Simulations of flow-induced director patterns in nematic liquid crystals through Leslie-Ericksen equations in two dimensions

A methodology for solving Leslie-Eriksen hydrodynamical equations in two dimensions is presented; applications to different geometries corresponding to common experimental setups are discussed. The non-linear system of partial differential equations, which describe the time evolution of the director field and of the velocity field for a nematic liquid crystal, are solved numerically. Time dependent distributions of the director orientations, influenced by competitive magnetic and mechanical torques are calculated to intepret rheological experiments