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

Author(s)

Cruz, Pedro A. ^[1] ; Tome, Murilo F. ^[2] ; McKee, Sean ^[3] ; Stewart, Iain W. ^[4]

Affiliation

^[1] Fed Univ Tocantins, Sci & Biotechnol, Gurupi, TO - Brazil

^[2] Univ Sao Paulo, Dept Appl Math & Stat, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Strathclyde, Dept Math & Stat, Glasgow, Lanark - Scotland

^[4] Univ Strathclyde, Fac Sci, Glasgow, Lanark - Scotland

• Document type: Journal article
• Source: Journal of Non-Newtonian Fluid Mechanics; v. 268, p. 30-45, JUN 2019.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC