A lattice boltzmann scheme for a nematic-isotropic interface

A lattice Boltzmann (LB) model of an interface between a nematic and an isotropic fluid is presented. The method is used to study, in two dimensions, the properties of a deformable colloidal droplet of an isotropic fluid suspended in a nematic matrix. The isotropic fluid is modelled by a standard lattice Bhatnagar–Gross–Krook (LBGK) scheme. The LB model of the nematic is a modified LBGK scheme in which a tensor density is used to recover the variable order parameter nemato-dynamics scheme proposed by Qian and Sheng. The interface between the two fluids is modelled by introducing appropriate forcing at the interface. The stress balance is achieved using an extension of a method proposed by Lishchuk et al, and the torque balance is achieved with an appropriate surface molecular field. The resulting interface algorithm recovers the macroscopic equations developed by Rey. Results are presented for the dependence of the shape of the droplet and the nematic defects upon the surface tension and the anchoring strength. A discussion is also presented of the effect of curvature rigidity on the droplet shape.