  Utilizing a 3D mean-field lattice-gas model, we analyze the effect of
confinement on the nature of capillary phase transition in granular aggregates
with varying disorder and their inverse porous structures obtained by
interchanging particles and pores. Surprisingly, the confinement effects are
found to be much less pronounced in granular aggregates as opposed to porous
structures. We show that this discrepancy can be understood in terms of the
surface-surface correlation length with a connected path through the fluid
domain, suggesting that this length captures the true degree of confinement. We
also find that the liquid-gas phase transition in these porous materials is of
second order nature near capillary critical temperature, which is shown to
represent a true critical temperature, i.e. independent of the degree of
disorder and the nature of solid matrix, discrete or continuous. The critical
exponents estimated here from finite-size scaling analysis suggest that this
transition belongs to the 3D random field Ising model universality class as
hypothesized by P.G. de Gennes, with the underlying random fields induced by
local disorder in fluid-solid interactions.
