  We consider a model fluid with long-ranged, dispersion interparticle
potentials confined between competing parallel walls. One wall is solvophilic
and would be completely wet at bulk liquid-gas coexistence while the other is
solvophobic and would be completely dry at bulk coexistence. When the wall
separation L is large and the system is below the bulk critical temperature and
close to bulk liquid-gas coexistence, a `delocalized interface' or `soft mode'
phase forms with a liquid-gas interface near to the centre of the slit; this
interacts with the walls via the power-law tails of the interparticle
potentials. We use a coarse-grained effective Hamiltonian approach to derive
explicit scaling expressions for the Gibbs adsorption, the surface tension, the
solvation force and the total susceptibility. Using a non-local density
functional theory (DFT) we calculate density profiles for the asymmetrically
confined fluid at different chemical potentials and, for sufficiently large L,
confirm the scaling predictions for the four thermodynamic quantities. Since
the upper critical dimension for complete wetting with power-law potentials is
<3 we argue that our (mean-field) scaling predictions should remain valid in
treatments that incorporate the effects of interfacial fluctuations. As the
wall separation L is decreased at bulk liquid-gas coexistence we predict a
capillary evaporation transition from the `delocalized interface' phase to a
dilute gas state with just a thin adsorbed film of liquid-like density next to
the solvophilic wall. This transition is connected closely to the first order
pre-wetting transition which occurs at the solvophilic wall in the
semi-infinite system. We compare the phase diagram for the competing walls
system with the phase diagrams for the fluid confined between identical
solvophilic and identical solvophobic walls.
