  This document reports investigations of models of multiphase flows using
Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog
techniques the corresponding macroscopic equations. The singular interface
(Young-Laplace-Gauss) model is described briefly, with a discussion of its
limitations. The diffuse interface theory is discussed in more detail, and
shown to lead to the singular interface model in the proper asymptotic limit.
The Lattice Boltzmann method is presented in its simplest form appropriate for
an ideal gas. Four different Lattice Boltzmann models for non-ideal
(multi-phase) isothermal flows are then presented in detail, and the resulting
macroscopic equations derived. Partly in contradiction with the published
literature, it is found that only one of the models gives physically fully
acceptable equations. The form of the equation of state for a multiphase system
in the density interval above the coexistance line determines surface tension
and interface thickness in the diffuse interface theory. The use of this
relation for optimizing a numerical model is discussed. The extension of
Lattice Boltzmann methods to the non-isothermal situation is discussed
summarily.
