Lattice model results for lamellar phases in slits

A mixture of oil, water, and surfactant confined between parallel hydrophilic walls is studied close to phase boundaries between lamellar and uniform phases within a vector lattice model in a mean-field approximation. Relations between energy and force-distance profiles, and the structure of the confined fluid (given by density profiles) are found and discussed. For large wall separations L elastic response to compression or decompression, accompanied by shrinking or swelling of the period lambda of the lamellar phase, is found for lamellar and induced (by capillary condensation) lamellar phases. Very good agreement with recent experiments is obtained. For L<4 lambda the system responds to decompression by swelling of the central, either oil- or water-rich layer, with the layers adsorbed at the surfaces remaining unaffected. The solvation force is very weak and independent of L when the central layer is swollen, and jumps to much larger values when new layers are introduced into the slit.