Splitting schemes for mixtures of nematic-isotropic flows with anchoring effects

Abstract

This work is devoted to the study of complex fluids composed by the mixture between isotropic (newtonian fluid) and nematic (liquid crystal) flows, taking into account how the liquid crystal molecules behave on the interface between both fluids (anchoring effects) and the influence of the shape of the liquid crystal molecules on the dynamics of the system (stretching effects). First, we present the PDE system to model Nematic-Isotropic mixtures, taking into account viscous, mixing, nematic, anchoring and stretching effects. Then, we provide a new linear unconditionally energy-stable splitting scheme. Moreover, we present numerical simulations to show the efficiency of the proposed numerical scheme and the influence of the different types of anchoring effects in the dynamics of the system.