The structure of a hard sphere fluid restricted by permeable walls

The structure of a hard sphere fluid restricted by permeable walls of thickness of the order of a molecular diameter is investigated by both computer simulation and theory. The permeable walls are represented by barriers with a finite height. Such a model has been introduced previously in the study of the behaviour of fluids in connected pores and of osmosis. Apart from the understanding of these processes that such a model can provide, the model also proves to be a good one on which to test different theories. These theories are all derived from density functionals and include Percus-Yevick (PY), hypernetted chain (HNC), Meister-Kroll and a modified form of Meister-Kroll. A surprising feature of the results is that, when compared with simulation, HNC provides as good density profiles as the more sophisticated theories. Presumably this will no longer be true when the theories are applied to fluids of molecules with long-range attractions. Not surprisingly, the predictions of PY get steadily worse as both the fluid density and the height of the barriers increase. None of the approximations agrees with the results of simulation over the entire range of parameters investigated.