Numerical Investigation of Tumbling Phenomena Based on a Macroscopic Model for Hydrodynamic Nematic Liquid Crystals (Communications in Computational Physics, 2018)
This paper is concerned with the numerical investigation of a macroscopicmodel for complex fluids in “1+2” dimension case. We consider the planar pressuredriven flow where the direction of the molecules is constrained in the shear plane. Themodified Crank-Nicolson finite difference scheme satisfying a discrete energy law willbe developed. By using this scheme, it is observed numerically that the direction ofthe molecules will tumble from the boundary layer and later on the inner layer with amuch longer time period. This is consistent with the theoretical prediction. Moreover,we find some complex phenomena, where the tumbling rises from boundary layer andis then embedded into the interior area more clearly when the viscosity coefficient µ ofthe macro flow has a larger value. The norm of the molecular director d will enduregreater change as well. This implies that the viscosity of flow plays the role of anaccelerator in the whole complex fluids. Comparing these results with the theoreticalanalysis, we can find that the gradient of the velocity has direct impact on the tumblingphenomena. These results show that the proposed scheme is capable of exploringsome physical phenomena embedded in the macro-micro model.