Finite element simulation of flow and director orientation of viscous anisotropic fluids in complex 2D geometries

Abstract

A simplified model of the Leslie–Ericksen theory is used to solve the flow of liquid crystalline polymers, seen as viscous anisotropic fluids, making the assumptions of high viscosities and neglecting the director elasticity in the viscosity terms. The resulting equations, known as Ericksen’s ‘‘Transversely Isotropic Fluids’’ equations involve four rheological parameters. Axisymmetrical isothermal steady flows are considered and the problem is divided into two parts using the method of the fixed point. The velocity calculation is performed by a variational method and a functional minimization technique and the equations are discretized with a finite element method. The director computation is made using a method of characteristics. The results of the computations describe the behavior of anisotropic viscous fluids as a function of flow geometries and rheological coefficients. Complex geometries including converging and diverging channels, expansion and contraction flows, as well as flow around spherical obstacles, are computed. The relative influence of the rheological parameters is also tested.