Flow of a Nematic Liquid Crystal Around a Sphere

Abstract

The flow of an incompressible nematic liquid crystal around a sphere is studied for arbitrary angles between the director and the flow velocity at infinite distances. We assume low Reynolds numbers and a fixed director orientation for the calculation on the basis of the Leslie-Ericksen equations. The calculations are performed with a finite difference method which is a combination of the artificial compressibility method for the pressure determination and a simultaneous over-relaxation (SOR, SSOR) for the solution of the momentum equations. We find strong differences in the stream line patterns of a usual liquid crystal as compared with those of an isotropic liquid if the direction of the director is perpendicular to the flow velocity. The force on the sphere is calculated. Equations are presented which allow the determination of the force for a broad range of anisotropies of the viscosity coefficients. The falling direction of a sphere deviates from the direction of gravity by 25° for a liquid crystal with η₁: η₂: η₃ = 10:1:3 if the angle between director and direction of gravity is 58°.