Numerical approximations of a hydro-dynamically coupled phase-field model for binary mixture of passive/active nematic liquid crystals and viscous fluids

摘要

We consider in this paper numerical approximations for the hydro-dynamically coupled phase-field model for an immiscible binary mixture of passive/active nematic Liquid Crystals (LCs) and viscous fluids. The passive model is a highly coupled nonlinear system that consists of the incompressible Navier-Stokes equations, the Cahn-Hilliard equations, and the constitutive equation for the polarization field. The active model can be viewed as an assembly of a passive part and a phenomenological active part. We then construct an efficient and linear time marching scheme to solve the passive model and further extend it to solve the active model. Various numerical simulations are presented to demonstrate the stability and accuracy of the proposed scheme in simulating some simulations in 2D and 3D, including the drop deformation dynamics and spinodal decompositions.