Linear unconditional energy-stable splitting schemes for a phase-field model for nematic-isotropic flows with anchoring effects

Two-phase flows composed of fluids exhibiting different microscopic structure are an important class of engineering materials. The dynamics of these flows are determined by the coupling among three different length scales: microscopic inside each component, mesoscopic interfacial morphology, and macroscopic hydrodynamics. Moreover, in the case of complex fluids composed by the mixture between isotropic (Newtonian fluid) and nematic (liquid crystal) flows, its interfaces exhibit novel dynamics due to anchoring effects of the liquid crystal molecules on the interface. Firstly, we have introduced a new differential problem to model nematic-isotropic mixtures, taking into account viscous, mixing, nematic, and anchoring effects and reformulating the corresponding stress tensors in order to derive a dissipative energy law. Then, we provide two new linear unconditionally energy-stable splitting schemes. Moreover, we present several numerical simulations in order to show the efficiency of the proposed numerical schemes and the influence of the different types of anchoring effects in the dynamics of the system. Copyright (C) 2016 John Wiley & Sons, Ltd.