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 $L<\mathrm{}4\mathrm{}\lambda$ 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.