Lattice Boltzmann nemato-dynamics

Lattice Boltzmann (LB) methods have been extensively studied for the mesoscopic modelling of isotropic fluids but little attention has been given to the problem of modelling anisotropic fluids. In this paper an LB scheme is presented which recovers the equations of the Ericksen-Leslie-Parodi theory of nemato-dynamics. The scheme introduces a second distribution which advects with the LB momentum densities and which represents the orientation of an ordered fluid element. The momentum evolution scheme requires the use of a linearized LB scheme with an anisotropic scattering matrix and the director evolution is achieved with an LBGK scheme. Results are presented which are in good agreement with the predictions of a Chapman-Enskog analysis of the algorithm. The method provides an initial step in the development of mesoscopic algorithms for modelling the flow of anisotropic fluids.