A lattice-gas model is constructed for oil-water-surfactant mixtures. The phase diagram of this model is obtained by using mean-field theory and Monte Carlo simulations aided by low temperature expansions. Microstructures, structure factors, and mean droplet lifetimes are also determined in some phases. Both two and three dimensions are studied, the former in more detail than the latter. It is shown that it is natural to interpret the paramagnetic phase in our model as a microemulsion. Our model is found to exhibit various properties that are in qualitative agreement with experimental observations of oil-water-surfactant mixtures: (1) two- and three-phase coexistence occurs between oil-rich, water-rich, and microemulsion phases along first-order phase boundaries or a triple line in certain regions of the phase diagram of our model; (2) the triple line, which ends in a tricritical point, is short and this leads to low oil- microemulsion and water-microemulsion interfacial tensions; (3) microstructures (including bicontinuous ones in three dimensions) and structure factors are similar to some experimental ones; (4) droplets in our microemulsion phase are long lived like their experimental counterparts; ( 5 ) long-lived, metastable phases, including long-period, lamellar, and glasslike phases, appear at low temperatures. The limitations of our model are discussed. Our study is compared with other studies of models of oil-water-surfactant mixtures.
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