Flow of a Nematic Liquid Crystal Around a Cylinder

The differential equations for the flow of an incompressible nematic liquid crystal perpendicular to an infinite long cylinder are developed for low Reynolds numbers and a fixed director orientation on the basis of the Leslie-Ericksen theory. Some general results are discussed. The velocities and the force on the cylinder only depend on the shear viscosity coefficients n1, n2, and α1, whereas the pressure additionally depends on the Leslie coefficient α5. In a “falling cylinder experiment”, the cylinder will not fall vertically if the director is neither parallel nor perpendicular to the gravitational field. Numerical calculations are performed with the aid of the artificial compressibility method. Stream line patterns as well as results on pressure and force on the cylinder are presented.