fluid-mechanics

U2 - 10.1016/j.jnnfm.2019.04.004

DO - 10.1016/j.jnnfm.2019.04.004

M3 - Article

VL - 268

SP - 30

EP - 45

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -