Lattice-Boltzmann simulations of complex fluids

We show that by including thermodynamic functions derived from a chosen free energy in a lattice-Boltzmann simulation of fluid how it is possible to ensure that the fluid relaxes to a well-defined equlilibrium corresponding to the minimum of the input free energy. Two examples are given of phase separation in a binary fluid: bulk two-phase coexistence and a lamellar phase stabilised by a competition between negative surface tension and positive curvature energy. The lattice-Boltzmann framework simulates the Navier-Stokes equations of fluid flow and hence allows investigation of the effects of hydrodynamics on the kinetics of phase separation and on the rheology of the ordered structures.