Application of material balance for the phase transition of fluid mixtures confined in nanopores

Abstract

It has been customary to describe the phase equilibria of confined fluids using an equation of state (EOS) coupled with the Young-Laplace equation to account for the effect of surface curvature due to confinement. The equilibrium phases in this approach are the vapor (V) in the bulk phase and the confined liquid-like phase (ℓ) in the pores, which are separated by a surface that introduces a pressure difference between the phases. Consequently, we refer to this approach as the Vℓ method. The condition of phase transitions for confined fluids has been assumed to be the same as that for bulk fluids, so that calculations for dew-point and bubble-point curves do not need a material balance because the mole fraction of the condensed phase is zero for the former and unity for the latter. However, the situation of confined fluids is different from that in the bulk because the equilibrium phases reside in separate regions that have different pressures. In the Vℓ method, the vapor phase resides in the bulk and drives the chemical potential of the whole system, while the liquid-like phase condenses inside the pores subject to strong interaction with the pore wall. As discussed in the paper, this situation needs a material balance to comprehensively describe the phase transitions. Supporting evidence is also presented from a static experiment using a gravimetric apparatus. New insights derived from generalization of the Vℓ method in this work enable further investigations that could disclose more unknowns in the phase behavior of confined mixtures.