Numerical investigation of director orientation and flow of nematic liquid crystals in a planar 1:4 expansion

Numerical solutions to the equations describing Ericksen-Leslie dynamic theory for 2D nematic liquid crystal flows subject to a magnetic field are obtained.The governing equations are solved by a finite difference technique based on the GENSMAC methodology.The resulting numerical technique was verified by comparing numerical solutions for 2D-channel flow by means of mesh refinement.To demonstrate the capabilities of this method, the flow of a nematic liquid crystal in a planar 1:4 expansion was simulated.Calculations were performed for various Ericksen and Reynolds numbers.The results showed that an increase in the Ericksen number caused the appearance of lip and corner vortices.