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 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.
arXiv.org, e-print archive, cond-mat/0105372 in http://xxx.lanl.gov/, This document reports on a project carried out by the authors in March-August, 2000. While waiting for renewed funding the results where not properly written up, but left in the form found here. It now being clear that the project has definitively been discontinued, the unfinished report is deposited as e-Print as is, in the hope that some of it may be of some use to someone somewhere.