Phase transitions of fluids in heterogeneous pores

Abstract: 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 $\kappa\approx-0.23$.