The effective interaction between two planar walls immersed in a fluid is
investigated by use of Density Functional Theory in the super-critical region
of the phase diagram. A hard core Yukawa model of fluid is studied with special
attention to the critical region. To achieve this goal a new formulation of the
Weighted Density Approximation coupled with the Hierarchical Reference Theory,
able to deal with critical long wavelength fluctuations, is put forward and
compared with other approaches. The effective interaction between the walls is
seen to change character on lowering the temperature: The strong oscillations
induced by layering of the molecules, typical of the depletion mechanism in
hard core systems, are gradually smoothed and, close to the critical point, a
long range attractive tail emerges leading to a scaling form which agrees with
the expectations based on the critical Casimir effect. Strong corrections to
scaling are seen to affect the results up to very small reduced temperatures.
By use of Derjaguin approximation, this investigation has natural implications
for the aggregation of colloidal particles in critical solvents.Comment: 15 pages, 16 figure
