Lattice Boltzmann for Binary Fluids with Suspended Colloids

A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number of simple benchmark problems involving a single particle at or near a fluid-fluid interface are undertaken and show good agreement with available theoretical or numerical results.