The structure of a fluid confined by permeable walls

Osmosis has been studied using the methods of molecular dynamics and for several different models of a semi-permeable barrier. One of these models has also been used in theoretical and Monte Carlo investigations of the effect of such a barrier on the structure of a hard sphere fluid (Marsh, P., Rickayzen, G., and Calleja, M., 1995, Molec. Phys., 84, 799; Kim, S.-C., Calleja, M., and Rickayzen, G., 1995, J. Phys.: condens. Matter, 7, 8053). Results presented in these papers showed that this problem also provides a sensitive test for the validity of various density functional theories. In order to bring the theory to bear on the problem of osmosis, this earlier study is extended to the hard core Lennard-Jones fluid. At the same time a new sum rule for the density of a fluid in a periodic potential, which provides a useful check on the computations, is derived. It is again found that the agreement between the computed and the simulated density profiles is good except at the centre of the barrier and when the bulk density and pressure are close to the critical.