We show that the flux-field expansion derived by Boghosian and Coveney for
the Rothman-Keller immiscible fluid model can be derived in a simpler and more
general way in terms of the completely symmetric tensor kernels introduced by
those authors. Using this generalised flux-field expansion we show that the
more complex amphiphilic model of Boghosian Coveney and Emerton can also be
derived from an underlying model of particle interactions. The consequences of
this derivation are discussed in the context of previous equilibrium Ising-like
lattice models and other non-equilibrium mesoscale models.Comment: To appear in Phil. Trans. Roy. Soc. (Proceedings of the Xth
International Conference on Discrete Simulation of Fluid Dynamics.
