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.
- nematic liquid crystal
- Ericksen–Leslie equations
- finite difference
- two-dimensional flow
Cruz, P. A., Tome, M. F., Stewart, I., & Mckee, S. (2011). Numerical investigation of director orientation and flow of nematic liquid crystal in a planar 1:4 expansion. Journal of Mechanics of Materials and Structures, 6(7-8), 1017-1030. https://doi.org/10.2140/jomms.2011.6.1017