  We study phase behaviour of a model fluid confined between two unlike
parallel walls in the presence of long range (dispersion) forces. Predictions
obtained from macroscopic (geometric) and mesoscopic arguments are compared
with numerical solutions of a non-local density functional theory. Two
capillary models are considered. For a capillary comprising of two
(differently) adsorbing walls we show that simple geometric arguments lead to
the generalized Kelvin equation locating capillary condensation very
accurately, provided both walls are only partially wet. If at least one of the
walls is in complete wetting regime, the Kelvin equation should be modified by
capturing the effect of thick wetting films by including Derjaguin's
correction. Within the second model, we consider a capillary formed of two
competing walls, so that one tends to be wet and the other dry. In this case,
an interface localized-delocalized transition occurs at bulk two-phase
coexistence and a temperature $T^*(L)$ depending on the pore width $L$. A
mean-field analysis shows that for walls exhibiting first-order wetting
transition at a temperature $T_{w}$, $T_{s}>T^*(L)>T_{w}$, where the spinodal
temperature $T_{s}$ can be associated with the prewetting critical point, which
also determines a critical pore width below which the interface
localized-delocalized transition does not occur. If the walls exhibit critical
wetting, the transition is shifted below $T_{w}$ and for a model with the
binding potential $W(\ell)=A(T)\ell^{-2}+B(T)\ell^{-3}+\cdots$, where $\ell$ is
the location of the liquid-gas interface, the transition can be characterized
by a dimensionless parameter $\kappa=B/(AL)$, so that the fluid configuration
with delocalized interface is stable in the interval between $\kappa=-2/3$ and
$\kappa\approx-0.23$.
