A lattice Boltzmann scheme for a nematic–isotropic interface

Abstract

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